Artificial Intelligence

Artificial IntelligenceDefinition of knowledge

Large collection of symbols is called as data.Large collection of data is called as information.If you have lot of information it is knowledge.If you have lot of knowledge then you are an intelligent.If you are an intelligent then you have wisdom.Knowledge is defined as the piece of information that helps in decision-making.Intelligence can be defined as the ability to draw useful inferences from the available knowledge.Wisdom is the maturity of the mind that directs its intelligence to achieve desired goals.

Knowledge Relation: Wisdom

Intelligence

Knowledge

Information

Data

Symbol

What is intelligence?An exact definition of intelligence has proven to be extremely elusive.Douglas Hofstadler suggests the following characteristics in a list of essential abilities for intelligence.

1.To respond to situations very flexibility.2.To make sense out of ambiguous or contradictory messages.3.To recognize the relative importance of different elements of a situation.4.To find similarities between situations despite differences, which may separate them.5.To draw distinctions between situations despite similarities, which may link them.

Turing Test: In 1950, Turing published an article in the Mind magazine, which triggered a controversial topic “Can a machine think”.Turing proposed an ‘imitation game’ which was later modified to Turing test. In the imitation game the players are three humans- a male, a female and an interrogator. The interrogator who is shielded from the other two, asks questions to both of them and based on their typewritten answers determines who is female. The aim of the male is to imitate the female and deceive the interrogator and the role of female is to provide replies that would inform the interrogator about her true sex.

Turing proposed that if the human interrogator in Room C is not able to identify who is in Room A or in Room B, then the machine possesses intelligence. Turing considered this is a sufficient test for attributing thinking capacity to a machine.

As of today, Turing test is the ultimate test a machine must pass in order to be called as intelligent test.

Importance of Turing test:

It gives a standard for determining intelligence.

It also helps in eliminating any bias in favour of living organism, because the interrogator focuses slowly on the content of the answers to the questions.

Definitions of Artificial Intelligence:

There is no universal agreement among AI researchers about exactly what constitutes AI.Various definitions of AI focus on different aspects of this branch of computer science including intelligent behavior, symbolic process, heuristics and pattern matching.

Some of the definitions of AI:1.AI is the study of how to make computer do things, which at the moment people do better.------Elaine Rich.2. McCarthy coined the term AI in 1956.Developing computer programs to solve complex problems by applications of processes that analogous to human reasoning processes.This definition has 2 major parts: computer solutions for complex problems and processes that are analogous to human reasoning processes.A.I is the study of mental faculties through the use of computational models.3.AI is the study of the computations i.e. possible to perceive, reason and action.

From the perspective of this definition AI differs from most of psychology because of the greater emphasis on computation and AI differs from most of computers science because of the emphasis on perception, reasoning and action4.AI is the part of computer science concerned with designing intelligent computer systems that exhibit the characteristics we associate with intelligent in human behavior.--- Arron Barrand Edward A.Feignbaum5.According to Bruce G Buchanan and Edward short life symbolic processing is an essential characteristics of AI.AI is the branch of computer science dealing with symbolic, non-algorithmic methods of problem solving.6. In an encyclopedia article, Bruce G Buchanan includes heuristics as key elements of AI.AI is the branch of computer science that deals with ways of representing knowledge using symbols rather than numbers and writes rules of thumb or heuristic methods for processing information.-----Bruce G Buchanan, encyclopedia Britannica.A heuristic is a rule of thumb that helps you to determine how is proceed.7. Another definition of AI focuses on pattern matching techniques.In simplified terms, AI works with pattern matching methods, which attempt to describe objects, events or processes in terms of their qualitative features and logical computational relationships.---Brattle researches corporation, AI and fifth generation computer technologies.1.what computers can do better than people?1. Numerical Computation 2. Information Storage3. Repetitive operations. 4. Computers are just machines.

What people can do better than computer?

1. Intelligence 2. Process3. Understand4. Make sense 5. Common sense.

Differences between human brains and computers

Human brains computer1. Living device. 1.Non living device. 2. Self-build and creative. 2.Dependent and must be programmed3. Has continuo nature. 3. Describe in nature.4. Limited size. 4. Unlimited memory size.5. Basic unit is nervous. 5. Basic unit is a ram cell.6. Storage devices are Electro chemicals 6. Store devices are electronic & in nature. magnetic. 7. Number punching is slow. 7. Faster.8. Speed of transmission is of order of 50 to 8. Speed of transmission is equal 100 meters of sec. to the Speed of electrons & speed of light.9. Has inducted detective reasoning 9. No reasoning power. capabilities. 10. Has an emotion. 10. Dumb and no emotions. 11. Has a capacity to learn. 11. Must be programmed.12. Volume is approximately 15 wt. 12. Volume is about 2000wats. 13. Power consumption 10 wt. 13. Power is 500 watts. 14. Logic adopted is fuzzy logic. 14. Logic adopted is binary logic.15.most sophisticated device and highly 15. Only intention and achieved a advanced with respect to intelligence. Certain degree of specification.

Areas of AI research (AI and related fields) and its applications:

1.Expert System: An expert system is a computer program designed to act as an expert in a particular domain also known as knowledge based system . An expert system is a set of programs that manipulate encoded knowledge to solve problems in a specialized domain that normally requires human expertise. The system perform their inference through symbolic computations.

Expert systems are currently designed to assist experts not to replace them. They have proven to be useful in diverse are as such as medical diagnosis, chemical analysis, and geological exploration and computer system configuration.Since the expert system field promises a great deal of practical application and commercial potential in the near future .it has begun to attract on enormous amount of attention.

2.Natural language processing:

The utility of computer is often limited by communication difficulties. The effective use of a computer traditionally has involved the use of a programming language or set of commands that you must use to communicate with the computer. The goal of natural language processing is to enable people and computers to communicate in a natural (human) language such as English rather in a computer language.The field of N.L.P is divided into 2 sub fields of : 1. Natural language understanding which investigates methods of allowing the computer to comprehend instructions given in ordinary English so computers can understand people more easily.2. Natural-language generations, which strives to have, computers produce ordinary English language so that people can understand

computers more easily.3. Speech recognition: The focus of N.L.P is to enable computers to communicate interactively with English words and sentences that are typed on paper or displayed on a screen. The primary interactive method of communication used by human is not reading and writing; it is speech.The goal of speech recognition research is to allow computers to understand human speech so that they can hear our voice and recognize the words. We are speaking speech recognition research seeks to advance the goal of natural language processing by simplifying the process of interactive communication between people and computers.4.Computer vision:It is a simple task to attach a camera to a computer so that the computer can receive visual images .it has proven to be a far more difficult task. However to interpret those images so that the computers can understand exactly what it is seeing. People generally use vision as their primary means of sensing their environmental .we generally see more than we hear, feel, smell of taste .the goal of computer vision research is to give computers this same facility for understanding their surroundings.

5. Robotics: A robot is an Electro mechanical device that can be programmed to perform manual tasks. The robotic industries association formally defines a robot as “ a re programmable multi functional manipulator designed to move material, parts, roots or specialized devices through variable programmed motions for the performance of a variety of tasks”.Not at all robotics is considered to be the part of AI .a robot that performs only the actions it has been pre programmed to perform is considered to be a ‘dumb’ robot processing no more intelligence.An intelligent robot includes some kind of sensory apparatus such as a camera that allows it to respond to changes in its environment, rather than just to allow instructions ‘mindlessly’.

Intelligent computer assisted instruction (ICAI):CAI has been in use for many years bringing the power of the computer to bear on the educational process. now AI methods are being applied to the development of intelligent computer –assisted instruction in an attempt to create computerized “tutors” that shape their teaching techniques to fit the learning patterns of individual students.

Automatic programming:In simple terms programming is the process of telling the computer exactly what you want it to do. Developing a computer program frequently requires a great deal of time. A program must be designed, written, tested, debugged and evaluated all as part of the program development process.The goal of automatic programming is to create special programs that act as intelligent “tool” to assist programmers and expedite each phase of the programming process. The ultimate aim of automatic programming is computer system that could develop programs by itself, in response to and in accordance with the specifications of a program developer.

Planning and decision support: When you have a goal, either you rely on luck and providence to achieve that goal or you design and implement a plan .the realization of a complex goal may require the construction of a formal and detailed plan.Intelligent planning programs are designed to provide active assistance in the planning process and are expected to be particularly helpful to managers with decision-making responsibilities.From the perspective of goals AI can be viewed as part of engineering and part of science. The engineering goal of AI is to solve real world problems using AI as an armamentarium of ideas about presenting knowledge; using knowledge and assembling system explain various sorts of intelligence.

Applications of AI should be judged according to whether there is well-defined task, an implemented program and a set of identifiable principles.AI can help us to solve difficult real world problems, creating new opportunities in business, engineering and many other application areas.

Characteristics of AI problems:

1. The problems that AI tackles have combinational explosion of solutions.2. AI programs manipulate symbolic information to a larger extent, in contrast to conventional programs, which deal with numeric processing.3. To cope with the combinational explosion of solutions, AI programs use heuristics to search tree.4. In order to classify system as an AI program, the fundamental criterion is that it must have vast quantities of knowledge must be represented in such a form that the system work on it can easily manipulate it. 5. AI programs deal with real life problems to a large extent. The assist humans in taking right decisions. Just a human expert has the capacity to handle uncertain, incomplete and irrelevant information.6. A very vital characteristic of an AI program is its ability to learn.

Differences between AI and conventional program.

Features AI Programming Conventional Programming (software)

1. Processing type Symbolic Numeric2. Technique used Heuristic search algorithmic search3. Solution steps not explicit Precise4. Answers sought Satisfactory Optional5. Control/Data separation Separate Intermingled6. Knowledge Imprecise Precise7. Modification Frequent Rare8. Involves Large Knowledge base large database9. Process Inferential Repetitive

Problems representation in AI:

Before a solution can be found, the prime condition is that the problem must be very precisely defined.To build a system to solve a particular problem, we need to do four things.1. Define the problem precisely: this definition must include precise specifications of what the initial situations will be as well as what final situations constitute acceptable solutions to the problem.2. Analyze the problem.3. Isolate and represent the last knowledge that is necessary to solve the problem.4. Choose the last problem solving techniques and apply it to the particular problem.

The most common methods of problem representation in AI are

1. State space representation 2. Problem reduction

State space representation:

A set of all possible states for a given problem is known as the state space of the problem. State space representations are highly beneficial in AI because they provide all possible states, operations and goals. If the entire state space representation for a problem is given, it is possible to trace the path from the initial state to the Goal State and identify the sequence of operators necessary for doing it. The major deficiency of this method is that it is not possible to visualize all states for a given problem. To overcome the deficiencies of this method, problem reduction technique comes handy.

Example1: Water

Boiled

BoilingWaterAdded coffee Milk powder

Decation Milk

Coffee

Added sugarPalatable coffeeExample2:A Water Jug Problem: You are given two Jugs, a 4-gallon one and a 3-gallon one. Neither have any measuring markers on it. There is a pump that can be used to fill the jugs with water. How can you get exactly 2 gallons of water into the 4-gallon jug?

The state space for this problem can be described as the set of ordered pairs of integers (x, y), such that x=0, 1,2,3, or 4 and y = 0,1,2, 0r 3; x represents the number of gallons of water in the 4-gallon jug, and y represents the quality of water in the 3-gallon jug. The Start State is (0,0). The goal state is (2,n) for any value of n (since the problem does not specify how many gallons need to be in the 3-gallon jug).

1 (x, y) - (4,y) Fill the 4-gallon jug.If x < 4

2. (x, y) - (x,3) Fill the 3-gallon jug.If y < 3

3 (x, y) - (x – d, y) Pour some water out of the 4-gallon jugIf x >0

4 (x, y) - (x, y - d) pour some water out of the 3-Gallon jugIf y > 0 5 (x, y) - (0, y) Empty the 4-gallon jug on the groundIf x > 0 6 (x, y) - (x, 0) Empty the 3-gallon jug on the groundIf y > 0 7 (x, y) - (4,y – (4 -x)) pour some water from the 3-Gallon jug in to theIf x + y> 4 and y > 0 4 - gallon jug until the 4 -gallon jug is full.

8 (x, y) - (x-(3-y),3) pour water from the 4 -Gallon jug in to theIf x + y> 3 and x > 0 3 -gallon jug until the 3 -gallon jug is full.

9. (x, y) - (x+y,0) pour all the water from the 3-Gallon jug in to theIf x + y <3 and x > 0 4- gallon jug

10 (x, y) - (x+y,0) pour all the water from the 4-Gallon jug in to theIf x + y < 3 and x > 0 3- gallon jug 11 (0,2) (2,0) pour all 2 gallons from the 3-Gallon jug in to the4-Gallon jug.12. (2,y) (0,y) Empty the 2 gallons in the 4.gallons in the 4-gallon jug on the

Ground.

Production rules for the water jug problem.

Gallons of water in the 4-gallon jug. Gallons of water in the 3-gallon jug Rule Applied0 0 20 3 93 0 23 3 4 2 70 2 5 0r 122 0 9 or 11

One solution for the water jug problem.

0 0 24 0 11 3 81 0 60 1 104 1 12 3 82 0 6

Second solution for the water jug problem

Problem Reduction: In this method a complex problem is broken down or decomposed into a set of preemptive sub problems. Solutions for these preemptive subprograms are easily obtained. The solutions for all the sub-problems collectively give the solution for the complex problem.

Example:We want to evaluate ?(x2+3x+sin2xcos2x)dx

We can solve this by breaking down into smaller problems.

? (X2 + 3x + sin2x cos2x) dx

? x2 dx ? 3x dx ? sin2x cos2x dx

x3 /3 3 x2/2 dx ? (1-cos2x)cos2x dx

3 x2 /2 ? (cos2x – cos4x) dx

The individual values can be combined (Integrated) to get the final result.

Major components of AI : Any AI system has four major components.

1. Knowledge representation2. Heuristic search3. AI programming languages and tools4. AI hardware

What are the underlying assumptions about intelligence.Newal and Siman proposed some hypothesisPhysical symbol system hypothesisPhysical symbol system consists of set of entities called symbols, with the help of these entities to make symbol structure (expression). Thus, a symbol structure is composed of a number of instances of symbols related in some physical way.

A physical symbol system is a machine that produces through time an evolving collection of symbol structures.

CreationModificationSet of operatorsReproductionDestruction

P.S.S. has the necessary and sufficient means to exhibit intelligence.

Intelligence requires knowledgeExperience gives knowledge

Intelligence requires knowledgeLess desirable properties of knowledge

There appears to be no way to prove or disprove it on logical grounds. So it must be subjected to empirical validation. We may find that it is false. We may find that the bulk of the evidence says that it is true. But the only way to determine its truth is by experimentation.The importance of the physical symbol system hypothesis is twofold. It is a significant theory of the nature of human intelligence and so is of great interest to psychologists. It also forms the basis of the belief that it is possible to build programs that can perform intelligent tasks now performed by people.

Properties of AI:

1. Must capture generalization.2. It must be understood be people, who must provide knowledge to it.3. It can be easily modified to reflect overview.4. It can be used in great money situations even if it is totally accurate or computable.5. It must overcome its own sheer bulk by narrowing down the range of possibilities.

AI Problems Non AI Problems

AI Techniques Non AI Techniques

What is an AI Techniques?

It is voluminousIt is hard to characterize accuratelyIt is constantly changingIt differs from data by being organized in a way that corresponds to the ways it will be used.

Organization of knowledge is situation dependent

The three important AI Techniques:

Search: Provides a way of solving problems for which no more direct approach is available as well as a frame work into which any direct techniques that are available can be embedded.

Use of knowledge: Provides a way of solving complex problems by exploiting the structures of the objects that are involved.

Abstraction: Provides a way of separating important features and variations from unimportant ones that would otherwise overwhelm any process.

Problem Characteristics:

Heuristic search is a very general method applicable to a large class of problems. In order to choose the most appropriate methods for a particular problem it is necessary to analyze the problem along several key dimensions.

1. Is the problem decomposable?2. Can solution steps be ignored or undone?3. Is the problems universe predicate?4. Is a good solution to the problem obvious without comparison to all other possible solutions? (Is a good solution absolute or relative?)5. Is the solution a state or a path?6. What is the role of knowledge?7. Does the task require interaction with a person?

1. Is the problem decomposable?

A decomposable problem: We want to evaluate (x2+3x+sin2xcos2x)dx We can solve this by breaking down into smaller problems.? (X2 + 3x + sin2x cos2x) dx

? x2 dx + ? 3x dx + ? sin2x cos2x dx

x3 /3 + ? 3x dx + ? (1-cos2x)cos2x dx

3 x2 /2 + ? (cos2x – cos4x) dx

The individual values can be combined (Integrated) to get the final result.A non-decomposable problem: Blocks World problem

On (C, A) On (B, C) and On (A, B)Operators available:

1. Clear (x) [ block x has nothing on it] ? On(x,table) [ Pick up x and put it on table]2. Clear(x) and clear(y) ? On(x, y) [put x on y]

A proposed solution: Decomposition produces two smaller problems

1. Is simple the start state. Simply put B and C.2. Is not simple. We have to clear off A by removing C before we can pick up A and put it on B this can be done easily.

1.We now try to combine the two sub-solutions into one solution we fail regardless of which one do first, we will not be able to so the second. I.e. 1 and 2 are independent.

2. Can solution steps be ignored or undone?

1. Theorem Proving: Suppose we want to prove a mathematical theorem we proceed by first proving a lemma that we think will be useful. Eventually, we realize that the lemma is not of help at all. Are we in trouble?

? No. All we have lost is the effort that was spent.

2. The 8 puzzle: The 8-puzzle is a square in which is placed eight square tiles. The remaining 9th square is uncovered. Each tile has a number on it. A tile that is adjacent to the blank space can be slid into that space. A game consists of a starting position and specified into the goal position by sliding the tiles around.3. Chess: Suppose we made a wrong move and we realized it a couple of moves later.

We cannot go back to correct the move.

The three problems are of three classes.

1. Ignorable: (Ex: Theorem proving) in which solution steps can be ignored.2. Recoverable: (Ex: 8-puzzle) in which solution steps can be undone.3. Irrecoverable: (Ex: Chess) in which solution steps cannot be undone.

Ignorable problems can be solved using a simple control structure that never back tracks.Recoverable problems can be solved using a simple control structure that backtracks.A great deal of effort is needed to solve irrecoverable problems.

3. Is the universe predicate?

Predictable – in 8-puzzle (certain outcome)Unpredictable – in bridge (uncertain outcome)• Playing bridge: But we can do fairly well since we have available accurate estimates of the probabilities of each of the possible outcomes.• Controlling a robot arm: The outcome is uncertain for a variety of reasons. Some one might move something in to the path of the arm. The gears of the arm might stick. A slight error could cause the arm to knock over a whole stack of this.• Helping a lawyer decide how much to defend his client against a murder charge. Here we probably cannot even list all the possible outcomes, much less assess their probabilities.

4.Is a good solution absolute or relative?

Ex: Consider a database of facts1. Marcus was a man.2. Marcus was a pompein3. Marcus was born in 40 AD4. All men are mortal5. All pompeians died whan the volcano erupted in 79 AD6. No mortal lives longer than 150 years7. It is now 1998 ADQuestion: “Is Marcus alive?”

There are two solutions

First solution is 1. Marcus was a man2. All men are mortal3. Marcus us mortal –from 1 and 44. Marcus was born in 40 AD5. It is now 1998 AD6. Marcus’ age is 1958 year -4 and 5

7. No mortal lives longer than 150 years.8. Marcus is dead -6 and 7

Second solution is 7. It is now 1998 AD5.All pompeians died in 79 AD9. All pompeians are dead now -7 and 52. Marcus was a pompiean10.Marcus is dead -9 and 2

So, to answer the question “Is Marcus alive” we can choose any one of the two solutions. Since each path will lead to answer. If we do follow one path successfully to the answer there is no reason to go back and see if some other path might also lead to a solution.

Now consider TSP:

Boston New York Miami Dallas San Fransisco

Boston ----- 250 1450 1700 3000New York 250 ---- 1200 1500 2900Miami 1450 1200 ----- 1600 3300Dallas 1700 1500 1600 ----- 1700S.F. 3000 2900 3300 1700 -------

Path 1 :

Boston---250---->New York---1450---->Miami---3050---->Dallas---4750---->S.F---7750---->Boston

Path 2 :

Boston---3000---->S.F.---4700---->Dallas---6200---->New York---7400---->Miami---8850---->Boston

We can’t say one path is the shortest one unless we try other paths also.

1. Marcus – any path problems can be solved in a reasonable amount of time.2. TSP – best path problems_ computationally harder than any path problems.

5. Is the solution a state or path?Natural language understanding:The bank president ate dish of pasta salad with the fork.

Several components in this sentence, each of which in solution, may have more than one interpretation. But, the whole sentence must give only meaning.

Source of Ambiguity:Bank financial institutions (or) side of rivers ? only one of these may have a president. Dish object of the verb ‘eat’, a dish was eaten? The Pasta Salad in the dish was eaten.

Pasta salad – a salad containing pasta.

Dog food – doesn’t normally contain dog.

So some search is required to find the interpretation of the sentence. But these will be anyone interpolation.

Ex: Water jug problem.

The solution is not just the state (2,0) but the path from (0,0) to (2,0).

6.What are the role of knowledge?

Chess: Knowledge required is very little (a set of rules for legal moves, a control mechanism that implements an appropriate search procedure, knowledge of good tactics by a perfect program.

Newspaper: Now consider the problem of scanning daily newspaper to decide which are supporting the democrats and which are supporting the republicans in some upcoming election. Again assuming unlimited computing power, how much knowledge would be required by a computer trying to solve this problem? This time the answer is a great deal.

1. The names of the candidates in each party.2. The fact that if the major thing you want to see done is has taxes lowered, you are probably supporting republicans.3. The fact that if the major thing you want to see done is improved education for minority students, you are probably supporting the democrats.4. The fact that if you opposed to big government you are probably supporting the republican.And so on.

These two problems chess and newspaper story understanding, illustrate the difference between the problems for which a lot of knowledge is important only to constrain the search for solution and those for which a lot of knowledge is required even to be able to

recognize a solution.

7. Does the task require interaction with a person.

Two types of problems.1. Solitary: The computer is given a problem description and produces an answer with no intermediate communication and with no demand for an explanation of the reasoning process.2. Conversational: These are intermediate communication between a person and the computer (either to provide additional assistance to computer or to provide additional information to the user or both).

Definition of Production System:

Production system is a mechanism that describes and performs the search process. It consists of

1. A set of rules.2. One or more knowledge or database.3. A control strategy that specifies the order of the rules to be applied.4. A rule applied.

Requirements of a good control strategy:

1. The first requirement is that it can cause motion.Consider the water jug problem. Suppose we implemented the simple control strategy of starting each time at the top of the list of rules and choosing the first applicable one.2. The second requirement is that it be systematic.The requirement that a control strategy be systematic corresponds to the need for global motion as well as for local motion.

Production System Characteristics:

We have argued that production systems are a good way to describe the operations that can be performed in a search for a solution to a problem.

1. Can production systems, like problems, be described by a set of characteristics that shed some light on how they can easily be implemented?2. If so, what relationships are there between problem types and the types of production system best suited to solving the problems?

Definitions of classes of production systems:

A monotonic production system: It is a production system in which the application of a rule never prevents the later application of another rule that could also have been applied at the time first rule was selected.

A non-monotonic production system: A non-monotonic production system is one in which this is not true.

Partially commutative production system: A partially commutative production system is a production system with the property that if the application of a particular sequence of rules transforms state x into state y then any permutation of those rules that is allowable (i.e. each rules preconditions are satisfied when it is applied) also transforms state x into state y. Partially commutative, monotonic production systems are useful for solving ignorable problems.

A commutative production system: A commutative production system is a production system that is both monotonic and partially commutative.

The significance if these categories of production systems lie in the relationship between the categories and appropriate implementation strategies.

Monotonic Non-monotonic

Partially Commutative Theorem proving Robot navigation

Non Partially commutative Chemical synthesis Bridge

Partially commutative, monotonic production systems are important from an implementation standpoint because they can be implemented with out the ability to backtrack to previous states when it is discovered that an incorrect path has been followed. Although it is often useful to implement such systems with backtracking in order to guarantee a systematic search, the actual database representing the problem state need not be restored.Non-monotonic, partially commutative systems, on the other hand are useful for problems in which changes occur but can be reversed and in which order of operations is not critical. Commutative production systems are useful for many problems in which irreversible changes occur. These are likely to produce the same node many times in the search process.

Searching Techniques

Every AI program has to do the process of searching for the solution steps are not explicit in nature. This searching is needed for solution steps are not known before hand and have to be found out. Basically to do a search process the following steps are needed.1. The initial state description of the problem.2. A set of legal operators that changes the state.3. The final or goal state.The searching process in AI can be broadly classified into two major parts.1. Brute force searching techniques (Or) Uninformed searching techniques.2. Heuristic searching techniques (Or) Informed searching techniques.

Brute force searching techniques:

In which, there is no preference is given to the order of successor node generation and selection. The path selected is blindly or mechanically followed. No information is used to determine the preference of one child over another. These are commonly used search procedures, which explore all the alternatives, during the searching process. They don’t have any domain specific knowledge all their need are the initial state , final state and the set of legal operators. Very important brute force searching techniques are 1. Depth First Search2. Breadth First Search

Depth first search: This is a very simple type of brute force searching techniques. The search begins by expanding the initial node i.e. by using an operator generate all successors of the initial node and test them.This procedure finds whether the goal can be reached or not but the path it has to follow has not been mentioned. Diving downward into a tree as quickly as possible performs Dfs searches.Root

A B

D E F I JG H

Goal StateAlgorithm:Step1: Put the initial node on a list START.Step2: If START is empty or START = GOAL terminates search.Step3: Remove the first node from START. Call this node a.Step4: If (a= GOAL) terminates search with success.Step5: Else if node a has successors, generate all of them and add them at the beginning Of START.Step6: Go to Step 2.The major draw back of the DFS is the determination of the depth citric with the search has to proceed this depth is called cut of depth.The value of cutoff depth is essential because the search will go on and on. If the cutoff depth is smaller solution may not be found. And if cutoff depth is large time complexity will be more.

Advantages: DFS requires less memory since only the nodes on the current path are stored.By chance DFS may find a solution with out examining much of the search space at all.

Breadth First Search (BFS): This is also a brute force search procedure like DFS. We are searching progresses level by level. Unlike DFS which goes deep into the tree. An operator employed to generate all possible children of a node. BFS being a brute force search generates all the nodes for identifying the goal. The amount of time taken for generating these nodes is prepositional to the depth “d” and branching factor “b” is given by 0(b)

Root

A B

D E F I JG H

Goal State

ALGORITHM:

Step 1. Put the initial node on a list “START”Step 2. If START is empty or goal terminate the search.Step 3. Remove the first node from the Start and call this node “a”Step 4. If a =”GOAL” terminate search with successStep 5. Else if node “a” has successors generate all of them and add them at the tail of “START”Step 6. Go to step 2.Advantages:1. BFS will not get trapped exploring a blind alley.2. If there is a solution then BFS is guaranteed to find it.3. The amount of time needed to generate all the nodes is considerable because of the time complexity.4. Memory constraint is also a major problem because of the space complexity.5. The searching process remembers all unwanted nodes, which are not practical use for the search process.

Heuristic Search Techniques: In informed or directed search some information about the problem space is used to compute a preference among the children for exploration and expansion.The process of searching can be drastically reduced by the use of heuristics. Heuristic is a technique that improves the efficiency of search process. Heuristic are approximations used to minimize the searching process. Generally two categories of problems are used in heuristics.1. Problems for which know exact algorithms are known & one needs to find an appropriate & satisfying the solution for example computer vision. Speech recognition. 2. Problems for which exact solutions are known like rebuke cubes & chess.The following algorithms make use of heuristic evolution 1. Generate & test2. Hill climbing3. Best first search 4. A* Algorithm5. AO* Algorithm6. Constraint satisfaction7. Means- ends analysis.

1.Generate and test: The generate & test strategy is the simplest of all the approaches. The generate & test algorithm is a depth first search procedure – since complete solutions must be generated before they can be tested. In its most systematic form, it is simply an exhaustive search of the problem space, It is also known as the British museum algorithm. A reference to a method for finding an object in British museums by wandering randomly.AlgorithmStep 1: Generate possible solutions. For some problems this means generating a particular point in the problem space. For others it means generating a path from a start state.Step 2: Test to see if these actually a solution by comparing the chosen point or the end point of the chosen path of the set of acceptable good states.Step 3: If a solution has been found, quit, otherwise, return to step 1.

Hill Climbing: It is a variant of generate a test in which feed back from the test in which feed back from the test procedure is used to help the generator decide which direction to move in the search space. In a pure generate & test procedure the test function response with only a yes or no. But if the test function is augmented with a heuristic function. That provides a estimate of how close given state is to a goal state. Hill climbing is often used when a good heuristic function is available for evaluating states. But when no other useful knowledge is available. This algorithm is also discrete optimization algorithm uses a simple heuristic function. The amount of distance the node is from the goal node in fact there is a practically no difference between hill climbing & DFS except that the children of the node that has been expanded are shorted by the remaining distance nodes.Root

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Goal StateAlgorithm:

Step1: Put the initial node on a list START.Step2: If (START is empty) or (START = GOAL) then terminate the search.Step3: Remove the first node form the start, call this node ‘a”. Step4: If ( a = GOAL) terminate search with success.Step5: ELSE if n ode “a” has successors generate all of them. Find out how form they are from the goal node. Sort them by the remaining distance from the goal and add them to beginning of the start.Step6: Go to step 2.

Problems of hill climbing:Local maximum: A state that is better then all its neighbors but not so when compared to states to states that are farther away.

Local Maximum

Plateau: The flat area of the search space in which all neighbors have the same value.

PlateauRidge: Described as a long and narrow stretch of evaluated ground or a narrow elevation or raised part running along or across a surface.

Ridge

In order to overcome these problems, adopt one of the following or a combination of the following methods.

1. Backtracking for local maximum. Backtracking helps in undoing what has been done so far and permits to try different path to attain the global peak.

2. A big jump is the solution to escape from the plateau. A huge jump is recommended because in a plateau all neighboring points have the same value.

3. Trying different paths at the same time is the solution for circumventing ridges.

Best first Search: Which is a way of combining the advantages of both depth-first-search and breadth-first-search in to a single method.Dfs is good because if allows a solution to be found without all competing branches having to be expanded. Bfs is good because it does not get trapped on dead end paths. One way of combining the two is to follow a single path at a time, but switch paths whenever some competing path looks more promising than the current one does.

In this procedure, the heuristic function used here called an evaluation function is an indicator of how far the node is from the goal node. Goal nodes have an evaluation function value of zero.

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Search process of best-first search. H

Step Node being Children Available nodes Node choosesExpanded

1. S A: 3, B: 6, C: 5 A: 3, B: 6, C: 5 A: 32. A D: 9, E: 8 B: 6, C: 5, D: 9, E: 8 C: 5 3. C H: 7 B: 6, D: 9,E: 8,H: 7 B: 64. B F: 12, G:14 D:9,E:8,H:7,F:12,G:14 H: 7 5. H I: 5, J: 6 D:9,E:8,F:12,G:14,I:5, I: 5

J : 6 6. I K:1, L:0, M:2 D:9,E:8,F:12,G:14,J:6, search stop K:1, L:0,M:2 goal is reached

There is an only minor variation between hill climbing and Best FS. In the former we sorted the children of the first node being generated. Here we have to sort the entire list to identify the next node to be expanded.

The paths found by best first search are likely to give solutions faster because it expands a node that seems closer to the goal. However there is no guarantee of this. Algorithm:

Step 1: put initial node on a list start. Step 2: if (start is empty) or (start =goal) then terminate search.Step 3: remove the first node from start. Call this node a.Step 4: if (a = goal) then terminate search with success.Step 5: else if node ‘ a’ has successors, generate all of them. Find out how far they are from the goal node. Sort all the children generated so far by the remaining distance from the goal.Step 6: name this list as start one.Step 7: replace start with start one.Step 8: go to step 2.

A* algorithm: The best first search algorithm that was just presented is a simplification an algorithm called A* algorithm which was first presented by HART. A part from the evolution function values one can also bring in cost functions indicate how much resources like time, energy, money etc. have been spent in reaching a particular node from the start. While evolution functions deal with the future, cost function deals with the past. Since the cost function values are really expanded they are more concrete than evolution function values. If it is possible for one to obtain the evolution function values then A* algorithm can be used. The basic principle is that the sum the cost and evolution values for a state to get its goodness worth and this is a yard stick instead evolution function value in best first search. The sum of the evolution function value and the cost along the path leading to that state is called fitness number. While best first search uses the evolution function value for expanding the best node A* uses the fitness number for its computations. 92 D

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2 B 4 F 1 KS 12 6 3 G 2 06 14 I L Goal 5 2 C 7 2 5 M5 7 H 6 6 j

Step Node being Children Available nodes Node choosesExpanded1. S A: 6, B: 8, C: 11 A: 6, B: 8, C: 11 A: 62. A D: 14, E: 13 B: 8, C: 11, D: 14, E: 13 B: 8 3. B F: 18,G: 17 C: 11,D: 14,E: 13,F: 18,G: 17 C: 114. C H: 18 D: 14,E: 13,F: 18,G: 17,H: 18 E: 13 5. E D: 14,F: 18,G: 17,H: 18 D: 14 6. D F: 18,G:17,H: 18 G: 177. G F: 18,H: 18 H: 188. H I: 23,J: 23 F:18, I: 23 ,J:23 F: 189. F I: 23,J: 23 I: 2310. I K: 20,L: 20,M: 21 J: 23, K: 20,L: 20,M: 21 L: 20search stopgoal is reachedAlgorithm:Step 1: put the initial node on a list start Step 2: if (start is empty) or (start = goal) terminate search.Step 3: remove the first node from the start call this node aStep 4: if (a= goal) terminate search with success.Step 5: else if node has successors generate all of them estimate the fitness number of the successors by totaling the evaluation function value and the cost function value and sort the fitness number.Step 6: name the new list as start 1.Step 7: replace start with start 1.Step 8: go to step 2.

Problem Reduction: In this method, a complex problem is broken down or decomposed into a set of primitive sub problems. Solutions for these primitive sub-problems are easily obtained. The solutions for all the sub-problems collectively given the solution for the

complex problem.Between the complex problem and the sub-problem, there exist two kinds of relationships, i.e AND relation and OR relation ship.In AND relation ship, the solution for the problem is obtained by solving all the sub-problems.(Remember AND gate truth table condition).In OR relationship, the solution for the problem is obtained by solving any of the sub-problems. (Remember AND gate truth table condition).This is why the structure is called an AND-OR graph.The problem reduction is used on problems such as theorem proving, symbolic integration and analysis of industrial schedules.

To describe an algorithm for searching an AND-OR graph, need to exploit a value, call futility. If the estimated coast of a solution becomes greater than the value of futility, then give up the search. Futility should be chosen to corresponds to a threshold such that any solution with a cost above it is too expensive to be practical, even if it could every be found.

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The AO* ALGORITHM

The problem reduction algorithm we just described is a simplification of an algorithm described in Martelli and Montanari, Martelli and Montanari and Nilson. Nilsson calls it the AO* algorithm , the name we assume.1. Place the start node s on open.2. Using the search tree constructed thus far, compute the most promising solution tree T3. Select a node n that is both on open and a part of T. Remove n from open and place it on closed.4. If n is a terminal goal node, label n as solved. If the solution of n results in any of n’s ancestors being solved, label all the ancestors as solved. If the start node s is solved, exit with success where T is the solution tree. Remove from open all nodes with a solved ancestor.5. If n is not a solvable node (operators cannot be applied), label n as unsolvable. If the start node is labeled as unsolvable, exit with failure. If any of n’s ancestors become unsolvable because n is, label them unsolvable as well. Remove from open all nodes with unsolvable ancestors.6. Otherwise, expand node n generating all of its successors. For each such successor node that contains more than one sub problem, generate their successors to give individual sub problems. Attach to each newly generated node a back pointer to its predecessor. Compute the cost estimate h* for each newly generated node and place all such nodes that do not yet have descendents on open. Next, recomputed the values of h* at n and each ancestor of n. 7. Return to step 2.

If can be shown that AO* will always find a minimum –cost solution tree if one exists, provided only that h*(n) <_ h(n), and all are costs are positive. Like A*, the efficiency depends on how closely h* approximates h.

Constraint satisfaction:

Many problems in AI can be viewed as problems of constraint satisfaction in which the goal is to discover some problem state that satisfies a given set of constraints. Constraint satisfaction is a search procedure that operates in a space of constraint sets. The initial state contains the constraints that are originally given in the problem description. A goal state is any state that has been constrained “enough”, where enough must be defined for each problem.

Constraint satisfaction is two-step process. First, constraints are discovered and propagated as far as possible through outs the system.

Algorithm: 1. Propagate available constraints. To do this, first set OPEN to the set of all objects that must have values assigned to them in a complete solution. Then do until an inconsistency is detected or until OPEN is empty : (a) Select an object OB from OPEN. Strengthen as much as possible the set of constraints that apply to OB.(b) If this set is different from the set that was assigned the last time OB was examined or if this is the first time OB has been examined, then add to OPEN all objects that share any constraints with OB (c) Remove OB from OPEN.

2. If the union of the constraints discovered above defines a solution, then quit and report the solution.

3. If the union of the constraints discovered above defines a contradiction, then return failure.

4. If neither of the above occurs, then it is necessary to make a guess at in order to proceed. To do this, loop until a solution is found or all possible solutions have been eliminated(a) Select an object whose value is not at determined and select a way of strengthening the constraints on that object.(b) recursively invoke constrain satisfaction with the current set of constraints augmented by the strengthening constraint just selected.

This algorithm apply it in particular problem domain requires the use of two kinds of rules. Rules that define the way constraints may validly be propagated and rules that suggest guesses when guesses are necessary.

The solution process proceeds in cycles, at each cycle two significant things are done.1. Constraints are propagated by using rules that correspond to the properties of arithmetic.

2. A value is guessed for some letter whose value is not yet determined.Problem1: S E N DM O R E=======M O N E Y==========LET M=1C3+S+1>9, C3 can be 0 or 1 => S=9 or 8C3+S+M can be either 9,10 or 11. It is 9 then no carry, If sum is 11 then O=1.But M is already assigned 1.So O=0 and C3=0. S=9 or 8.Let C3=0 & S=9C2+E+O=N if C2=0, E=N It is wrong.So c2 =1, 1+E =N.Let E=2 then N=39 2 3 D1 0 R 2======10 3 2 Y R=9 & C1 = 0 wrongR=8 & C1 = 1 correct9 2 3 D1 0 8 2=====1 0 3 2 Y to get carry D>8 => D= 8 or 9 clash, Similarly E= 3 & 4 clashNow for E=5 then N=69 5 6 D1 0 R 5=====1 0 6 5 Y C2+6+R = 1 5C2= 0 => R=9 wrongC2= 1 => R =89 5 6 D1 0 8 5=====1 0 6 5 Y Now D+5>9=>D>4D=6 then Y=1 It is wrongD= 7 then Y=2 It is correctD= 8 or 9 wrongResult: 9 5 6 71 0 8 5=====1 0 6 5 2Values: S=9,E=5, N=6 , D= 7, M=1,O=0,R=8,E=5M=1,O=0,N=6,E= 5,Y=2.

Problem2:

D O N A L DG E R A L D=========R O B E R TD+D = C1.T C1+ L+ L = C2.RC2+A+A = C3.E C3+N+R= C4.BC4+O+E= C5.O C5+D+G= R

Let us assume that there are no carries then O+E = O => E = 0 or 9.D+G>=9.Let D=1 then T= 2.Let L=3 then R= 6.Let A=4 then E=8Now we have to take N and R-values from 5,7,9. But it is not possible. if it we get carry and O+E=0 condition will failConsider E=9C+O+E=0C4=1; E=9Let D=1=>T=2;L=3 => R=6A=4 =>E=8 contradictionLetD=5 => T=01+L+L=R Let L= 8 then 1+8+8 = 17 => R=7 and L=8.Since E=9; 1+A+A =E=>A=4.Let B=3 then N+R=BN+7=BB should be either 1,2,3 if B=1 means B=11.N=4 with carryBut A=4.

Let B=2; N=5 But D=5.So B=3,D+G+Carry = R5+G+1 =7So G=1.Result: D O N A L D 5 2 6 4 8 5G E R A L D 1 9 7 4 8 5R O B E R T 7 2 3 9 7 0 Values: D=5 ;T=0; L=8; R=7;A=4;N=6;B=3;O=2;E=9;G=1.Problem3:C R O S S 9 6 2 3 3R O A D S 6 2 5 1 3D A N G E R 1 5 8 7 4 6Values: C=9;R=6,O=2;S=3;A=5; D=1;E=4;N=8;G=7.

Means-ends-analysis:We have presented a collection of search strategies that can reason either forward of backward, but for a given problem, one direction or the other must be chosen. Often, however, a mixture of the two directions is appropriate. Such a mixed strategy would make it possible to solve the major parts of a problem first and then go back and solve the small problems that arise in “gluing” the big pieces together. A technique known as means-ends analysis allows us to do that.

The means-ends analysis process centers on the detection of differences between the current state and the Goal State. Once such a difference is isolated, an operator that can reduce the difference must be found. But perhaps that operator cannot be applied to the current state. So we set up a sub problem of getting to a state in which it can be applied. The kind of backward chaining in which operators are selected and then sub-goals are set up to establish the preconditions of the operators is called operator sub-goaling.

Just like the other problem solving techniques we have discussed, means-end- analysis relies on a set of rules that can transform one problem state into another. These rules are usually not represented as a left side that describes the conditions that must be met for the rule to be applicable (these conditions are called the rule’s preconditions) and a right side that describes those aspects of the problem state that will be changed by the application of the rule.Algorithm: 1. Compare CURRENT to GOAL. IF there are no differences between them then return.2.Otherwise, select the most important difference and reduce it by doing the following until success or failure is signaled.(a) Select an as yet untried operator 0 that is applicable to the current difference. If there are no such operators, them signal failure.(b) Attempt to apply 0 to CURRENT. Generate descriptions of two states: 0-START, a state in which 0’s preconditions are satisfied and 0-RESULT, the state that would result if 0 was applied in 0-START.(c) If (FIRST-PART ?MEA(CURRENT, 0-START))And (LAST-PART ? MEA (0-RESULT, GOAL)are successful, then signal success and return the result of concatenating FIRST PART, 0, and LAST-PART.Ex: Initial state: ( (R & (~P?Q)&S)) Goal State:( ((Q V P) & R)&~S)(R & (~P?Q)

(~P?Q) & R

(~~P V Q) & R

(P V Q) & R

(Q V P) & R

Knowledge Representation

Knowledge is an intellectual acquaintance with, or perception of, fact or truth. A representation is a way of describing certain fragments or information so that any reasoning system can easily adopt it for interfacing purpose. Knowledge representation is a study of ways of how knowledge is actually picturised and how effectively it resembles the representation of knowledge in human brain.

A knowledge representation system should provide ways of representing complex knowledge and should possess the following characteristics.

1. The representation scheme should have a set of well-defined syntax and semantics. This help in representing various kinds of knowledge.2. The knowledge representation scheme should have a good expression capacity. A good expressive capability will catalyze the inference mechanism in its reasoning process.3. From the computer system point of view, the representation must be efficient. By this we mean that it should use only limited

resources with out compromising on the expressive power.

Representations and mappings:

In order to solve the complex problems encountered in AI, one needs both a large amount of knowledge and some mechanisms for manipulating that knowledge to create solutions to new problems. A variety ways of representing knowledge have been exploited in AI programs.

Facts: truths in some relevant world. These are the things we want to represent.Representations: Representations of facts in some choose formalism. These are the things we will actually be able to manipulate.

One way to think of structuring these entities is as two levels:

The knowledge level: The knowledge level at which facts are described.The symbol level: The symbol level at which representations of objects at the knowledge level are defined in terms of symbols that can be manipulated by programs.

English EnglishUnderstanding generation

Mappings between Facts and Representation

We will call these links representation mappings. The forward representation mapping maps from facts to representations. The backward representation mapping goes other way from representation to facts.One representation of facts is so common that it deserves special mention. Natural language (particularly English) sentences. Regardless of the representation for facts that we use in a program, we may also need to be concerned with an English representation of those facts in order to facilitate getting information in to and out of the system. In this case we must also have mapping functions from English sentences to the representation we are actually going to use and from is back to sentences,

Consider the English sentence:

Spot is a dog.

The fact represented by that English sentence can also be represented in logic as:

Dog (Spot)

Suppose that we also have a logical representation of the fact that all dogs have tails:

? x: dog (x)--? has tail (x)

Then using the deductive mechanism of logic, we may generate the new representation object:

Has tail (spot)Using appropriate backward mapping function we could then generate the English sentence:

Spot has a tail.

It is important to keep in mind that usually the available mapping functions are not one-to-one. In fact, they are often not even functions but rather many-to-many relations. This particularly of the mapping involving English representations of facts. For example the two sentences “All dogs have tails” and “Every dog has a tail” could both represent the same fact, namely that every dog has at least one tail. On the other hand the former could represent either the fact that every dog has at least one tail or the fact that each dog has several tails. The latter may represent whither the fact that every dog has at least one tail or the fact that there is a tail that every dog has. As we will see shortly, when we try to convert English sentences in to some other representation, such as logical propositions, we must first decide what facts the sentences represent and then convert those facts in to the new representation.

Approaches to knowledge in a particular domain should possess the following four properties.

1. Representational Adequacy: The ability to represent all the kinds of knowledge that are needed in that domain.(Ex: Axioms of water-jug problem(12)).2. Inferential Adequacy: The ability to manipulate the representational structures in such a way as to derive new structures corresponding to new knowledge inferred from old. (Ex: Solutions of a water-jug problem).3. Inferential Efficiency: The ability to incorporate in to the knowledge structure additional information mechanisms in the most promising directions. (Ex: A doctor solves the patient’s decease). 4. Acquisitional Efficiency: The ability to acquire new information easily. The simplest case involves direct insertion by a person of new knowledge into the database.(Ex: An expert).

ISSUES IN KNOWLEDGE REPRESENTATION:

? Are any attributes of objects so basic they occur in almost every problem domain? If there are, we need to make sure that they are handled appropriately in each of the mechanisms we propose if such attributes exist, what are they?

? Are their any important relation ships that exist among attributes of objects?

? At what level should Knowledge represent? Is there a good set of primitives into which all knowledge can be broken down? Is it helpful to use such primitives?

? How should sets of objects be represented?

? Given a large amount of knowledge stored in a database, how can relevant parts be accessed when they are needed?

The following steps are clarified above questions1. Important Attributes.2. Relationships among attributes.3. Choosing the granularity of Representation.4. Representing sets of Objects.5. Finding the Right Structures as Needed.

1 Important Attributes: There are two attributes that are of very general significance. That is Instance and is attributes are important because they support property inheritance. They are called a variety of things in AI systems. They represent class member ship and class inclusion and that class inclusion is transitive. In logic-based systems, these relation¬ ships may be represented this way or they may be represented implicitly by a set of predicates describing particular class.

2.Relationships among Attributes: The attributes that we use to describe objects are themselves entities that we represent. There are four properties. (1) Inverse 2) Existence in an is a hierarchy (3) Techniques reasoning about values (4) Single valued attributes.

1.Inverses: Entities in the world are related to each other in many different way us. But as soon as we decide to describe those relation ships as attributes, we commit to a perspective in which we focus on one object and look for binary relation ships between it and others. We used the attributes instance, is a, and team. Each of those was being described and terminating at the object representing the value of the specified attribute. In many cases, it is important to represent this other view of relationships. There are two good ways to do this. The first is to represent both relation ships in a single representation that ignores focus. Ex: Team = (Sagar, cricket) The second approach is to use attributes that focus on a single entity but to use them in pairs, one the inverse of the other, • One associated with sagar: Team = Cricket • One associated with cricket: Team member = Sagar.

2. Existence in an is_a hierarchy: Just as there are classes of objects and specialized subsets of those classes, there are attributes and specialization of attributes. These are generalization - specialization relationships are important for attributes for the same reason that they are important for other concepts - they support inheritance.

3. Techniques for reasoning about values: Some times values of attributes are specified explicitly when acknowledge base is created. But often the reasoning system must reason about values it has not been given explicitly. Several kinds of information can play a role in this reasoning.

? Information about the type of the value.Ex:Length must be a number.? Constraints on the value often stated in terms of related entities.Ex: Age of a person cannot be greater than the age of person’s parent.? Rules for computing the value when it is needed. These rules are called backward rules. Such rules have also been called if needed rules? Rules describe should taken if a value every became known. These rules are called forward rules or sometimes if added rules.

4. Single valued attributes: A specific but very useful kind of attributes is one that is guaranteed to take a unique value. Knowledge - representation systems have taken several different approaches to providing support for single - valued attributes.

? Introduce an explicit notation for temporal interval. If two different values are ever asserted for the same temporal interval, signal a contradiction automatically. ? Assume that the only temporal interval that is of interest is now so if a new value is asserted. Replace the old value.

? Provide no explicit support.3.Choosing the granularity of representation: Regardless of the particular representation formalism, we choose, it is necessary to answer the question “ At what level of details should the world be represented”. Another way this question is often phrased is “ what should be our primitives?” should there be a small number of low-level ones or should there be a larger number covering a range of granularities?

The major advantage of converting all statements into a representation in terms of a small set of primitives is that the written only in terms of the primitives rather than in terms of the many ways in which the knowledge may originally have appeared. Several AI programs including those described by schank and Abelsan and woks are based on knowledge bases described in terms of a small number of low-level primitives. There are several arguments against the use of low-level primitives. One is the simple high level facts may require a lot of storage when broken down into primitives. A second but related problem is that if knowledge is initially presented to the system in a relatively high level form such as English, and then substantial work must be done to reduce the knowledge into primitive form. A third problem with the use of low-level primitives is that in many domains; it is not at all clear what the premises should be.

Ex: John spotted Sue.Who spotted Sue?.Here the direct answer to the question is ‘yes’.Did John see Sue?.The obvious answer that we may give is “yes”.But for AI to reason it out we need to add a fact: Spotted(x,y)?sow(x,y).Here we break the idea of spotting into more primitive concept of seeing.

5. Representing sets of objects: It is important to be able to represent sets of objects for several reasons. One is that there are some properties that are true of sets that are not true of the individual members of a set. There are two ways to state a definition of a set and its elements. The first is to list the members. Such a specification is called an extensional definition. The second is to provide a rule that when a particular object is evaluated, returns true or false depending on where the object is in the set or not. Such a rule is called an intensional definition. While it is trivial to determine whether two sets are identical if extensional descriptions are used, it may be very difficult to do so using intension descriptions. Intensional representations have two important properties that extensional an lack. The first is they can be used to describe infinite sets and sets not all of whole elements are explicitly known. Thus we can describe intentionally such sets as prime numbers. The second thing we can do with intensional descriptions is to allow them to depend on parameter that can change, such as time or spatial location.

The advantages that an intensional definition has over the extensional definition are:

1. intensional representations can be used to describe infinite sets and sets not all of whose elements are explicitly known.Ex: sets of prime numbers or kings of England.2. intentional definition allows us to depend on parameters that can change.Ex: the president of the united states used to be a pemocrot.

5. Finding the right structures as needed: In fact, in order to have access to the right structure for describing a particular situation, it is necessary to solve all of the following problems.1. How to perform an initial selection of the most appropriate structure2. How to fill in appropriate details from the current situation. 3. How to find a better structure if the one chosen initially terms cut not to be appropriate.4. What to do if none of the available structures is appropriate.5. When to create and remember a new structure.

General-purpose method for solving all these problems. Some knowledge representation techniques solve it of them. In this section we survey some solutions to two of these problems. Now to select an initial structure to consider and how to find a better structure if one terms out not to be a good match.1. Selecting an initial structure: Selecting candidate knowledge structures to match a particular problem-solving situation is a hard problem. There are several ways in which it can be done. Their important approaches are the following.

1. Index the structures directly by the significant English words that can be used to describe them.Disadvantages:a. many words may have several different meanings.Ex: I. john flew to newyork.II. john flew the kite.“flew” here had different meaning in two different contexts.

b. it is useful only when there is an English description of the problem.

2. Consider each major concept as a pointer to all of the structures in which it might be involved.Ex:I. the concept steak might point to two scripts, one for restaurant and the other for supermarket.II. The concept bill might point to as restaurant script or a shopping script. We take the intersection of these sets get the, structure that involves all the content words.

Disadvantages:I. if the problem contains extraneous concepts then the intersection will result as empty.II.. It may require a great deal of computation to compute all the possible sets and then to interest them.3. Locate one major clue in the problem description and use if to select an initial structure.Disadvantages:I. We can’t identify a major clue in some situation.II. It is difficult to anticipate which clues are important and which are not. 2. Revising the choice when necessary: Depending on the representation we are using, the details of the matching process will vary. If may require variables to be bound to objects. If may require attributes to have their values. Compared in any case, if values that satisfy the required restrictions as imposed by the knowledge structure can be found, they are put into the appropriate places in the structures. If no appropriate structure can be found them a new structure must be selected. The way in which the attempt to instantiated this first structure failed may provide useful can as to which one to try next if on the other hand, appropriate values can be found, them the current structure can be taken to be appropriate for describing the current situation.

FRAME PROBLEM

Frame problem is a problem of representing the facts that change as well as those that do not change.For ex. Consider a table with plant on it under a window. Suppose we move it to the center of the room. Here we must infer that plant is now in the center, but the window is not.Frame axioms are used to describe all the things that do not change when an operator is applied in state to goto another state say n+1.

Ex: colour(x,y,s1) ^move (x,s1,s2) ? colour(x,y,s2)This axiom says that an object x has a colour y in state 1. moving x from state 1 to state 2 will not change the color of the object x. once a change of state occurs how we undo the changes if we need to back track the two ways that are provided are I. Do not modify the initial state description. At each node, simply store an indication of the specific change that should be made. In order to refer to the current state, we start from the initial state and look back all the nodes on the path from start state to current state.II. Make the changes to the initial state as they occur but every node where a change takes place, gives what to do to undo the move or change if we need to back track.

Different kinds knowledge:Simple relational knowledge.Inheritable knowledge.Inferential knowledge.Procedural knowledge.Epistemology.Meta knowledge

One can represent information about an object or an event by means of a database manipulated about an object or an event by means of a database management system even though holds information, do not hold the facility for representing and manipulating of facts like

All carnivorous have sharp teeth.Cheetah is a carnivore.

Hence cheetah has sharp teeth from the first two statements, the last one can be informed. In a DBMS until one specifies that cheetah has a sharp tooth. It is not possible to get this information.

Database Knowledge Base

1. Collection of data representing facts 1. Has information at higher level of Abstraction2. Large volume of data and facts change 2. Significantly smaller thanover time database and changes are gradual3. Operates on a single object 3. Operates on a class of objects rather than a single object4. Updates are performed by clerical 4. Updates are performed by domain personnel experts5. Correctness of facts can be determined 5. Correctness in a sense is very by comparing the data value with real elusiveworld observations6. All information needed to be explicitly 6. Has the power of inferencingstated7. Maintained for operational purpose 7. Used for data analysis and planning8. Represented by relational or network 8. Knowledge representation is by hierarchical model logic or rules or frames or semantic rules.9. Predominant way of interaction is by 9. Has to have a consultation with transaction programs and report the system and provide neededgenerators data to obtain the solution

Different kinds of knowledge representations:

Declarative representation of knowledge: This controversy raged in 1970’s where in there was a heavy debate on which type of representation should be used in AI programs.

A Declarative representation declares every piece of knowledge and permits the reasoning system to use the rules of inference like modus ponens, modus tokens, etc., to come out with new piece of information.

Ex: All Carnivorous have sharp teeth.Cheetah is a carnivore.

This can be represented using a declarative representation as

? x (carnivore(x)? sharp teeth(x))Carnivore (cheetah)

Using these two representations, it is possible to deduce that “cheetah has sharp teeth”.

Advantages: 1. Declarative approaches are flexible.2. Each piece of knowledge is an independent chunk on its own. Hence modularity is higher.3. It is enough that you represent the knowledge only once.

For all x (carnivore (x)?sharp teeth (x))The variable x engulfs on wide variety of animals, which are carnivorous in nature.

Procedural representation of knowledge: This represents knowledge as procedures and the inferencing mechanism manipulates these procedures to arrive at the result.

Procedure carnivore (x);If (x = cheetah) then return true else return falseEnd procedure carnivore (x)

Procedure sharp_teeth (x);If carnivore (x) then return true else return falseEnd procedure sharp_teeth (x)

Advantages: Procedural representations also have many advantages. First and foremost, heuristic knowledge can be easily represented which is vital. Secondly, one has the control over search, which is not available in declarative knowledge representation.

A knowledge representation scheme should have both procedural and declarative schemes for effective organization of the knowledge base.

Knowledge may be declarative or procedural. Procedural knowledge is compiled knowledge related to the performance of some task. For example, the steps used to solve and algebraic equation are expressed as procedural knowledge. Declarative knowledge on the other hand is passive knowledge expressed as statements of facts about the world. Personnel data in a database is typical of declarative knowledge such data are explicit pieces of independent knowledge. We define knowledge as justified belief.

Two other knowledge terms, which we shall use occasionally, is epistemology and meta knowledge.

Epistemology is the study of the nature knowledge whereas meta knowledge is knowledge that is what we know.Different kinds of widely known knowledge representation:

1. Semantic Nets 2. Frames 3. Conceptual dependency 4. Scripts

Semantic Networks: Network representations provide a means of structuring and exhibiting the structure in knowledge. In a network, pieces of knowledge are clustered together into coherent semantic groups. Networks also provide a more natural way to map to and from natural language than do other representation schemes. Network representation gives a pictorial presentation of objects, their attributes and the relationships that exist between them and other entities. These are also known as associative networks. Associative networks are directed graph with label nodes and arcs or arrows. A semantic network or semantic net is a structure for representing knowledge as a pattern of interconnected nodes and arcs. It is also defined as a graphical representation of knowledge. The knowledge used in constructing a network is based on selected domain primitives for objects and relations as well as some general primitives.

Ex :

1. flycan Bird tweety yellowA knid of colourHas parts Wings

2.is_a is_aScooter Two_wheeler Motor_bike

has hasBrakes Moving_vehicle Engine

has hasElectrical_system Fuel_System

Semantic nets were introduced by Quillian (1968) to model the semantics of English sentences and words. He called his structures semantic networks to signify their intended use.

The main idea behind semantic nets is that the meaning of a concept comes from the ways in which it is connected to other concepts. In a semantic net, information is represented as a set of nodes connected to each other by a set of labeled arcs, which represent relation ships among the nodes.Semantic nets are a natural way to represent relationships that would appear as ground instances of binary predicates in predicate logic.

A semantic net representing a sentence.

John gave the book to Mary.

Instance Instance Agent Object Beneficiary

John height is 72.Height

John is taller than Bill.

Height Height

Greater than

Height

Nodes: In the semantic net, nodes represent entities, attributes, states or events.Arcs: In the semantic net, arcs give the relationship between the nodes.Labels: In the semantic net, the labels specify what type relationship actually exists or describe the relation ship.

Classification of nodes in a semantic net :

Generally, the nodes in the semantic net are classified as

1. Generic nodes 2. Individual or instance nodes

A generic node is a very general node. In figure for the semantic network of Bharathiar university computer center, the mini computer system is a generic node because many minicomputer systems sexists and that node have to center to all of them.

Individual or instance nodes explicitly state that they are specific instances of a generic node. HCL Horizon-III is an individual node because it is a very specific instance of the mini-computer system.

1. Generic node to generic nodeIs-a

2. Individual node to generic nodeIs-a

An is-a link is a special type of link because it provides facilities to link a generic node and a generic node and individual node and a generic node.

Another major feature of the is-a link is that it generates hierarchical structure with the network.

This is a link has another major property which is called inheritance. The property of inheritance is that the properties, which a most a generic node possesses, are transmitted to various specific instances of the generic node.

Reasoning using semantic networks: Reasoning using semantic networks is an easy task. All that has to be done is to specify the start node. From the initial node, other nodes are pursued using the links until the final node is reached. To answer the question “What is the speed of the line printer?” from the above figure.

The reasoning mechanism first finds the node of line printer. It identifies the arc that has the characteristics speed since it points to the value 300, the answer is 30.

The ‘is a’ link structure can be easily represented using predicate logic. Road vehicle is a land vehicle.

?x: road-vehicle (x)? land-vehicle (x)

1. Marcus is a man Man (Marcus) (in predicate logic)

Marcus? man (in semantic net)

Partitioned Semantic net: Suppose we want to represent simple quantified expressions in semantic nets. One way to do this is to partition the semantic net into a hierarchical set of spaces, each of which corresponds to the scope of one or more variables.

Ex:- The dog bit the mail carrier.

The nodes dog, bite and mail carrier represent the class of dog, biting and mail carriers respectively, while the nodes d, b and m represent a particular biting and a particular mail carrier. This fact can be easily be represented by a single net with no partitioning.But now suppose that we want to represent the fact

Every dog has bitten a mail carrier.

To represent this fact, it is necessary to encode the scope of the universally quantified x. The node g stands for the assertion given above. Node g is an instance of the special class GS of general statement about the world. Every element of GS has as least two attributes. A form, which states the relation that is being asserted, and one or more ? connections, one for each of the universally quantified variables. There is only one such variable d., which and stand for any element of the class dogs. The other two variables in the form, b and m are under stood to be existentially quantified. In other words, for every dog d, there exists a betting event b, and mail Carrie n, such that d is the assailant of b and m is the victim.

Every dog in town has bitten the constable

In this net, the node c representing the victim lies out side the form of the general statement. Thus it is not viewed as an existentially quantified variable whose value may depend on the value of d, instead it is interpreted as standing for a specific entity. (in this case, a particular constant), just as do other nodes in a standard, non partitioned.

Every dog has bitten every mail carrier

Would be represented. In this case, g has two ?links, one pointing to d, which represents any dog, and one pointing to m, representing any mail carrier.An inclusion hierarchy relates the spaces of a partitioned semantic net to each other For example, in above space SI is included in space SA. Whenever a search process operates in a partitioned semantic net, it can explore nodes and arcs in the space from which it starts and in other spaces that contain the starting point, but it cannot go downwards, except in special circumstances, such as when a form are is being traversed. So, returning to above figure, from node d it can be determined that d must be a dog. But if we were to start at the node dogs and search for all known instances of dogs by traversing is a links, we would not find d since it and the link to it are in the space SI, Which is at a lower level than space SA, which Contains Dog’s. This is important, since d does not stand for a particular dog; it is merely a variable that can be instantiated with a value that represents a dog.

Example:Every batter hit a ball. Forall x: Batter(x) ? there exist:Ball(Y)and hit(x,y)

All the batters like the pitcher. For all x: Batter(x)?like(pitcher)

Conceptual Graphs: A conceptual graph is a graphical portrayal of a mental perception, which consists of basic of primitive concepts and relationships that exists between the concepts. A single conceptual graph is roughly equivalent to a graphical diagram of a natural language sentence where the words are depicted as concepts and relationships. Conceptual graphs may be regarded as formal building blocks for associative networks which when linked together in a coherent way, from a more complex knowledge structure. A concept may be individual or generic.

Ex : “Joe is eating soup with a spoon”Joe and food(soup) are individual (objects)Eat and spoon are generic

Instrument

SpoonConceptual graphs offer the means to represent natural language statements accurately and to perform many forms of inference found in common sense reasoning.

Frames : Frames were first introduced by Marvin Minsky (1975) and a data structure to represent a mental model of a stereotypical

situation such as driving a car, attending a meeting or eating in a restaurant.Frames are general record like structures, which consist of a collection of slots and slot values. The slots may be of any size and any type. Slots typically have names and any number of values.A frame can be defined as a data structure that has slots for various objects and collection of frames consists of expectations for a given situation.A frame structure provides facilities for describing objects, facts about situations, procedures on what to when a situation is encountered because of these facilities a frame provides, frames are used to represent the two types of knowledge. Declarative/factual and procedural.Ex :

Name of the frame

Slots in the frame

Declarative and Procedural frames: A frame that merely contains description about objects is called a declarative type/factual/situational frame.

A part from the declarative part in a frame, it is also possible to attach slots, which explain how to perform things. In other words it is possible to have procedural knowledge represented in a frame. Such frames which have procedural knowledge embedded in it are called action procedure frames. The action frame has the following slots.1. Actor slot: which holds information about who is performing the activity.2. Object slot : this frame information about the item to be operated on3. Source slot: source slot holds information from where the action has to begin.4. Destination slot: holds information about the place where action has to end.5. Task slot: This generates the necessary sub-frames required to perform the operation.

Ex :

The generic frame merely describes that, the expert in order to clean the nozzle of the scooter has to merely perform, the following operations:

Removing the carburetor from the scooterOpening it up to expose all partsCleaning the nozzleRefitting it in the scooter.Here source and destination is scooter.

Reasoning using frames: The task of action frames is to provide facility for procedural attachment and help transforming from initial to goal state. It also helps in breaking the entire problem in to sub-tasks, which can be described as top-down methodology. It is possible for one to represent any tasks using these action frames.

Reasoning using frames is done by instantiation. Instantiation process begins when the given situation is batches with frames that already exist. The reasoning process tries to match the frame with the situation and latter fills up slots for which values must be assigned. The values assigned to the slot depict a particular situation and but this reasoning process tries to move from one frame to another to match the current situation. This process builds up a wide network of frames, there by facilitating one to build a knowledge base for representing knowledge about common sense.

Frame-based representation language:

Frame representations have become popular enough that special high level frame-based representation language have been developed. Most of languages use LISP as the host language. They typically have functions to create access, modify updates and display frames.

Implementation of frame structures: One way to implement frames is with property lists. An atom is used as the frame name and slots are given as properties. Facets and values with in slots become lists of lists for the slot property.

Putprop ‘train((type(value passenger))(class(value first second sleeper))(food(restaurant(value hot-meals))(fast-food(value cold snacks)))’ land transport)

Another way to implement frames is with an association list ( an-a-list), that is, a list of sub lists where each sub list contains a key and one or more corresponding values. The same train frame would be represented using an a-list as

(set Q train ‘((AKO land transport)(type(value passenger))(class(value first second sleeper))(food(restaurant(value hot-meals))(fast-food(value cold snacks)))

It is also possible to represent frame like structures using Object oriented programming extensions to LISP languages such as Flavors.

Scripts: Scripts are another structures representation scheme introduced by “Roger Schank” (1977). They are used to represent sequences of commonly accruing events. They were originally developed to capture the meanings of stories or to understand natural language test.

A script is a predefined frame-like structure, which contains expectations, inferences and other knowledge that is relevant to a stereotypical situation.

Frames represented a general knowledge representation structure, which can accommodate all kinds of knowledge. Scripts on the other hand help exclusive in representing stereotype events that takes place in day-to-day activity.

Some such events are

1. Going to hotel, eating something, paying the bill and exiting.2. Going to theatre, getting a ticket, viewing the film and leaving.3. Going to super market, with a list of items to be purchased, putting the items needed on a trolley, paying for them.4. Leaving home for office in a two-wheeler, parking the two-wheeler at the railway station, boarding the train to the place of work and going to the place of work.5. Going the bank for with drawl, filling the with drawl slip/check, presenting to the cashier, getting the money and leaving the bank.

All the situations are stereotype in nature and specific properties of the restricted domain can be exploited with special purpose structures.

A script is a knowledge representation structure that is extensively used for describing stereo typed sequences of action. It is a special case of frame structure. These are interested for capturing situations in which behavior is very stylized. Scripts tell people what can happen in a situation, what events follow and what role every actor plays. It is possible to visualize the same and scripts present a way of representing them effectively what a reasoning mechanism exactly understand what happens at that situation.

Reasoning with Scripts: Reasoning in a script begins with the creation of a partially filled script named to meet the current situation. Next a known script which matches the current situation is recalled from memory. The script name, preconditions or other key words provide index values with which to search for the appropriate script. An inference is accomplished by filling in slots with inherited and defaults values that satisfy certain conditions.

Advantages:1. Permits one to identify what scenes must have been proceed when an event takes place.2. It is possible using scripts to describe each and every event to the minutest detail so that enough light is thrown on implicitly mentioned events.3. Scripts provide a natural way of providing a single interpretation from a variety of observations.4. Scripts are used in natural language understanding system and serve their purpose effectively in areas for which they are applied.

Disadvantages:

1. It is difficult to share knowledge across scripts what is happening in a script is true only for that script.2. Scripts are designed to represent knowledge in stereo type situations only and hence cannot be generalized.

Important components:

1. Entry condition: Basic conditions that must be fulfilled. Here customer is hungry and has money to pay for the eatables.2. Result: Presents the situations, which describe what, happens after the script has occurred. Here, the customer after satisfying his hungry is no hungrier. The amount of money he has is reduced and the owner of the restaurant has now more money. Captional results can also be stated here like the customer is pleased with the quality of food, quality of service etc., or can be displeased.

3. Properties: These indicate the objects that ate existing in the script. In a restaurant on has tables, chairs, menu, food money, etc..4. Roles: What various characters play is brought under the slot of roles. These characters are implicitly involved but some of them play an explicit role. For example waiter and cashier play an explicit role where the cook and owner are implicitly involved.5. Track: Represents a specific instance of a generic pattern. Restaurant is a specific instance of a hotel. This slot permits one to inherit the characteristics of the generic node.6. Scenes: Sequences of activities are described in detail.

Ex1: Going to a restaurant

Ex 2 : Going to super market

Conceptual Dependency (CD): Conceptual dependency is a theory of how to represent the kind of knowledge about events that is usually contained in natural sentences. The goal is to represent the knowledge in a way that

? Facilitates drawing interference from the sentences.? Is independent of the language in which the sentences were originally stated.

The theory was first described in Schank 1973 and was further developed in Schank 1975. It has been implemented in a variety of programs that read and understand natural language text. Unlike semantic nets provide only a structure in to which nodes representing information at any level can be placed. Conceptual dependency provides both structure and a specific set of primitives, at a particular level of granularity out of which representations of particular pieces of information can be constructed.

Conceptual dependency (CD) is a theory of natural language processing which mainly deals with representation of semantics of a language. The main motivation for the development of CD as a knowledge representation techniques are given below.

To construct computer programs that can understand natural language.To make inferences from the statements and also to identify conditions in which two sentences can have similar meaning.To provide facilities for the system to take part in dialogues and answer questions.To provide a necessary plank that sentences in one language can be easily translated into other languages.To provide means of representation which are language dependent.

Knowledge is represented in CD by elements what are called as conceptual structures.

Apart from the primitive CD actions one has to make use of the six following categories of objects

1. PP’s (Picture producers) : Only physical objects are physical procedures.2. Acts : Actions are done by an actor to an object.

Major acts :CD primitives Explanationa. ATrans Transfer of abstract relationship (eg. Give)b. PTrans Transfer of physical location of an object (eg. Go)c. PROPEL Application of physical force of an object(eg. Throw)d. Move Movement of a body part of an animal by the animal (eg. Kick)e. GRASP Grasping of an object by an actor (eg. Hold)f. INGEST Taking of an object by an animal to the inside of that animal (eg. Drink,eat) g. EXPEL Expulsion of an object from inside the body by an animal to the words (eg. Spit)h. MTrans Transfer of mental information between animals or within animal (eg. Tell)i. MBuild Construction of a new information from an old information (eg. Decide)

j. Speak Actions of producing sound (eg. Say)

k. Attend Focussing a sense organ towards a stimulus (eg. Listen)

3. Locs : LocationsEvery action takes place at some locations and serves as source and destination4. Ts : TimesAn action can take place at a particular location at a given specified time. The time can be represented on an absolute scale or relative scale.5. AAs : Action AidersThese serve as modifiers of actions. An actor PROPEL has a speed of actor associated with it which is an action aider.6. PAs : Picture AidersServe as aides of pictures procedures. Every object that serve as a PP, needs certain characteristics by which they are defined. PAs practically serve PPs by defining the characteristics.

The main goal of CD representation is to make explicit of what is implicit. That is way, every statement that is made has not only the actors and objects but also time and locations, source and destinations.

The following set conceptual tenses make usage of CD more precise

O - Object case relationshipR - recipient case relationshipP - past tenseF - future tenseT - transitionTs - start transitionTf - finished transitionK - continuing? - interrogative/ - negative, nil-present, delta-timeless, c-conditional

CD brought forward the notation of language independence because all acts are language independent primitives.CD is a special purpose of semantic networks in which specific primitives are used in rebuilding representations. It still remains today as a fundamental knowledge representation structure in natural language processing system.

Ex : PP ACT Bird Ptrans Bird flew

PP PP Joe student Joe is a student

Act PP Joe PROPEL door Joe pushed the doorPP SueAct Joe Atrans Joe gave a flower suePP Joe

flower

JoeAct Joe INGEST

dosoupspoonJoe ate some soupCD is a theory of representing fairly simple actions.

I gave a book to manCD representation is tomanI ATRANS o bookIfrom

Where the symbols have the following meanings • Arrows indicate direction of dependency• Double arrow indicates two way link between actor and action.• P Indicates past tense.• A trans is one of the primitive acts used by the theory, it indicates transfer possession• O indicates the direct case relation• R indicates the recipient case relation

Since smoking can kill you, I stopped.

ONEOne INGEST o smoke

I CIGARETTE

C TfPIINGEST o smoke

ONE DEAD CIGARETTE

ALIVE

The vertical causality link indicates that smoking kills one. Since it is marked, however we know only that smoking can kill one, hot that it necessarily does.The horizontal causality link ordinates that it is first causality that made me stop smoking. The qualification p attached to the depending between I and INGEST indicates that the smoking has stopped and that the stopping happened.

There are three important ways in which representing knowledge using the CD model facilities reasoning with the knowledge. 1. Fewer inference rules are needed would be required if knowledge were not broken down into primitives.2. Many inferences are already contained in the representation it self.3. The initial structure that is built to represent the information contained in one sentence will have that need to be billed. These holes can serve as an attention focuser for the program that must understand using sentences.

LOGIC

Logic can be defined as a scientific study of the process of reasoning and the system of rules and procedures that help in the reasoning process.

Basically, the logic process takes in some information (called premises) and produces some outputs (called Conclusions).

Logic is basically classified into two categories.

1. Propositional logic 2. Predicate logic

Propositional logic: This is the simplest form of logic. Here all statements made are called propositions. A proposition in propositional logic takes only two values, i.e. either the proposition is True or it is False.

Ex : Rubber is a good conductor of electricity. (False)Diamond is a hard material. (True)

There are two kinds of propositions. They are atomic propositions (also called simple propositions) and molecule propositions (also called compound propositions).

Combining one or more atomic propositions using a set of logical connective forms molecular propositions.

Ex : “Baskar is a golfer” is an atomic proposition.“Baskar is a golfer and Ravi is not a doctor” is a molecular proposition because it is formed from two atomic propositions connected by the logical connectives AND and NOT.

Molecular propositions are much more useful than atomic propositions because real world problems involve more of molecular propositions.

Syntax of propositional logic :

1. ~A (Negation of A)2. A & B (Conjunction of A with B)3. A v B (Inclusive disjunction of A with B)4. A? B (A implies B)5. A B (Material bi-conditional of A with B)6. A B (Exclusive disjunction of A with B)7. A B (Joint denial of A with B)8. A B (Disjoint denial of A with B)

Semantics of logical propositions: A clear meaning of the logical propositions can be arrived at by constructing appropriate truth tables for the molecular propositions.

Truth table :

A B ~A ~B AvB A&B A?B A B A + B A | B A B

T T F F T T T T F F FF T T F T F T F T T FT F F T T F F F T T FF F T T F F T T F T T

Logical equivalences :

1. A ~~A, A&A2. A&B B&A3. AvB BvA4. (A&(B&C)) ((A&B)&C)5. (Av(BvC)) ((AvB)vC)6. (A&(BvC)) ((A&B)v(A&C))7. (Av(B&C)) ((AvB)&(AvC))8. ~(A&B) ~Av ~B9. ~(AvB) ~A& ~B10. A?B ~AvB, ~(A& ~B), (~B? ~A)11. A?(B?C) ((A?B)?C)12. A B (A&B)v(~A& ~B), (A?B)&(B?A)

Tautologies: Propositions that are true for all possible combinations of truth values of their atomic parts are called tautologies. This implies that a tautology is always true.Ex : ((A&(A?B))?B) is a tautology.

A B A?B A&(A?B) (A&(A?B))?B

T T T T TT F F F TF T T F TF F F F T

Contradiction: Whenever the truth value of a sentence is always false for all combinations of its constituents, then the sentence is called contradiction. Ex : A & ~A.

Contingent: A statement is called a contingent if its truth table has both true and fales as its output. Ex : A? B.

Normal forms in prepositional logic: There are two major Normal forms of statements in prepositional logic. They are Conjunctive Normal Form (CNF) and Disjunctive Normal Form (DNF).

A formula A is said to be in CNF if it has the form A=A1 & A2 & A3&…&An, n>=1 where each A1, A2, A3,…,An is a disjunction of an atom or negation of an atom.

A formula A is said to be in DNF if it has the form A=A1 v A2 v A3v…v An, n>=1 where each A1, A2, A3,…, An is a conjunction of an atom or negation of an atom.

Conversion procedure of Normal Form :

Step 1 : Eliminate implication and bi-conditionals. A?B = ~AvBA B = (A?B)&(B?A) = (~AvB)&(~BvA).Step 2 : Reduce the scope of NOT symbol by the formula (~(~A)) = AStep 3 : Use distributive laws and other equivalent formulas.

Convert the formula (A?((B&C)?D)) into DNF.Sol : (A?((B&C)?D)~Av((B&C)?D)~Av ~(B&C)vD~Av~Bv~CvD ------------> DNF

Convert the formula ((A?B)?C) into CNF.Sol : ((A?B)?C)~(A?B)vC~(~AvB)vC(Av ~B)vC(AvC)&(~BvC) ---------->CNF

Inference Rules : The inference rules of PL provide the means to perform logical proofs or deductions.

Modus ponens: from p and p->q infer q .p->q/qEx: joe is the father (given)Joe is the father (and)Joe has a child(conclude)

Chain rule: from p->q and q->r, infer p->r .p->qq->r/p->r.ex:(programmer likes lisp)->(programmer hates cobol)programmer hates cobol->programmer likes recursionprogrammer likes lisp->programmer likes recursion Simplification: from p and q infer pConjunction: from p and from q ,infer p& qTransposition: from p->q ,infer ~q->~pIf we want to prove something, we apply some manipulation procedures on the given statements to deduce new statement .if we are totally sure that the given statement are true then the newly derived statements are also true. Manipulation procedures that help one to do so are called rules of inference.

First Order Predicate Logic

FOPL: It was developed by logicians as a means for formal reasoning primarily in the areas of mathematics.In FOPL statements form a natural language like English are translated into symbolic structures comprised of predicates, functions, variables, constants, quantifiers and logical connectives .the symbols form the basic building blocks for the knowledge and their combination into valid structures is accomplished using the syntax for FOPL

Ex: "all employees of the AI software co. are programmers " might be written in FOPL as For all x(AI ,software -co-employee cx)->programmer(x))Ai software-co-employee (jm)Programmer (jim) 1.all students in computer science must take pascal.2.john is a computer science major.Propositional logic works fine in situations where the result is either true or false but not both .however there are many real life situations that cannot be treated this way. in order to over come this deficiency, first order logic or predicate logic uses three additional notions .These are predicates ,terms and quantifiers.Predicates: a predicate is defined as a relation that binds 2 atoms together.

Ex: Bhaskar likes Aero planes is represented as Likes (baskar, aero planes)Here likes is a predicate that likes 2 atoms "baskar" and aero planes.

The symbols and rules of combination of a predicate logic are:(1). Predicate symbol : Rama loves sita Love(Rama,Sita) Here love is a predicate symbol.(2). Constant symbol : Here constant symbols are Ram,Sita(3). Variable symbol : X loves Y Here X&Y are variable symbols.(4). Function symbol : These symbols are used to represent special type of relation ship or mapping.It is also possible to have a function as an arguement.Ravi's father is rani's mother is represented as father (father(ravi),rani)Here rani is a predicate and father ravi is a function.Constant,variables and functions are referred to as terms and predicates and reffered to as atomic formulas.The statements in predicate logic are termed as well formed formulas i.e WFFs. A predicate with no variable is called a ground atom.Connectives : The formula in predicate calculus can be combined to form more complex formula using several connectives. OR connective( V), AND connective ( ^), Implies connective ( ?) Negation connective(¬).

Quantifiers: a quantifier is a symbol that permits one to declare or identify the range or scope of the variables in a logical expression.There are 2 basic quantifiers used in logic. they are universal quantifiers (for all) and existential quantifier.If a is variable then for all a is read as 1. for all a 2.for each a 3.for every a Similarly if a is a variable then there exists a is read as 1.there exists a 2. for some 3. for every a

Variables:Free and bound variables: a variable in a formula is free if and only if the occurrence is outside the scope of a quantifier having the variable.A variable is also free in a formula if at least one occurrence of it is free.For all x there exists y (A(x, y,z)) and for all z (B(y, z))--------(1)In this formula, the variable z is free in the first portion for all x there exists y (A(x, y, z))A variable is a formula is bound if and only if its occurrence is with in the scope of the quantifier .a variable is also bound in situations where at least one occurrence of it is bound.Ex: for all x (A(x)->B(x))In this formula, the quantifier for all applies over the entire formula.(A(x)->B(x)) then the scope of the quantifier is A(x)->B(x)any change in the quantifier has an effect on both A(x) and B(X).hence the variable x is bound .Normal forms in predicate logic: in predicate logic, one normal form is there .i.e called prefix normal form .a formula A in predicate logic is said to be in prefix normal form if it has the form (Q1, x1)(Q2,,x2)……….(Qn, xn)BWhere Qixi is either a for all or there exists and B is formula without any quantifier.Convert the formula for all x(A(x)->there exists y(B(x, y)) in to prefix normal form Sol: for all x(A(x)->there exists y B(x,y))

=for all x (~A(x)or there exist y ((B(x,y))

=for all x there exists y (~(A(x)orB(x,y))->PNF.

Syntax for FOPL:

Connectives: there are 5 connective symbols .~, &, or, -> ,<->.

Quantifiers: there are 2 quantifier symbols .for all ,there exists.

Constants: constants are fixed value term that belong to a given domain of discourse.

Variables: variables are terms that can assume different values over a given domain.

Functions: function symbols denote relations defined on domains.

Predicates: predicate symbol denotes relations or functional mappings from the elements of a domain D to the values true or false.Capital letters and capitalized words are used to represent the predicates.Constants, variables and functions are referred to as terms and predicates are referred to as atomic formulas or atoms.Symbols left and right parenthesis, square brackets braces and the periods are used for punctuation in symbolic expressions.Ex:1. all employees earning $1400 or more per year pay taxes .

For all x(E(x)& GE(i(x),1400))->T(x))2.some employees are sick today. There exists (E(y)->delta(y)).

Semantics for FOPL:WFF(Well Formed Formulas): A language such as predicate calculus is defined by its syntax. To specify a syntax we must specify the alphabet of the symbols to be used in the language of how these symbols are put together to form legitimate(valid) expression in the language. The legitimate expression of the predicate calculus are called WFF.Properties of WFF: (1).Equivalence: Not(Not X) is equivalent X.(2). Demorgans theorem: Not(x & y) = notx Vnot y.(3). Distributive property:(4). Commulative property:(5). Associative property.(6). Constrapositive: x?y =not x?not y.

Clause form: A clause is defined as a WFF consisting of a disjunction of literals. The resolution process when it is applicable is applied to pair of parents and producer a new clause.

Conversion to clasual form: one method we shall examine is called resolution of requires that all statements to be converted into a normalized clasual form .we define a clause as the disjunction of a number of literal. A ground clause is one in which no variables occur in the expression .A horn clause is a clause with at most one positive literal.To transform a sentence into clasual form requires the following steps:1. Eliminate all implication and equivalence symbols.2. Move negation symbols into individual atoms.3. Rename variables if necessary so that all remaining quantifiers have different variable assignments.4. Replace existentially quantified variables with special functions and eliminates the corresponding quantifiers.5. Drop all universal quantifiers and put the remaining expression info CNF(disjunctions are moved down to literals).6. Drop all conjunction symbols writing each clause previously converted by the conjunction on a separate line.We describe the process of eliminating the existential quantifiers thru a substitution process. This process requires that all such variables are replaced by something called skolem functions, arbitrary functions which can always assume a correct value required of an existentially quantified variable.

Example in prepositional logic:? u :? v: ? x :? y: p (f(u), v, x, y)->Q(u, v, y)

The skolem form is ? v :?x: p(f(q),v, x, g(v, x))->Q(a ,v, g(v, x))

Convert expression into clasual form

? x: ? y (?z p(f(x),y, z)?(? u Q(x, u)& ? v (R(y, v))

We have after application of step 1

? x: ? y (?? z p(f(x),y,z)or ? uQ(x, u)&( ?y R(y, u)))

After application of step2 we obtain

? x ? y (? z ?p(f(z),y, z)or(? u Q(x, )&( ? v)R(y, v)))

After application of step 4 (step 3 is not required)

? y (?p(f(a),y, g(y)or (Q(a, h(y &R(y,1(y)))

After application of step 5 the result is

? y: ((?p (f(a),y, g(y)or Q(a, h(y))&( ?p(f(a),y, g(y) or R(y,1(y))

Finally , after application of step 6 we obtain the clasual form

?p(f(a),y, g(y) or (Q(a, h(y))?p(f(a),y, g(y) or R(y,1(y))

Example in Predicate logic: Suppose we know that “all Romans who know marcus either hate Caesar or think that any one who hates any one is crazy”.

?x: ?Roman (x)?know(x,marcus)? ? ?hate(x,Caesar) ? (?y: ?z:hate(y,z) ?thinkcrazy(x,y))?

1. Eliminate implies symbol using the fact that a ? b = ?a?b.

?x: ? ?Roman (x)?know(x,marcus)? ? ?hate(x,Caesar) ? (?y: ?( ?z:hate(y,z) ? thinkcrazy(x,y))?

2. Reduce the scope of each ? to a single term.

?x: ?? Roman (x) ? ?know(x,marcus)? ? ?hate(x,Caesar) ? (?y: ?z: ?hate(y,z) ? thinkcrazy(x,y))???(a ?b) =?a? ? b. ??x:p(x) = ?x: ? p(x) .

3. Standardize variables so that each quantifier binds a unique variable. Since variables are just dummy names, this process cannot affect the truth value of the wff.

?x:P(x) ? ?x:Q(x) = ?x:P(x) ? ?y:Q(y)

4. Move all quantifiers to the left of the formula with out changing their relative order.

?x: ?y: ?z: ?? Roman (x) ??know(x,marcus)? ? ?hate(x,Caesar) ? ?hate(y,z) ? thinkcrazy(x,y))?

5. Eliminate existential quantifiers.In our example, there are no existential quantifiers at step 4. There is no need to eliminate that quantifiers. If that quantifiers occurs then use skolem functions to eliminate that quantifiers.

6. Drop the prefix.From (4).?? Roman (x) ??know(x,marcus)? ? ?hate(x,Caesar) ? ?hate(y,z) ? thinkcrazy(x,y))?

7. Convert the matrix into a conjunction of disjuncts. In our problem that are no (ands) disjuncts. So use associative property.

(a?b) ?c = a?(b ?c).

? Roman (x) ??know(x,marcus) ? hate(x,Caesar) ? ?hate(y,z) ? thinkcrazy(x,y).

Unification: Unification is a procedure that compares two literals & discovers whether there exists a set of substitutions that makes them identified.Any substitution that makes 2 or more expressions equal is called a unifier for the expressions. applying a substitution to an expression E produces an instance E' of E where E'=E. given 2 expressions are unifiable, such as expressions c1,c2 with a unifier B with C1B=C2,we say that B is most general unifier (mgu) if any other unifier & is an existence of B. for ex: 2 unifiers for the literals p(u, b, v) and p(a, x y) are & ={a/u, b/x, c/y} and B={a/u, b/x, c/v, c/y}.Unification can sometimes be applied to literals with in the same single clause. When an mgu exists such that 2 or more literals with in a clause are unified, the clause remaining after deletion of all but one of the unified literals is called a factor of the original clause.The basic idea of unification is very simple. to attempt to unify 2 literals, we first check if their initial predicate symbols are the same, if so we can proceed otherwise there is no way they can be unified, regardless of their arguments.Unification has deep mathematical roots and is a useful in many AI programs. for ex: theorem proving and natural language parser.Algorithm:1.If l1, l2 are both variables or constants then a) If l1, l2 are identical then return NIL.b) Else if l1 is a variable the if l1 occurs in l2 then return {fail} , else return (l2/l1}c) Else if l2 is a variable then if l2 occurs in l1 then return {fail} ,else return (l1/l2}.d) Else return {fail}.2. If the initial predicate symbols in l1, l2 are not identical then return {fail}.3. If l1 , l2 have a different no. of arguments then return {fail}4. Set subset to Nil (At the end of this procedure, subset will contain all the substitutions use to unify l1 , l2.5. For i<-1 to no. of arguments in l1.a) Call unify with the I th argument of l1 and the I th argument of l2 putting result in s.b) If s contains fail then return {fail}.c) If s is not equal to nil then

1.Apply s to the remainder of both l1, l22. Subset = append (s, subset).3. Return subset.

Resolution: Robinson in 1965 introduced the resolution principle, which can be directly applied to any set of clauses.The principle is " Given any two clauses A, B if there is a literal p1 in A which has a complementing literal p2 in B, delete p1 ,p2 from A,B and strut a disjunction of the remaining clauses .the clause so constructed is called the resolvent of A,B .

Resolution in propositional logic:

EX: A: P V Q V R , B:~P V Q V R C: ~Q V RP V Q V R ~ P V Q V R

Q V R ~Q V R

REX:2 A: P V Q V R B:~P V R ; C:~Q D: ~RX = Q V R Resolvent of A &B .Y = R Resolvent of X &C.Z = Nil Resolvent of Y & D.The resolution procedure is a simple iterative process. At each step two clauses, called the parent clause are compared (resolved) yielding a new clause that has been inferred from them. The new clause represents ways that the 2 parent’s clauses interact with each other.Resolution work on the principle of identity complementary literals in 2 clauses and deleting them there by forming a new literal . the process is simple and straight forward when one has identical literals . In other words for clauses containing no variables resolution is easy. When there are variables the problem becomes complicated and the necessities one to make proper substitutions.There are 3 major types of substitutions 1. Substitution of a variable by a constant.2. Substitution of a variable by another variable.3. Substitution of a variable by a function that does not contain the same variable.Algorithm: 1. Convert all the statements of F to clause form.2. Negate P and convert the result to clause form. Add it to the set of clauses obtained in 1.3. Repeat until either a contradiction is found, no progress can be made, or a predetermined amount of effort has been expended.a) Select 2 clauses. call these the parent clauses.b) Resolve them together. The resolving will be the disjunction of all the literals of both parent clauses with appropriate substitution performed & with the following exception. If there is 1 pair of literals T1,T2 such that one of the parent clause contains T1 and the other contains T2 and if T1,T2 are unifiable then neither T1,T2 should appear in the resolving. We call T1,T2 complementary literals.use the substitution produced by the unification top create the resolving if there is more than 1 pair of complementary literals, only pair should be omitted from the resolvent.c) if the resolvent is the empty clause , then a contradiction has been found. if it is not, then add it to the set of clauses available to the procedure .

Resolution in predicate calculus:

Theorem proving using resolution.There are two basic methods of theorem proving.Method1: Start with the given axioms, use the rules of inference and prove the theorem.Method2: Prove that the negation of the result cannot be true.The second method is commonly known as theorem proving using refutation. The methodology for that isStep1. Find the negation of the result to be proved.Step2. Add it as a valid statement to the given set of statements.Step3. Perform resolution on these statements until a contradiction is encountered.Step4. Conclude that the contradiction is due to the assumed negation of the result.Step5. So the negated assumption that is false or the result to be proved is true.The following simple example will show how these two methods help in theorem proving.Example:Given that a) ?x [Physician (x)-? known-surgery (x)]b) Physician (Bhaskar)Prove that knows- surgery (Bhaskar)Proof Using method 1:Modus ponens states that if there is an axiom of the form P?Q and another of the form P, and Q logically follows. Assuming Physician (Bhaskar) as P and [physician (x)? knows-surgery (x)] as Q the result knows-surgery (bhaskar) logically follows.

Proof Using Method2:Assume the negation of the result? Knows-surgery (Bhaskar) ………(1)The given axioms arePhysician (Bhaskar) ……(2)?x [Physician (x) ? knows-surgery(x)] ……………. (3)

Equation 3 can be written as? Physician (x) V knowns-surgery (x) (4)(the quantifier is universal. If it had been existential, the skolem function has to be used.)

In Eq(4), substitute x= Bhaskar. So we have? Physician (Bhaskar) V knows-surgery (Bhaskar) (5)Resolving Eq (1) and (5) , we have ? Physician (Bhaskar) (6)Resolving Eq(2) and (6) we have a contradiction.

This contradiction was due to the assumption that was made. i.e the negation of the result . Hence the negation of the result is false or the result is true.Resolving using refutation is much simpler that the method using the rules of inference.Question-answering:Chang (1973) divides the questions into four major classes.Class 1 type where in the question that requires an “yes” or “no” answer.Ex: “yes, flaght 312 has left coimbattor” or“no, kerala express is running 45 minutes late.Class 2 type: The kind of question that requires “where is” or “who is” or “under hat condition as an answer.Ex: Ravi is vishaka patnam.Kumar should not light a matchstick if there is an LPG leak.Class 3 type: Here answer is in the form of sequence of action and the order is importantEx: Add concentrated sulphuric acid slowly to water and then add the diluted acid to the salt.Class 4 type: Questions whose answers require testing of some conditions.Ex: If possible do colour Doppler evalution of if not do echocardiography.Ex:1. marcus was a man man(marcus) 2. marcus was a Pompeian Pompeian (marcus)3. marcus was born in 40 A.D born (marcus,40)4.all men are mortal for all x : man(x)->mortal(x)5.all Pompeian was died when the volcano erupted in 79 A.D.6.erupted volcano 79 and for all x [Pompeian(x)->died (x,79)]7.no mortal lives longer than 150 years .for all x :for all t1: for all t2 : mortal(x) and born (x1t1) and gt(t2-t1,150) -> dead (x,t2)8. it is now 1991 - now=19919.alive means not dead.For all x:for all t:[alive (x,t)->->dead (x,t)]and [->dead (x,t)->alive(x,t)]10.if someone dies ,then he is dead at all later times.For all x:for all t1:for all t2 :died (x,t1)and gt(t2,t1)->dead(x,t)Question : is marcus alive -> alive (marcus ,now )^(9,substitution)dead(marcus,now)^ (10,substitution )^ died(marcus,t1)and gt(now ,t1)Pompeian (marcus)and gt(now ,79)^ (2)gt(now,79)^ (8,substitute equals) gt(1991,79)^ compute gt nilmarcus is died.Ex2: 1. Steve only likes easy courses.?x: easycourse(x)?likes(x,Steve) 2. Science courses are hard.Hard(science courses)3. All the courses in the basketweaving department are easy.?x: basketweaving dept(x) ? easy(x).4. BK301 is a basket weaving course.Basketweaving course(Bk301).From(1) ?x: ?easycourse(x) V likes(x,steve) ---------(5).From (3) ?x: ?basketweaving dept(x) V easy(x). ---------(6).Resolvent from (5) and (6) ?basketweaving dept(x) V likes(x,steve)-------(7).Resolvent from (4) and (7) likes(Bk301,steve) x/Bk301.?Steve would like Bk301.Refutation Method: Assume steve does not Bk301? likes(x,steve)

?easycourse(x)

?basketweaving dept(x)

Nil

So our assumption is wrongSo Steve likes Bk301.Exampe3: John likes all kinds of food…………..?x: food(x)?likes(x,John)………(1)Apples are food……………………………………. Food(apples)Chicken is food……………………………………. Food(chicken)

Anything any one eats and is not killed by is food… ?x: ?y: [person(y)^ eats(y,x)^ ~killed(y)] ? food(x) ..(2)Bill eats peanuts and is still alive…………………..eats(peanuts,bill)^ ~killed(bill)………(3)Eats(x,bill)?person(bill)Sue eats everything that bill eats…………………?x: eats(x,bill)? eats(x,sue) ….(4)

From (1)……~food(x)Vlikes(x,john)…………..(5)From (2)….~[ person(y)^ eats(y,x)^ ~killed(y)] V food(x)……..(6)From(3) ….~eats(peanuts,bill)V person(x)From (4) …..~eats(x,bill)v eat(x,sue)

Resolvent(5) and (6) likes(x,steve)V ~ person(y) V~eats(x,y) V killed(y)…..(7)Here we substitute x= peanuts and y = Bill.Resolvent (3) and (7) likes(peanuts,john) V ~ person(Bill)From stmt 5 person(bill)…………………………………………………………..(8)Resolvent from (7) and (8) likes(peanuts , John)So John likes peanuts.Refutation Method:Assume John does not likes peanuts.~likes(peanuts,john)

~food(x)

~person(y) V ~eats(peanuts ,y) V killed(y)

~person(bill)

NilNote: Additional knowledge that Bill is a person. We can justify the knowledge because Bill eats peanuts &still alive.So Bill is a person.

So our assumption is wrong.So John likes peanuts.

Several types of resolution are depending on the number and types of parents. Some of them.Binary resolution: 2 clauses having complementary literals are combined as disjunct to produce a single a clause after deleting the complementary literals.~p(x,a) or q(x) and ~q(b) or r (x)~p(b,a) or r (b)Unit resulting resolution: a number of clauses are resolved simultaneously to produce a unit clause. All except one of the clauses are unit clauses and that one clause has exactly one more literal than the number of unit clause.Linear resolution : when each resolved clause ci is a parent to the clause ci+1 (i=1,2,…n-1) the process is called linear resolution.Linear in resolution: if one of the parents in a linear resolution is always from the original set of clauses (the Bi) we have linear resolution .

Limitation of logic as acknowledge representation scheme:

1.logic and theorem proving techniques are monotonic in nature. The derived axioms hold good under all circumstances. Real world is never monotonic for information obtained is seldom complete.2.logic does not provide facilities for handling uncertainty. Every information it deals has to either correct or incorrect but never partially.3.codificaiton of the problem in logic is a tough task and requires considerable effort on the part of the user.4.even though various techniques do exist for speeding resolution, it takes considerable amount of time to prove statements in logic.5.one major constraint in logic is that unless you are sure that a solution exists, the search will not terminate .we will be going on adding clause after but the solution will be still elusive.

Forward versus Backward Reasoning:

The object of a search procedure is to discover a path through a problem space from an initial configuration to a goal state. There are actually two directions in which such a search could proceed.

Forward, from the start states Backward, from the goal states.

The production system model of the search process provides an easy way of viewing forward and backward reasoning as systematic processes.Forward reasoning from initial states:1. Root: A tree of move sequences, that might be solutions, is built by starting with the initial configuration at the root of the tree.2. Generate of the next level: The next level of the tree is generated by building a tree by finding all the rules whose left sides are matched against the current state(root node) and the right sides are to generate new nodes by creating new configuration. Generate next level by taking each node generated at the previous level and continue the above reasoning forward till a configuration matches

the goal state.Back ward reasoning from the goal states:1. Root: A tree of move sequences, that might be solutions, is built by starting with the goal configuration at the root of the tree.2. Generate the next level: The next level of the tree is generated by finding all the ruleswhose right sides match the root node. The left sides are used to use to generate the new nodes, representing new goal states to achieve. Generate the next level of the tree by taking each node at the previous level and continuing the above reasoning until a node that matches the initial state is generated. It is often called goal-directed reasoning.

It does not make much difference whether we reason forward or backward, about the same number of paths will be explored in either case. But this is not always true. Depending on the topology of the problem space, if may be significantly more efficient to search in one direction rather than the other.Four factors influence the question of whether it is better to reason forward or backward.

(1) Are there more possible start states or goal states?Count the number of start states of goal states. Move from the smaller set of states to larger set of states.(2) In which direction is the branching factor greater?Find the direction in which the branching facto is low and proceed in that direction.(3) Will the program be asked to justify its reasoning process to a user?If the program is asked to justify its reasoning process then proceed in the direction that corresponds more closely with the way the user think.(4) If it is the arrival of a new fact, forward reasoning make sense. If it is a Query to which a response is desired, backward reasoning is more natural.Example:1. To solve the problem of symbolic integration, it is better to reason forward.2. For the problem of proving theorems, is would be much better to reason backward.

Principle:

Forward rules, which encode knowledge about how to respond to certain input configurations.

Backward rules, which encode knowledge about how to achieve particular goals.

Forward and backward chaining rule systems:

Forward-chaining rule system:

1. Instead of starting from the goal state, we start the search by incoming data.2. In this, left sides of rules are matched against the state description.3. If they match, we apply if and a new state generated will be represented at the right side.This process repeats until the goal state is reached.4. Matching is more complex than backward ones.

Backward-chaining rule system:

1. In this, we start the search from the goal state as an initial state and make a move to the state we want.2. The number of state computed to generate are said to be chain of links.3. If one state, in the path is removed the entire path will be collapsed.

PROLOG is an example of backward – chaining system.

We can also search both forward from the start state and backward from the goal simultaneously until two paths meet some where in between. This strategy is called bi-directional search. It seems appealing if the number of nodes at each step grows exponentially with the number of steps that have been taken. In fact, many successful AI applications have been written using a combination of forward and backward reasoning and most AI programming environments provide explicit support for such hybride reasoning.

Non-Monotonic Reasoning Systems

Monotonic NonMonotonic 1. It is complete with respect to It is incomplete.the domain of interest.

2. It is consistent. It is not consistent.

3. New facts can be added only when New facts will contradict and invalidatethey are consistent with the facts the old knowledgethat have already been as sorted.

A monotonic reasoning system cannot work effectively in real life environments because Information available is always incomplete.As process goes by situation change and so are the solutions. Default assumptions are made in order to reduce the search time and for quick arrival of solutions.

Basic concepts of non-monotonic reasoning systems:

AI systems provide solutions for those problems whose facts and rules of inference are explicitly stored in the database and knowledge

base. But as mentioned above the data and knowledge are incomplete in nature and generally default assumptions are made.Non-monotonic reasoning systems are more complex then monotonic reasoning systems. Monotonic reasoning systems generally do not provide facilities for altering facts, deleting rules it will have an adverse effect on the reasoning process.One of major systems that has been implemented using non-monotonic reasoning system with dependency. Directed back tracking is the Truth maintenance system of Doyle.Dependency -directed back tracking helps to great deal in nom monotonic reasoning systems. A monotonic system evades contradictions .a contradiction occurs when the system finds that the new state discovered is inconsistent with the existing ones.

TMS: TMS also known as belief revision and revision maintenance are companion components to inference systems. The main job of the TMS is to maintain consistency of the knowledge being used by the problem solves and not to perform any inference functions. The TMS also gives the inference component the latitude to perform non-monotonic inferences. When new discovers are made, this more recent information can displace previous conclusions that are no longer valid .in this way the set of beliefs available to the problem solver will continue to be current and consistent.Diagram:

Tell

Ask

Architecture of the problem solver with a TMS

The role played by the TMS a part of the problem solver. the inference engine solves domain problems based on its current belief set, while the TMS maintains the currently active belief set .the updating process is incremented .after each inference ,information is exchanged between the 2 components .the IE tells the TMS what the deductions has made. The TMS in turn, asks questions about current beliefs and reasons for failures. It maintains a consistent set of beliefs for the I.e. to work with even if now knowledge is added & removed.The TMS maintains complete records of reasons of justifications for beliefs. Each proposition having at least 1 valid justification is made a part of current belief set. Statements lacking acceptable justifications are excluded from this set. When a contradiction is discovered the statements responsible for the contradiction are identified & an appropriate one is retracted. This in turn may result in other retractions & additions. The procedure used tp perform this process is called dependency back tracking.The TMS maintains records to reflect retractions and additions & that will always know its current belief set. The records are maintained in the form of dependency network. The node in the network represents KB entries such as premises, conclusions, inference rules and the like. Attached to the nodes are justifications, which represent steps from which the node was derived. Nodes in the belief set must have valid justifications. a premise is a fundamental belief which is assumed to be always true. Premises need no justifications. They form a base from which all other currently active nodes can be explained in terms of valid justifications.

Premises Assumptions Datum Justification

There are 2 types of justifications records maintained for nodes. Support lists (SL) and conceptual dependencies. SL’s are the most common type. They provide the supporting justifications for nodes. The data structure used for the SL contains 2 lists of other dependent node names on in list and an out list.(SL )CP justifications are used less frequently than the SLS. They justify a node as a type of valid hypothetical argument.(CP)Example for truth maintenance system.

TMS maintains the consistency of the knowledge being used by the problem solves.It maintains the currently active belief set.It maintains the records of reasons of justification for beliefs.Records are maintained in the form of dependency network.

Example: ABC murder story.Initially Abbot is believed to be the primary suspect the reason is non-monotonic. The three assertions believed initially are.? Suspect Abbot (Abbot is the primary suspect)? Beneficiary Abbot (Abbot is a beneficiary of the victim)? Alibi Abbot (abbot was at on Albony hotel at that time.)

Representation in TMS:A TMS dependency network offer a purely syntactic,domain-independent way to represent belief and change it consistently.

Suspect Abbot [IN] ] supported belief

Justification

Beneficiary Abbot Alibi AbbotJustification:

1. The assertion ”Suspect Abbot” has an associated TMS justification. An arrow to the assertion it supports connects the justification.2. Assertions in a TMS dependency network are believed when they have a valid justification.3. Each justification has two parts:a. An IN-list [connected to justification by ‘+’]b. An OUT-list [connected to justification by ‘-‘]4. If the assertion corresponding to the node should be believed, then in the TMS it is labeled IN.5. If there is no reason to believe the assertion, then it is labeled OUT.

Premise Justification: Premise justifications are always considered to valid. Premises need no justifications.

Labeling task of a TMS: The labeling task of a TMS is to label each node so that three major criteria of dependency network are met.1. Consistency2. Well-founded-ness3. Resolving contradictions.

Ex .1: Consistency criterions:

The following two cases show how consistency is maintained while changing Abbot’s state.

Case(i). Abbot is beneficiary. We have no further justification for this fact. We simply accept it.The following figure shows a consistent labeling for the network with premise justification.

Suspect Abbot[IN]

+ _

Beneficiary Alibi Abbot[Out]Abbot[IN] Empty IN and OUT lists

Labeled nodes with premise Justification.

Case (ii): If abbots alibi is obtained, then some more justifications are added. Then consistency is maintained in the following ways, by making the following inclusions.

Abbott was registered is a hotel Premise justification So INHotel is far away Premise justification. SO INRegister might be forged Lacks any justification. SO OUTAbove 3, shows that “Suspect about” no longer has a justification SO OUT

Suspect Abbot[OUT]

+ _

Beneficiary Alibi Abbot[IN]Abbot[IN]

Registered Abbot[in] Far away[in] Register forged[OUT]Charged labeling

Well-Founded ness criterion: (1) It is defined as the proper grounding of a chain of justifications on a set of nodes that do not themselves depend on the nodes they support.

(2) For example : Cabot justification for his alibi that he was at a ski show is hardly valid.

The only support for the alibi of attending the ski show is that Cabot is telling the truth.---------?(1)The only support for his telling the truth, would be if we knew he was at the ski show.----------?(2)

Above (1) and (2) statements show a chain of IN- List links to support the “Alibi Cabot “ Node.So, In such cases the node should be labeled Out for well-founded ness.

Suspect Cabot [IN]

+

Beneficiary Cabot [IN] Alibi Cabot [OUT] +

+ TellsTruthCabot [OUT]

Cabot Justification --- Well Founded ness.

Resolving Contradictions Criterion:

(1) A contradiction in TMS is a state of the database explicitly declared to be undesirable.(2) Example: In our example, a contradiction occurs if we do not have at least one murder suspect or If there are suspects other than Abbot, Babbitt, Cabot.

Contradiction [out]

Suspect Abbot Suspect Babbit Suspect Cabot Other suspect

(3) Initially there is no valid justification for other suspects so, contradiction is labeled OUT.(4) Suppose Cabot was seen on T.V that he was at the ski slopes, then is causes “Alibi Cabot” node to be labeled IN. So, it makes ‘ Suspect Cabot’ node to be labeled OUT.(5) The above point gives a valid justification for contradiction and hence is labeled IN.

Contradiction [IN]

Alibi Abbot Alibi Babbit Alibi Cabot[IN] Other suspects

(6) The job of TMS is to determine how the contradiction can be made OUT. I.e the justification should be made invalid.(7) Non monotonic justifications can be invalidated, by asserting some fact whose absence is required by the justification(8) That is we should install a justification that should be valid only as long as it needs to be.(9) A TMS have algorithms to create such justifications, which is called Abductive justification.

Default reasoning: Default reasoning is one type of non-monotonic reasoning, which treats conclusions as, believed until a better reason is found to believe something else.Two different approaches to deal with non-monotonic system are:(1) Non- monotonic logic (2) Default logic(1) Non-monotonic logic: Non-monotonic logic is one in which the language of FOPL is augmented with a modal operator m, which can be read as “is consistent”.Non-monotonic Logic defines the set of theorems that can be derived from a set of WFF’s A to be the intersection of the sets of theorems that results from the various ways in which the WFF’s of A might be combined.A ? MB ? B¬A ? MB ? BWe conclude:MB ? B.(2) Default Logic:

Another form of uncertainty occurs as a result of in complete knowledge .one way human’s deal with this problem is by making plausible default assumptions. That is we make assumptions, which typically hold but may have to be retracted if new information is obtained to the contrary.Default reasoning is another form of non-monotonic reasoning .it eliminates the need to explicitly store all the facts regarding a situation. Reiter 1980 develops a theory of default reasoning within the context of traditional logics .a default is expressed as

A (x): M (b1 (x)…Mbk (x)

C (x)

Where a (x) is a precondition wff for the conclusion wff c (x) M is a consistency operator and the bi (x) are conditions, each of which must be separately consistent with the Kb for the conclusion c (x) to hold.Default theories consist of a set of axioms and set of default inference rules with schemata. The theorems derivable from a default system are those that follow from first order logic and the assumptions assumed from the default rules. Suppose a Kb contains only the statements Bird (x): Mfly (x)/fly (x)A default proof of fly is possible.but if KB also contains the clause. Ostrich (tweety).Ostrich (x)->~fly (x)Fly (tweety) would be blocked since the default is now in consistent. Default rules are especially useful in hierarchal kB.because the default rules are transitive property inheritance becomes possible.Transitivity can also be a problem in Kb with many default rules. Rule interactions can make presentations very complex.Two kinds of non-monotonic reasoning that can defined in these logics are:1. Abduction 2. Inheritance

1. Abduction: Abductive reasoning is described “ Given two WFF’s (A ? B) & (B) for any expressions A & B , if it is consistent to assume A then do so”.Example: Suppose it is given that “people who have had too much to drink tend to stagger when they walk”. Then “we may conclude that a person who is staggering is drunk” though this may be incorrect sometimes.So we make a conclusion only if it is consistent enough to assume it.2. Inheritance: Inheritance is another form of non-monotonic reasoning which inherit attribute values from a prototype description of a class to the individuals entities that belong to a class.Default rules are useful hierarchical knowledge bases. Because the default rules are transitive, property inheritance becomes possible.

Minimalist Reasoning: Minimalist reasoning follows the idea that “there are many fewer true statements than false ones. If something is true and relevant it makes sense to assume that is has been entered into our knowledgebase. Therefore, assume that the only true statements are those that necessarily must be true in order to maintain the consistency of knowledge base”.Two kinds of minimalist reasoning are:(4) Closed world assumption (CWA).(5) Circumscription.Closed world assumption: Another form of assumption made with regard to incomplete knowledge, is more global in nature than single defaults. This type of assumption is useful in application where most of the facts are and it is, therefore, reasonable to assume that if a proposition cannot be proven, it is false. This is known as the closed world assumption with failure as negation. This means that in a kb if the ground literal p(a) is not provable, then ~p(a) is assumed to hold true. CWA is another form of non-monotonic reasoning. CWA is essentially the formalism under which prolog operates and prolog has been shown to be effective in numerous application.

Disadvantages: 1. A knowledge base augmented with CWA is not consistent.2. CWA assumptions are not always true in the world.3. CWA forces completion of a knowledge base by adding the negation assertion ¬P whenever it is consistent to do so. But the assignment of a property to some predicate P and its complement to the negation of P may be arbitrary. Predicate completion: Limiting default assumptions to only portions of a KB can be achieved through the use of completion or circumscription formulas. Unlike CWA, these formulas apply only to specified predicates and not globally to the whole KB.Completion formulas are axioms which are added to a kb to restrict the applicability of specific predicates, if it is known that only certain objects should satisfy given predicates, formulas which make this knowledge explicit are added to the kb. T his technique also requires the addition of the unique names assumption ie formulas which state that distinguished named entities in the KB are unique.As an ex: of predicate completion, suppose we have the following kb.owns(joe,food) ,student(hoe),owns(jill,chevy),student(jill),owns(sam,bike),programmer(Sam),student(Mary).If it is known that joe is the only person who owns a ford, this fact can be made explicit with the following completion formula.For all (x)(owns (x,ford)->equal (x,joe)-----(1)I n addition, we add the inequality formula ~equal (a,joe)---(2)Which has the meaning that this is true for all constants, which are different from joe. Likewise, if it is known that mary also has a ford and only mary and joe have fords, the completion and corresponding inequality formulas in this case would be for all owns (ford,x)->equal(x,joe) or equal (x,mary)~Equal (a, joe)~Equal (a,mary)In addition, we add another statement ~owns (jill, ford)

1..~Owns (x, food) or equal (x, joe)

2. ~Equal (a,joe)

3.owns(jill,ford) from 1 & 3 we get equal (jill,joe)----(4)from 2 & 4 [ ]->nil

Circumscription: Circumscription is another form of minimalist reasoning introduced by john Mc carthy (1980) . It is similar to predicate completion in that all objects that can be shown to have same property p are in fact the only objects that satisfy p.CWA does not capture all of the idea. If has two limitations:3. CWA operates on individual predicates with out considering the interactions among predicates that are there in the knowledge base.4. CWA assumes that all predicates have all of their instances listed. But this is not true in many knowledge-based systems.Circumscription overcomes that above limitations.

To explain what is a circumscription considers a day-to-day activity. We have our house on a 2 wheeler go to the railway station, park out vehicle, board the train to our destination, reach the destination and attend the college.office. Here the system that works for the solution to a problem in this case is expected to recognize certain ground conditions such as :1.There is no fuel in the 2 wheeler 2.Two-wheeler is in a good condition 3.There is no block able during your travel 4.train journey is safe etc.In fact, it is not possible to consider all the qualifications that needs to be included to minimize time and solution space, we make certain explicit assumptions that if there is something that is not mentioned, it need not be taken into consideration, so far the above problem one need not bother about the factors. Practically if corresponds to minimization of objects under consideration. In short, in any problem one considers only those existences is required for getting the clear picture of the solution. This principle of avoiding all unnecessary details and taking into account only that is absolutely called as circumscription. This method is based on the use of completion formula.

Modal logic: The standard approach is to use a modal logic such as defined in Hintikkal 1962.modal logic extend the expressions of classical logic by permitting the notions of possibility, necessity obligation, belief and the like. a number of different modal logics have been formalized and inference rules comparable to propositional and predicate logic are available to permit different forms of non monotonic reasoning.Modal logics are derived as extensions of PL and FOPL by adding modal operators and axioms to express the meanings and relations for concepts such as consistency, possibility, necessity obligation, belief, known truths and temporal situations like past, present and future .the operators take predicate as arguments and are denoted and so on.Modal logic are classified by the types of modality they express .for ex: alethic logic are concerned with necessity and possibility denotic logics with what is obligatory or permissible, epistemic logic’s with belief and knowledge and temporal logics with tense modifiers like sometimes, always, what has been, what will be or what is.Temporal logic: Temporal logic use modal operators in relation to concepts of time, such as past, present, future some times, always, precedes, succeeds as so on .an ex: of 2 operators which correspond to necessity and possibility are always A and some times (S).A(Q)->s Q (If always Q then sometimes Q)AQ->Q (if always Q then Q)Q->SQ(if Q then sometimes Q)SQ->~A~Q (if sometimes Q THEN NOT ALWAYS NOT q)EX: tweety flies (present tense)P(tweety flies) past tense: tweety flewF(tweety flies) future tense:tweety will fly Fp(tweety flies) future perfect tense:tweety will have flown.The semantics of a temporal logic is closely related to the frame problem. The frame problem is the problem of managing changes, which occur from one situation to another cr from frame to frame as in a moving sequence.Fuzzy logic: fuzzy logic was introduced to generalize and extent the expressiveness of traditional logics. Fuzzy logic is based on fuzzy set theory, which permits partial set membership.Lofti azadeh of university of california , Berkely first introduced fuzzy sets in 1965.his objectives were to generalise the notions of a set and positions to accommodate the type of fuzziness or vagueness. Since its introduction in 1965, much research has been conducted in fuzzy set theory and logic. As a possibility distributions fuzzy static’s, fuzzy random variables and fuzzy set functions.Fuzzy predicates such small, large, young, safe, much large than seen. Fuzzy quantifier such as most, means, few, several often usually. Fuzzy probabilities expressed as quite possible. Almost impossible.Fuzzy truth values such as very, quite, extremely, somewhat, and slightly.Fuzzy sets associated with the ability to use linguistic variables. Linguistic variables provide a link between a natural quantification such as fuzzy propositions. A linguistics variable is a variable that assumes a value consisting of words or sentences rather than numbers.A formula, more elegant def. Of linguistic variable is one, which is based on language theory concepts for this; we define a linguistic variable as the quintuple.(x,T(x),U,G,M) Where as x is the name of variable (AGE)T(x) is the terminal set of x (very young, young, not young ,not old)U is the universe of the discourse (years of life)G is a set of syntactic rules, the grammar that generates the values of x and M is semantic rule, which associates each value of x with its meaning M (x), a fuzzy subset of U.

FUZZY SET: You have asked by your friends to arrange for a small party what does small mean’s it possible for us exactly to identify certain characteristics that tell that the party is small. If you are a fluent small has one meaning and if you belong to middle income flow income group, the word small has a different meaning.Hence, one can say that sets for which the boundary is ill defined are called fuzzy sets.Operations on fuzzy sets are somewhat similar to the operations of standard set theory they are also intuitively acceptable.~ ~A= B if and only if u A(x)=u B(x) for all x belongs u equality

~ subset of ~A B if and only if u A(x)<=u B(x) for all x belongs to u containment

? A and B(x)=min(x)( ? A(x), ? B(x)) intersection .

? A or B (x)=max {? A (x), ? B (x)} union

? A or (x)=1-? A (x). Compliment set.

A part from these basic operations fuzzy set theory provides the following additional operations called hedges for the purpose of handling fuzziness in effective way.

Dilation: The dilation of ~ is defined as Dil( ~)=[? A(x)]1/2 ? x in ? .A ( A)

Concentration: The concentration of ~ is defined as con( ~)=[? A(x)]2 ? x in ?.A (A)

Normalization: The normalization of ~ is defined as Normal (~ )= ? A(x)/max(? A(x)) ? x in ?.A (A)

Intensification: The intensification of ~ is defined as int ( ~ )=a*[? A (x)]2 ? in ?.A (A)

DIAGRAMS :

Reasoning with fuzzy logic: The characteristic function for fuzzy sets provides a direct linkage to fuzzy logic. The degree of membership of x in ~A corresponds to the truth-value of the statement x is a member of ~A where ~A defines some propositional or predicate class.Generalized modus ponens for fuzzy sets have been proposed by a number of researches. They differ from the standard modus ponens in that statements, which are characterized by fuzzy sets, are permitted and the conclusion need not be identical to the implicand in the implication.

Premise: This banana is very yellow.Implication: If a banana is yellow then the banana is ripe.Conclusion: This banana is very ripe.Now let x & y be two universes and let ~ and ~ be fuzzy sets in x & x*y respectively. Define fuzzy A BRelations ~ (x), ~ (x , y) and ~ (y) in x ,x*y and y respectively. Then the compositional rule of R A R B R C Inference is the solution of the relational equation.~ ~ (x) O ~ (x,y)=max x min(u A(x), u B (x,y) } where the symbol O signifies the composition R C y= R A ROf ~ & ~ . As an example let x=y={1,2,3,4}A B ~A ={little}={(1/1),(2/.6),(3/.2),(4.0)}~R =approximately equal , a fuzzy relation defined by Y 1 2 3 41 1 . 5 0 0~ 2 .5 1 .5 0 R 3 0 . 5 1 .5 4 0 0 5 1 Then applying the max_min composition rule ~ max min{u (x),u (x,y)}R = x A R=maxx{min(1,1),(.6,.5),(.2,0),(0,0),min[(1,.5),(.6,1)(.2,.5) (0,0)],min[(1,0),(.6,.5),(.2,1),(0,.5)]min[(1,0),(.6,0),(.2,.5),(0,1)]}max {[1,.5,0,0],[.5,.6,.2,0],[0,.5,.2,0],[0,0,.2.0]}x={[1],[.6],[.5],[.2]}there fore the solution is ~R C (y) ={(1,1),(2/.6),(3/.5),(4/.2)}

Probability Based Reasoning :

In the previous section, we saw that the non-monotonic reasoning systems have some influence in the development of AI based systems. Where it takes for granted that certain parameters exist or known with certainly, solutions can be found out. Belief revision

takes place whenever one encounters a piece of information that decreases the belief on the fact. The source for all the uncertainties is the real world. The following sources constitute the major chunks of uncertainties.

Most information is not obtained personally but got from sources on which one has lot of belief. Uncertainty prevails when the source does not send information in time or the information provided is not understood.

In laboratory experiments one takes it for granted that the equipment is properly calibrated and error free. If the equipment is faulty, the picture one gets about the situation is not correct which loads to uncertainty.

In judicial courts we would have seen or hard delivering judgements acquitting for 1.lack of evidence 2.lack of certainty in evidence they’re by giving the benefit of doubt to the accused.We are interested in examining the geological evidence at a particular location to determine whether that would be a good place to dig to find a desired mineral. If we know the prior probabilities of finding each of the various minerals and we know the probabilities that if a mineral is present then certain physical characteristics will be observed.To handle the uncertain data, probability is oldest technique available. Probabilistic reasoning is some times used when out comes unpredictable.Bayes theorem: Bayes theorem is used for the computation of probabilities, this theorem provides a method for reasoning about partial beliefs. Here every event that is happening or likely to happen is quantified dictate how these numerical values are to be calculated. This method introduced by Clergyman Thomas bates in the 18 century. This form of reasoning depends on the use of conditional probabilities of specified events when it is known that other events have occurred. for 2 events H & E with the probability p(E)>0 the condition probability of events H, given event E has occurred is defined as .

P (H/E)=P (H&E)/P (E).--------(1)

Read this expression as the probability of hypothesis H given that we have observed evidence.

The conditional probability of event E given that event H occurred can likewise be written as P(E/H)=P(H&E)/P(H)----------(2)

From Eq1 & Eq 2 We get P(H/E)=P(E/H)*P(H) / P(E)----------------(3)

This equation expresses the notion that probability of event H occurring when it is known that event E occurred is the same as the probability that E occurs when it is known that H occurred, multiplied by the ratio of the probabilities of the 2 events H, E occurring.

The probability of an arbitrary event B can always be expressed as

P (B)=P (B&A)+P (B&~A) = P (B/A)/P(A) + P (B/~A) P (~A)

Using this result 3 we can be written as P (H/E)=P (E/H) P (H) / P (E/H) P (H)+P (E/~H) P (~H)

The above equation can be generalized for an arbitrary no. of hypothesis Hi i=1,2……k thus suppose the Hi partition the universe, i.e. the Hi are naturally exclusive .then for any evidence E1We have P (E)=?k P (E & Hi)= ?k P (E/Hi) P (Hi)I=1 I=1And hence P(Hi/E)=P(E/Hi)P(Hi)/ ?k P(E/Hj)P(Hj)J=1

Where P(Hi/E)= the probability that hypothesis Hi is true given evidence E.P(E/Hi)= the probability that we will observe evidence E given that hypothesis I is true.P(Hi) = the a priori probability that hypothesis I is true in the absence of any specific evidence. These probabilities are called prior probabilities of priors.K = the number of possible hyphthesis.Disadvantages:(1) The knowledge acquisition problem is insurmountable; too many probabilities are to be provided.(2) The space required to store all the probabilities is large.(3) The time required to compute the probabilities is large.

Problem: consider an indescent bulb-manufacturing unit. here machines M1,M2,M3 make 30%,30%,40% of the total bulbs .of their o/p lets assume that 2%,3%,4% are defective .a bulb is drawn at random and is found defective. What is the probability that the bulb is made by machine M1, M2, and M3.Solution: let E1, E2, E3 be the events that a bulb selected at random is made by M1, M2, M3 .let Q denote that it is defective prob(E1)=0.3,prob(E2)=0.3 and prob(E3)=0.4 given data .These represent the prior probabilities Prob of drawing a defective bulb made by M1=prob(Q/E1)=0.02Prob of drawing a defective bulb made by M2=prob(Q/E2)=0.03Prob of drawing a defective bulb made by M3=prob(Q/E3)=0.04These values are the posterior prob’sProb(E1/Q)=prob(E1)*prob(Q/E1)/summation from i=1 to 3 prob(Ei)*prob(Q/Ei)=(0.3)*(0.02/(0.03*0.2)+(o.o3*0.3)+(0.04*0.4)=0.1935similarly prob (E2/Q)=0.3*0.03/(0.03*0.2)+(0.03*0.3)+(0.04*0.4)=0.2903prob E3/Q=(1-(prob(E1/Q)+prob(E2/Q))=0.5162.BAYESIAN NETWORKS: Network representations of knowledge have been used to graphically exhibit the interdependencies, which

exist between related pieces of knowledge. Much work has been done in this area to develop a formal syntax and semantics for such representations. Network representations for uncertain dependencies are further motivated by observations made earlier. If we wish to represent uncertain knowledge related to a set of propositional variables x1……xn by their joint distribution P(x1…….xn) It will require some 2n entries to store the distribution explicitly .further more, a determination of any one of the marginal probabilities xi requires summing p(x1……xn)over the remaining n-1 variables. Clearly the time and storage requirements for such computations quickly become impractical inferring with such large no.s of prob’s does not appear to model the human process either. on the contrary, humans tend to single out only a few propositions which are known to be casually linked when reasoning with certain beliefs. This metaphor leads quite naturally be a form of network representations.To represent casual relationships between the propositional variables x1…..x6 one can write the joint probability p(x1……x6) by inspecting as a product of conditional prob’s.

P(x1,……x5)=p(x5/x2,x3)p(x4/x1,x2)p(x5/x1))p(x2/x1)p(x1)Diagram:

X1

X2 X3

X4 X5

Ex2:A Bayes network is directed a cyclic graph whose nodes are labeled by random variable. Bayes network are some times called causal networks because the areas connecting the nodes can be though of as representing causal relationship.To construct a Bayesian network for a given set of variable, we draw arcs from cause variable to immediate effects. We preserve the formalism and rely on the modularity of the world. We are trying to model. Consider an example:S: Sprinkler was on last nightW: Grass is wetR: It rained last nightWe can write MYCIN style rules that described predictive relationships among these three events.IF: The sprinkler was on last night then there is evidence that the grass will be wet this morning.

Taken alone, this rule may accurately describe the world. But consider a second rule:IF: the grass is wet this morning then there is evidence that it rained last night.Taken alone , this rule makes sense when rain is the most common source of water on the grass.

There are two different ways that propositions can influence the likelihood of each other. The first is that causes influence the likelihood of their symptoms; the second is that observing a symptom affects the likelihood of all of its possible causes. The basic idea behind the Bayesian network structure is to make a clear distinction between these two kinds of influence.DEMPSTER SHAFER THEORY : The Bayesian approach depends on the use of known prior and likely prob’s to compute conditional prob’s .The dempster Shafer approach on the other hand is a generalization of classical prob theory which permits the assignment of prob’masses (beliefs) to all subsets of the universe and not just to the basic element.A generalization theory has been proposed by Arthur Dempster 1968 and extended by his student Glenn shafer (1976). It has come to be known as the Dempster theory of evidence. The theory is based on the notion that separate prob masses may be assigned to all subsets of a universe of discourse rather than just to indivisible single members are required in traditional prob theory.In the Dempster, we assume a universe of discourse ? and a set correspond to n propositions exactly one of which is true . The propositions are assumed to be exhaustive and mutually exclusive let 2 ? denote all subsets of U including the empty set and u itself M:2 pow u->[0,1]?m m(A)=1.A??The function m defines a prob distribution on 2 pow u it represents the measure of belief committed exactly to A .a belief function, Bel

corresponding to specific m for the set A is defined as the sum of beliefs committed to every subset of A by m. Bel(A) is a measure of the total support or belief committed to the set A and sets a minimum value for its likelihood .Bel(A)=summation over B subset of a m (B).The Dempster ,a belief interval can also be defined for a subset A .It is represented as the sub internal [BEL(a),p(a)]OF [0,1].Bel(A) is also called the support of A and p(A)=1-Bel(~A) the plausibility of (A).when evidence is available from two or more independent knowledge sources Bel 1,BEL 2 one would like to pool the evidence to reduce the uncertainty .for this dempster has provided such has combining function denoted as bel1 o bel 2 the total prob mass committed to C.C= summation over Ai and Bj m1(Ai)m2(Bj)The sum in above equation must be normalized to account for the fact that some intersections Ai and Bj =pie will have positive prob which must be discarded .the final form of dempster of combination is then given by m1om2=summation over Ai and Bj =C mi(Ai)m2(Bj)/summation over Ai and Bj not to 0m1(Ai)m2(Bj)where the summations are taken overall I and j.AD_HOC methods: The SO_called ad_hoc methods of dealing with uncertainty are methods, which have no formal theoretical basis. Although they are usually patterned after probabilistic concepts. These methods typically have an intuitive, if not a theoretical, appeal. They are chosen over formal methods as a pragmatic solution to a particular problem. When the formal methods impose difficult or impossible conditions.Different ad_hoc procedures have been employed successfully in a no. Of AI systems, particularly in expert system. ad_hoc methods have been used in a large no. of knowledge base systems more than have the more formal methods. This is largely because of the difficulties encountered in acquiring large no. of reliable probabilities related to the given domain and to the complexities of the calculations.Heuristic methods: Heuristic methods are based on the use of procedures, rules and the other forms of encoded knowledge to achieve specified heuristics; one of several alternative conclusions may be chosen through the strength of positive versus negative evidence presented in form of justifications and endorsements. The endorsement weights employed in such systems need not be numeric. Some form of ordering a preference selection scheme must be used.

Reasoning using certainty factors: Probability based reasoning adopted bayes theorem for handling uncertainty, unfortunately, to apply bayes theorem one, needs to estimate a priori and conditional probableties which are difficult to be calculated in many domains. Hence, to circumvent this problem, the developers of MYCIN system adopted certainty factors.

A certainty factor (CF) is a numerical estimate of the belief or disbelief on a conclusion in the presence of a set of evidence. Various methods of using CF’s have been adopted, Typical of them are as under.

1. Use a scale from 0 to 1 where 0 represents total disbelief and 1 stands for total belief. Other values between 0 to 1 represent varying degrees of belief and disbelief.

2. MYCIN’s CF representation is one scale from –1 to +1. The value of 0 stands for unknown. In Expert systems, every production rule has a certainty factor associated with it. The values of the CF are determined by the domain expert who creates the knowledge base.

A certainty Factor(CF[h, e]) is defined in terms of two components:(i) MB[(h, e)]: a measure (between 0 and 1) of belief in hypothesis h given the evidence e. MB measure the extent to which the evidence supports the hypothesis. It is zero if the evidence fails to support the hypothesis.(ii) MD[h, e]: a measure (between 0 & 1) of disbelief in hypothesis h given the evidence e . MD measure the extent to which the evidence supports the negation of the hypothesis. It is zero if the evidence supports the hypothesis.We can define the certainty factor asF[h,e]= MB[h,e}- MD[h,e].

Matching

Matching is a basic function that is required in almost all A.I programs. It is an essential part of more complex operations such as search and control. In many programs it is known that matching consumes a large fraction of the processing time.

Matching is the process of comparing two or more structures to discover their likeness or differences. The structures may represent a wide range of objects including physical entities, words or phrases in some language, complete classes of things, general concepts, relations between complex entities and the like . The representations will be given in one or more of the formalisms like FOPL, networks or some other scheme and matching will involve comparing the component parts of such structures.

Matching is used in a variety of programs for different reasons. It may serve to control the sequence of operations, to identify or classify objects, to determine the best of a number of different alternatives or to retrieve items from a database. It is an essential operation in such diverse programs as speech recognition, natural language understanding, vision, learning, automated reasoning, planning, automatic programming and expert system as well as many others.

Matching is just process of comparing two structures or patterns for equality. The match fails if the patterns differ in any aspect.Different types of matching are:(1). Indexing(2). Matching with variables.(3). Complex and Approximate Matching(4). Conflict resolution.

(i) Indexing: Incase of indexing we use the current state as an index into the rules in order to select the matching ones. Consider chess. Here we assign a number to each board position. Then we use a hosting function to treat the number as an index into the rules.

(ii) Matching with variables: In this case we try to match many rules against many elements in the state description simultaneously. One efficient algorithm is RETE, which gains efficiency from 3 major sources these sources are:

(b) The temporal natural of the date. Any rule should into make changes radically but must add one or two elements, or delete one or two.(c) Structural similarity in rules. There may be a situation where some rules may or two conditions other conditions being the same.

For Example:Mammal (x) -> jaugqr (x)Feline (x)Carnivours (x)Has – stripes (x)Now if we consider a tiger all the first 3 conditions are same but the 4th one changes, instead of has spots (x) we have

Has - stripes (x)

Here we need repeat the rules again. RETE stores these similar structures in memory so that they can be shared.

Persistence variable binding consistency

For Example:

(ii) son (x,y) ^ son (y,z) -> grandparent (x,z)(iii) Son (mary,joe)(iv) Son (Bill, Bob)

Here the rules (ii) & (iii) can be matched but must satisfy the values of y.

(iii) Complex & Approximate Matching: An approximate matching is one, which is used when the preconditions approximately match the current situation.

Consider an example of a dialogue between ELIZA & a user. Here ELIZA ill try to match the left side of the rule again the users last sentence and use the correct right side to generate a response. Let us consider the following ELIZA rules:

(X me Y) -> (X you Y)(I remember X) -> (who do remember X just now?)(My {Family-member} is Y) -> (Who else in your family is Y?)

Suppose the use says, “ I remember Mary” How ELIZA will try to match the above response to the left hand side of the given rules. It finds that it matches to the first rule & now it takes the right hand side and asks “ why do remember Mary just now?”

This is how the conversation proceeds taking into consideration the approximate matching.

(iv) Conflict Resolution: Conflict Resolution is a strategy in which we incorporate the decision making into the matching process. We have three basic approaches.

(b) Preference based on Rules(c) Preference based on Objects(d) Preference based on states.

(a) Preference Based on Rules: Here we consider the rules in the order they are given or we give some priority to special case rules. There are two ways in which a matcher will try to decide how one rule is more general than the others. This allows us in decreasing the search size by more general rules. The two ways are:

1. If one rule contains all the preconditions that another rule has and some additional then Second rule is more general they the first.2. If one rule contains preconditions with variables and the other contains the same A precondition with constants then the first rule is more general.

(b) Preference based on Object: Here we use keywords to match into the rules consider the example of ELIZA. It takes specific keywords form the user’s response and tries to match the keywords with the given rules. Like previously it uses the “remember” keyword to match the L.H.S. rule.

(c) Preference Based on States: In this case we fire all the rules that are waiting they lead us to some states. Using a heuristic function we can decide which state is the best.

Partial matching: For many AI applications complete matching between two or more structures is in appropriate. For example, input representations of speech waveforms or visual scenes may have been corrupted by noise or other unwanted distortions. In such cases, we do not want to reject the input out of hand. Our systems should be more tolerant of such commonly occurring problems. Instead, we want our systems to be able to find an acceptable or best match between the input and some reference description.

The RETE Matching algorithm:

A typical system will contain a Knowledge Base which contains structures representing the domain expert’s knowledge in the form of rules or productions, a working memory which holds parameters for the current problem, and an inference engine with rule interpreter which determines which rules are applicable for the current problem.

The basic inference cycle of a production system is match, select, and execute as indicated in figure. These operations are performed as follows:

I

O

Match: During the match portion of the cycle, the conditions in the left hand side(LHS) of the rules in the knowledge base are matched against the contents of working memory to determine which rules have their LHS conditions satisfied with consistent bindings to working memory terms. Rules which are found to be applicable (that match) are put in a conflict set.

Select: From the conflict set, one of the rules is selected to execute. The selection strategy may depend on regency of usage, specificity of the rule, or other criteria.

Execute: The rule selected from the conflict set is executed by carrying out the action or conclusion part of the rule, the right hand side (RHS) of the rule. This may involve an I/O operation, adding, removing or changing clauses in working Memory or simply causing a halt.

The above cycle is repeated until no rules are put in the conflict set or until a stopping condition is reached.A typical knowledge base will contain hundreds or even thousands of rules and each rule will contain several (perhaps as many as ten or more) conditions. Working memories typically contain hundreds of clauses as well. Consequently, exhaustive matching of all rules and their LHS conditions against working-memory clauses may require tens of thousands of comparisons. This accounts for the claim made in the introductory paragraph that as much as 90& of the computing time for such systems can be related to matching operations. To eliminate the need to perform thousands of matches per cycle, an efficient match algorithm called RETE has been developed (Forgy, 1982). It was initially developed as part of the OPS family of programming languages (Brownston, et al., 1985). This algorithm uses several novel features, including methods to avoid repetitive matching on successive cycles. The main timesaving features of RETE are as follows.Advantages:

a. In most expert systems, the contents of working memory change very little from cycle to cycle.b. Many rules in a knowledge base will have the same conditions occurring in their LHS.c. The temporal nature of data.d. Structural similarity in rules.e. Persistence of variable binding consistency.

PROLOG

The name PROLOG was taken from the phrase “PROgramming in LOGic” .The language was originally developed in 1972 by Alain Colmerouer and P.Roussel at the university of Marseilles in France. Prolog is unique in its ability to infer facts and conclusions form other facts.Prolog has been successful as an AI programming language for the following reasons.

1.The syntax and semantics of prolog are very close to formal logic. by this time , It must be clear to you that most AI program reason using logic.

2. Prolog language has in it a built in inference engine and automatic backtracking facility. This helps in efficient implementation of various search strategies.

3. This language has high productivity and easy of program maintenance.

4. Prolog language is based on the universal formalism of Horn Clause.

5. Because of the inherent AND parallelism, prolog language can be implemented with ease on parallel machines.

6. The clauses of prolog have a procedural and declarative meaning. Because of this understanding of the language is easier.

7.In prolog, each clause can be executed separately as though it is a separate program. Hence modular programming and testing is possible.

Horn clause consists of a set of statements joined by logical Ands

Procedural languages A.I languages (Basic,cobol,pascal) (prolog,lisp)

1.use previously defined procedures use heuristic to solve problems.to solve problems.

2.most efficient at numerical processing. Most efficient at formal reasoning.

3.systems created and maintained by programmers. Systems developed and maintained by knowledge engineers. 4.use structured programming. Interactive and cyclic developments.

The main part of a prolog program consists of a collection of knowledge about a specific subject. This collection is called a database and this database is expressed in facts and rules.Turbo prolog permits you to describe facts as symbolic relationships.Ex: The right speaker is dead.This same fact can be expressed in turbo prolog as Is (right_speaker, dead)This factual expression in prolog is called a clause. Notice the period at the end of the clause.In this ex: right speakers and dead are objects.The word “is” is the relation in this ex. relation is a name that defines the way in which a collection of objects.The entire expression before the period in each case is called a predicate. A predicate is a function with a value of true or false predicates express a property or relationship .the word before the parenthesis is name of relation. The elements with in the parenthesis are the arguments of the predicate, which may be objects or variables. Clauses|Facts rules |Predicates period|relations argumentsarguments|objects variables.

A rule is an expression that indicates the truth of a particular fact depends upon one or more other facts. Consider this ex: if there is a body stiffness or pain in the joints.AND there is sensitivity to infections.Then there is probably a vitamin C deficiency.This rule could be expressed as the following turbo prolog clause.Hypothesis (vit_deficiency ) if Symptom (arthrities ) and symptom (infection_senstivity)

Notice the general form of the prolog rule. The conclusion is stated first and is followed by the word if. Every rule has a conclusion is stated and antecedent rules are important part of any programming short hand has been developed for expressing rules. in this abbreviated form the previous rule becomes:Hypothesis (vitc_deficiency ):-Symptom (arthrities)Symptom (infection_Senstivity)The :-operator is called a break a comma expression and relationship and semicolon expresses an or relationship.The process of using rules and facts to solve a problem is called formal reasoning.A turbo prolog program consists of 2 or more sections. The main body of the program, the clause section contains the clause and consists of facts and rules. The relationships used in the clauses of the clause section are defined in the predicate section. Each relation in each clause must have a corresponding predicate definition in the predicates section predicate definition in the pre dicta section does not end with a period. The domains section also is apart of most turbo prolog programs .If defines the type of each object. The domain section turbo prolog controls the typing of object.6 basic object types are available to the user.Character.Integer.Real.String.SymbolFile.Character –single character (enclosed between single quotation marks)Integer-integer from -32768 to 32767Real- floating point number (lE-307 to 1E-308)String –character sequence (enclosed between double quotation marks)Symbol- character sequences of letters numbers and under series with the first character a lower case letter File-symbolic file name.

In a turbo prolog program the sections should always be in the following.1.domains. 2. Predicates 3. Clauses.Variables:A variable name must begin with a capital letter and may be from 1 t o250 characters long. Except for the first character in the name you may use uppercase or lower case letters, digits o the under line character. Names should be meaningful.Bound & free variables: if a variable has a value at a particular time it is said to be bound or instantiated .if a variable does not have a value at a particular time is said to be free or uninstantiated.Anonymous variables: The anonymous variable stands for all values while in a goal it is satisfied if at least one value correspond to it.Backtracking: One of the most important principles of prolog execution is backtracking. The solution of the compound goal proceeds

from left to right. If any condition in the chain fails, prolog back tracking to the previous condition tries to prove it again to see if the failed condition will succeed with the new binding. Prolog moves relentlessly forward and backward through the conditions, trying every available binding in an attempt to get the goal to succeed in as many as possible.

Input & Output operators: Turbo prolog has 3 output predicates.Write.Write device.Write f.

The write predicate:Go:-hypothesis (patient, disease),write(patient, ”probably has “,”disease”,.”),n1.The write predicate displays the values of these variables in an English like sentence.Charlie probably has german measles.

(Since patient = Charlie; disease = germane measles)The general form of the write predicate is write (E1,E2,………En)Where E1,E2,…….En represent prolog variables or objects of the standard domain .the write predicate executes immediately and always evaluates as true. You can mix objects and variables in the arguments .Test: write (“this is an example “)Write (“of multiple write statements “)Displays This is an ex: of multiple write statements.nl:- now return to the nl after the write predicate .this is a built in predicating the new line function .This function writes a carriage return and a line feed in the output.Write (“this is an example”)Write (“of multiple write statements”)Write (“this is an example “,”\n”)Write (“of multiple write statements)Displays This is an example:Of multiple write statement?Turbo prolog provides 3 back slash commands. \n, \t, \bBackslash commands must appear inside of either single or double quotations marks nl, write “\n”) write \n)are equal.

Write device: Any O/P to the display can be directed instead to a printer or a file .to redirect O/P uses the write device built-in predicate.Write device (print)Write (“this will on the printer”)Write device (screen)

Writef predicate:Some times you may wish to format o/p for ex: you may want the decimal points in a table to be aligned with turbo prolog, you can use the writef built in predicate to force alignment of numbers a text.Writef (format E1, E2…En)The variable format is a control code of the type.% - m.p-Hyphen forcing the left justification, default is right justm minimum field width .p precision of a decimal floating point number.Writef (“%-10#%5.0$3.2\n”, an, 3, 3.1)Displays (fan#23$3.10)Input operators:Turbo prolog provides several built in I/P predicates for this ex:Readln string or symbolRead char character Read int integer.Read real realInkey,Key pressed

The readln predicate: The readln predicate permits a user to read any string symbol into a variable.

Ex: readln(replay)Replay (‘”yes”)Read predicate: The read car predicate permits a user to read any character in to variable.Ex: readchar(replay)Replay =’y’The read int. predicate can be used to read an integer value to a variable.Ex: read int (Age)Read real: The read real predicate can be used to read floating point numbers into a variable.Ex: read real (price)Price=12.50Inkey: The inkey predicate reads a single character from the I/p the predicate form is inkey (char)If there is no i/p the predicate fails. Otherwise the character is returned bound to the char.

Key pressed: key pressed predicate to determine whether has been pressed with out a character being returned. Controlling execution predicates.

Fail predicate: In prolog, forcing a rule to fail under certain conditions is a type of control and is essential to goal programming. Failure can be the forced In any rule by using the built in fail predicate. The fail forces back tracking in an attempt to unify with another clauses. Whenever this predicate is invoked the goal being proved immediately fails, and back tracking is initiated .the predicate has no arguments, so failing of the fail predicate is not dependent on variable binding .the predicate always fails.Ex: 1 go: -Test,Write (“you will never get here”)Test: -Fail.Here goal: go FalseHere the write predicate will never be executed.2.go: Write (“you will get here”)Test Test:-FailHere goal: goYou will get hereFalse

The Cut predicate: The cut is one of the most important and one of the most complex features of prolog.The primary purpose of the cut is to prevent or block backtracking based on a specified condition. The cut predicate is specified as an exclamation point. If has no argument the cut predicate succeeds and once it succeeds, it acts a fence, effectively blocking any back tracking beyond the cut. If any premise beyond the cut fails, prolog cans only back track as far as the cut to try another path.

The basic purpose of the cut is to eliminate certain search path is in the problem space, you can think of the paths through the database as the limbs of a tree. If you get cut on one limb and discover failure, you normally can move back towards the trunk, find another limb and start moving outward again the cut act like a fence where it is placed in the program you cannot back beyond the cut.

The cut can be used for any or all of 3 purposes.

1. To terminate the search for any further solutions to a goal. Once a particular rule has been tested.

2. To terminate the search for any further solutions to a goal once a particular rule has been forced to fail with the fail predicate.

3.To eliminate paths in the database to speed up execution .the cut is not always the best solution.

Types of cuts: there are 2 types of cuts in prolog namely.Green cut & red cut: the green cut is used to force binding to be retained, once the right abuse is reached green cuts are used to express determination.

The red type of cut is used to omit explicit conditions. Cuts improve the clarity and efficiency of most programs of the 2 types of cut, the green cut is the more acceptable type. You can often use the not predicate instead of the red cut.

EX: state (tamlnadu)State (kerala)State (A.P)State (U.P)State (karnataka)State (M.P)State (S);Write (“do u belong to”)Write (S)Write (“&”)Readln (Reply)Reply =”yes”?Write (“so u belong to “)Write (S)Output: do u belong to tamilnadu ?NoDo u belong to kerala ?NoDo u belong to A.PNoDo u belong to U.PYesSo u belong to U.PQuality operator: =Comparison operator: <, >, =, <=, >=, -, =, <>

Arithmetic operator: +, -, *, %, mod, div, +(positive),-(negative)

Recursion: Recursion is one of the prologs most important Execution control technique. If often is used with the fail or cut predicate. Recursion is a technique in which some thing is defined in terms of itself. In prolog recursion is the technique of using a clause to invoke copy of it-self.

Ex: If you specify the goal as count (1) you should see the following output -> 1 2 3 4 5 6 7 8 true Contains a copy itself.Count (~)(Statements)Count (NN)Program: Predicates Count (integer)Clauses Count (9).Count (N): -Write (“ “, N).NN=N+1.Count (NN).

The repeat predicate: One predicate that uses recursion is the repeat predicate. Although repeat is not a built – in predicate it is so important that you will probably want to add it to many programs its format is

RepeatRepeat:-RepeatThe repeat predicate is useful for forcing a program to generate alternate solutions through back tracking. When the repeat predicate is used in a rule, the predicate always succeeds .if a later premise causes failure of the rule, or log will back tracking to the repeat predicate.Basic rules of recursion:1.a program must include some method of terminating the recursion loop.2.variable binding in a rule of fact apply only to the current layer.3.in most applications the recursive procedure should do its work on the way down.Recursion is not always the best programming choice. Recursion complex and the flow of execution is not always easy to follow.

Length (list, length): The length utility simply measures the list, reporting either how long it is ,which lists are of a specified length or whether a specified list has the specified length.Length([],0).Length([|Tail],len):-Length(Tail,len1).Len = Len1+1.Location (Position, list, object): This predicate can either find the location of the specified object, find the object at the location or confirm the presence of the object at the position.

Location (Num, list, item):-Sides (Pos, item, list),Length (pos, N), Num=N+1.

Insert, Extract, Replace: These three utilities share a common argument pattern.(Object, location, list, new list)

Insert (object, location, list, new list): The insert utility differs from append in it allows you to select the location in the list for doing your insertion.Insert (Item, l, list, [item | list]):-!Insert (item, loc [Head | rest], [head | Rest 1]:-Loc1 = Loc-1, insert (item, loc1, rest, rest1).Replace (object, location, list, new list): The replace utility goes to the specified location and substitutes the specified object for the object at location.Replace (item, l,[-|Rest],[Item | Rest]):-!Extract (object, location, list, new list); The extract utility shortens the list by removing the item of the specified location.APPEND: (List, list, list). Using append, you can add an element to a list. Since an empty list is still a list, this means you can use append to build a list from scratch.Append ([], L, L).Append ([X|L1], L2, [X|L3]: -Append (L1, L2, L3).

DELETE (Object, list, new list): Deleting an object from a list is also a recursive process.

Delete (X, [X|List2], List2)Delete (X, [Other| Rem], [Other\Rem1]):-Delete (X, Rem, Rem1).Dup (List): The dup utility simply checks for the presence of duplicate elements. If all you want to do is check, it is help full.

Dup ([]): -! Fail.

Dup ([H|T]): -Member (H, T)!Dup ([_| T):-Dup (T), !.Reverse (list,list): As its name suggests, the reverse utility takes a specified list and reverses the order of its elements.Reverse ([],[]).Reverse ([H|T],newlist):-Reverse (T, L2),Append (L2,[H},newlist).Notice that no cut markers are included in the utility. Optimizing it for large lists would require a cut in the null lists rules and in the append null list rules.Shift (list,list): This utility puts the head of a list at the end shifting all elements one position to the left.For a left shift ([1,2,3]) becomes ([2,3,1]).Lshift([H|T],newlist):-Append (T,[H],newlist).For a right shift ([1,2,3]) becomes [3,1,2].Rshift(oldlist,[H|T]):-Append (t,[H],oldlist).

Simple problems: LENGTH OF THE LIST.Program:DomainsList = integer*PredicatesLength_of (list, integer)ClausesLength-of ([],0).Length-of ([-|],l):-Length-of [(T,Taj] length),L= Taillength+1.Result:Goal: length_of([1,2,3],l)L=3.

/*TO SEE IF A STRING IS IN THE LIST OR NOT*/Domains Object=symbollist=object*PredicatesMember (object,list)ClausesMember (X,[ X|_] ).Member (X,[_| Tail] ):-Member (X, Tail).

Goal: Member( Ram, [Ram,Sam,Krishna] )True1 solution/*TO DELETE AN ITEM*/

DomainsInteger list= integers*Item = integerPredicates Delete (Item, [Item | Tail], Tail).

Delete (Item, [X | Tail], [X| Tail 1]: -Delete (Item, Tail 1).

Goal: delete (Anand, [ Anand, Rajesh, krishna, Praveen ], 1 )

L=[“Rajesh”, “Krishna”, “Praveen”]

1 solution.

/* ADDING AN ELEMENT TO THE LIST */

Domainsobjectlist = symbol *item = symbol

Predicates

add ( symbol, objectlist, objectlist )

Clauses

add ( X, list, list ):- List = [ X | List ].Result:Goal: add(vijay,[giri,vamsi,koti])

L=[vijay,giri,vamsi,koti].

* SUM OF INTEGER LIST * /

DomainsList = integer *Sum = integerPredicatessum_of_list ( list, sum )Clausessum_of_list ( [], 0 ).sum_of_list ([head| tail],sum):-sum_of_list (tail,addtail),sum=head+addtail.Result: sum_of_list([ ],sum)Sum=0;Sum-of-list([1,2,3,4,5],sum)Sum= 15.

/*CALCULATE FACTORIAL*/DomainsX,factx = integerPredicatesfactorial(x,Factx)Clausesfactorial (1,1).factorial (x,Factx):-Y=x-1, factorial (y,Facty),Factx=x*Facty. Result:Goal: factorial (5,x)X= 120/* APPENDING TWO LISTS*/Domainsobjects = integerlist=integer*item=integerPredicatesappend(list,item,list)ClausesAppend ([], item, list).Append ([h|list1], item,[h|list3]):-Append (list1,item, list3).Result:Goal: append ([Rajesh, Mahesh],[Divya, Deepthi],l).L=[rajesh, Mahesh, divya, deepthi].

LISP

LISP (List Processing) is an AI programming language developed by John Mc Carthy in late 1950.Lisp is a symbolic processing language that represents information in lists and manipulates these lists to derive information. Till today different dialects of lisp language have been developed .the foundations of these dialects remain the same while the syntax and functionality show a marked change.LISP DIALECTSS. No Dialects Developed by 1 Common Lisp Gold Hill computers 2 Franz Lisp Franz Inc 3 Inter Lisp Xerox 4 Mu lisp Microsoft Inc ,the software house5 Portable standard Lisp University of Utah 6 Vax lisp Digital equipment corp.7 X lisp Blue users group 8 Zeta lisp LMI, symbolic, Xerox

Features of LISP:1. LISP is the equivalence of form between programs and data in language, which allows data structures to be executed as programs and programs to be modified as data.2. LISP is heavy reliance an recursion as a control structures, rather than iteration (looping) that is common in most programming language.3. LISP has an interpreter which implies that the debugging facilities would be unmatched by any compiled language.4. LISP encourages the use of dynamic data structures which leads to design of a flexible system.5. LISP macro facility allows new languages to be defined and embedded within the LISP system.

Preliminaries of Lisp: LISP language is exclusively used for manipulating lists. The major characteristic is that the basic elements are treated as symbols irrespective of whether they are numeric or alphanumeric. The basic data element in lisp, An atom is indivisible. Lisp has 2 basic types of atoms. No’s and symbols. Numbers represent numerical values. Any type of number such as positive or negative integers, floating point or decimals are acceptable. Symbols represent alpha numeric character symbols can be a combination of alphabets and numerical (apple orange grapes mango)(millimeter container decimeter meter)(78 65 71 70 68)(Bullock_ cart (Hercules atlas hero)(tvs 50 kelvinator mofa))Such a combination of lists within lists are called “nested” or “multiple” or “complex” list. Only 1 thing to be mind is that the number of parenthesis, opening and closing must be same,. If not, the system will flash an error message. Because if the parenthesis problem, lisp is jovially referred as a language that has “Lots of Infuriating stupid parentheses”.

LISP FUNCTIONS: A lisp program is a collection of small routines, which define simple functions . In order that complex functions may be written; the language comes with a set of basic functions called primitives. These primitives serve commonly required operations. a part from these primitives ,lisp permits you to define your own functions. Because of this independence, lisp is highly flexible since tailor made functions are defined and manipulated, modularity is high. Lisp uses prefix notations for its operations. The basic primitives of lisp are classified as:1. Arithmetic primitives2. Boolean primitives 3. List manipulation primitives

1. Arithmetic primitives: + addition,- subtraction ,* multiplication ,/ division / |+adds | to its argument to the the power specified by its second argument. Quotient and remainder together give the result of division between integers, recipe gives the reciprocal, max and min return the maximum and minimum of their argument.

(+ 6 2) =>8 ; (* 6 2)=>12 (- 6 2) =>4; (/ 6 2)=>3 (Remainder 14 3)=>2 ;(Recip(5))=>.2 ;max( 8 3 9 )=>9 (min 8 3 9)=>3

Boolean primitives: these primitives provides a result which is Boolean in nature i.e. true or false. Some of them require only 1 argument while others more than 1.Some such primitives are:1. Atom : the purpose is to find out whether the element is an atom or not Ex:(ATOM RAMAN)=>T(ATOM 26)=>Nil2.Number p: determines if the atom is a number or not.Ex: (number p raman)=>nil ;(numberp 20)=>T3.list p: determines if the input is a list or not.Ex: (list p (25 35 46 75) =>T(List p raman )=>NIL4. Zero p:to find out whether the number is zero or not Ex:(zero 26)=>nil ;(zerop 0)=>T5.Odd p;to find out whether the i/p is odd.

Ex:(ODD p 65)=>T ;(ODD p 60)=>Nil6.even p;to find out whether th i/p is even or not Ex: (even p 78)=>T;(EVENP 89)=>nil7.equaL P; To find out whether the given lists are equal Ex: (equal ‘(janaki raman sarukesi )’(janiki raman sarukesi) =>T(Equal ‘(75 67 94)’(4 3 65 987)8.greater p: to find out the 1 is greater than the second Ex: (greater p ’46 ’86)=>nilEx: (greater p ’86 ’46)=>T9.lesser p: to find out whether 1 is lesser than the 2.

List manipulation of primitives: The purpose of list manipulation primitives are for 1.creating a new list 2 . Modifying an existing list with addition, deletion or replacement of an atom 3. Extracting portions of LISTFor these lisp provides some primitives and well specified functions can be developed from these .in lisp values are assigned to variables by set Q property .the primitive has 2 arguments, the 1 being the variable & the second, the value to be assigned to the variable. The value could be an atom or list itself.Ex: 1 (SET Q A 22) when evaluated assigns 22 to variable A.2. (Set q TV ‘onida) would assign TV=ONIDA whenever.3. (Set pressure-1 22) would assign pressure-1 =22(Set q pressure 2 pressure1) would assign pressure 2 =22Set q pressure ‘ pressure 1 would assign to pressure 2=pressure 1List construction: lists are constructed using CONS primitive. Cons primitive adds new element to the front of the existing list. This primitive needs 2 arguments and returns a single list.Ex:1.((CONS ‘p ‘(Q R S )) =>(P Q R S )

2. (CONS ‘RAM ‘(LAXMAN, GOPI, RAJ))=>(RAM,LAXMAN, GOPI, RAJ )

3. (SET Q A ‘(B C D ))(SET Q X ’(X Y Z))(Cons A X) =>(B C D X Y Z)While the cons primitive adds a new list to the front the existing list, the primitive append adds it to tail of the existing list.

Extracting portions of a list:Extracting portions of a list pertains to decomposing the list and getting an atom out of it. For this purpose, LISP provides two major primitives. They are CAR and CDR.

The CAR primitive returns the first element of list.

EX: 1. (CAR ‘(RAM LAXMAN BHARATH SHATRUGHNAN)) ? RAM(CAR ‘((32 36) (56 54) (67 31) 67 87 89)) ? (32 36)

The CDR Primitive returns the list excluding the first element.Ex: 1. (CDR ‘(RAM LAKSHMAN BHARATH SHATRUGHNAN))(LAKSHMAN BHARATH SHATRUGHNAN)2. (CDR ‘((32 36) (56 54) (67 31) (67 87 89))((56 54) (67 31) 67 87 89)

Using these two list-manipulating primitives it is possible to extract any porting of the list. For example if we would like to get the element BHARATH from the list given as follows:( RAM LAKSHMAN BHARATH SHATRUGHANAN)we will have to adopt the following method.Step 1: Break the list into two using CDR function.(CDR ‘ (RAM LAKSHMAN BHARATH SHATRUGHNAN)(LAKSHMAN BHARATH SHATRUGHAN)Step 2: Apply CDR primitive again to remove LAKSHMAN out of the list.(CDR’ (LAKSHMAN BHARATH SHATRUGHNAN))(BHARATH SHATRUGHNAN)Step 3: Apply CAR function on the list to get the element BHARATH.(CAR ‘ (BHARATH SHATRUGHNAN))(BHARATH)The entire operation can be written as a single LISP statement as (CAR (CDR (CDR ‘(RAM LAKSHMAN BHARATH SHATRUGHNAN))))One important point to note is that CAR and CDR primitives’ operatives operate on lists only. When you try to operate them on individual atoms, the system will flash an error message.

Example: When you try to evaluate the LISP statement(CDR (CAR ‘(35 46 76 98 24)), an error message is flashed.Apart from these primitives, there exist other functions for operations on LISP. Some of them are:1. LENGTH : A LISP function to find the length of the list2.REVERSE : A function to reverse the given length3. LAST : To return the last element of the list4. LOCATE : To identify where a particular element exists in the list5. REPLACE replaces a particular element in the list.

So far, we have discussed about primitives a LISP dialect provides. In the initial sections of the chapter, we had pointed out that LISP provides facilities for defining our own functions. Let’s examine how it is done.

Defining functions & conditions: The functions named define is used to define functions. it requires 3 arguments . 1 The new function name 2. The parameter for the function 3. The functions body or lisp code, which perform the desired function on operations.Syntax: (define name (parm1, parm2, , , ,) body)Define does not evaluate its arguments .if simply builds a function which may be called like any other function.Ex: we define a function named average to compute the average of 3 no’s ->(Define average ((n1, n2, n3)( / (+ n1 n2 n3)3)Average ->->(Average (10, 20, 30)20->The condition (cond): Predicates are 2 way to make tests in program & take different actions based on the outcome of the test. We need some construct to permit branching.Syntax: (cond ()(<TEST2)….. )

Each ()I=1…k is called a clause. Each clause consists of a test portion and an action result portion.Ex: find the max of 2 numbers ->(defun Maximum2(a, b)(cond((> a b) a)( t b)))Maximum2->Note the t in the second clause preceding b. This forces last clause to be evaluated when the first clause is (nil) (not).->Maximum2 (234 320)->320Find maximum of 3 numbers ->(Defun Maximum3 (a b c )(cond((>a b) (cond((>a c) a)( t c)))((> b c) b ) (t c)))Maximum 3->->Maximum3 (20 30 25)30->Logical functions: Like predicate, logical functions may also be used for flow of control. The basic logical operations are AND, OR , NOT. Not is the simplest, it takes one argument & returns if the argument to nil.Input, output and local variables: The operations we need for this are performed with the input-output functions. The most commonly used i/o functions are read, print, print, princ, terpri and format.

Read: Read takes no argument- >(+5 (read))6(enter through key board)Print: takes 1 argument. it prints the argument as it is received and then return the argument.

Ex: ->(print (a b c))ABCABC->(Print “hello there”)“Hello there”“Hello there”

prinl: It is the same as print except that the new line characters and space are not provided.

->(Print ‘(hello))(print ‘(hello))(Hello)(Hello)

princ: We can avoid the double quotation makes in the output by using the printing function princ. it is same as prinl except it does not print the unwanted quotation marks.

->(princ “hello there”)hello there “hello there “->

Terpri: Tt takes no arguments .it introduces a new line (carriage return and line feed) wherever it appears and then return nil.

Format: The format function permits us to create cleaner output then is possible with just the basic printing functions.->(Format )Destination specifies where the o/p is to be directed. String is the desired o/p string but intermixed with format directives, which specify how watch argument is to be represented. Directives appear in the same string in same order the argument is to be printed. Each directive is preceded with a tilde character (~)

to identify, it as a directive.

~^ the argument is printed through princ were used.

~S the argument is printed through prinl were used.

~D the argument which must be an integer is printed as a decimal number.

~F the argument must be a floating-point number is printed as a decimal floating point number.

~C the argument is printed as character

~% a new line is printed.

Ex: suppose x=3.0 ;y=9.42

>format t “circle radius =~2f ~% circle area=~3f”x

“Circle radius =3.0Circle area=9.42”->Ex: program find area of a circle(defun circle-area()(terpri)(princ “please enter the radius”(Set Q radius read))(princ “the area of the circle is”)(princ (*3.1416 radius )(terpri)circle-area->(circle-area)please enter the radius 4the area of the circle :50.2656->Iteration: we introduce a structured form of iteration with the DO construct, which is some what like the while loop in pascal.The do statement has the form (DO ())()()The S expressions forming the body of the construct are optional Ex:-> (defun factorial (n)(Do ((count n (-count 1))(Product n (*product (-count 1))((Equal 0 count) product)))Factorial->Recursion: For many problems, recursion is the natural method of solution. Such problems occur frequently in mathematical logic and the use of recursion will often result in programs that are both elegant & simple. A recursion function is one which cal itself successively to reduce a problem to a sequence of simple steps. Recursion requires a stopping condition and a recursive step.We illustrate with a recursive version of factorial. The recursive step in factorial is the product of n and factorial (n-1) .the stop condition is reached when n=0.-_(defun factorial (n)(cond ((zero p n)1)(t (*n(factorial(- n 1))))Factorial ->Factorial (6)720 ->Property lists: one of the unique and most useful features of lisp an AI language is the ability to assign properties atoms. Property list functions permit one to assign such properties to an atom and to retrieve, replace them as required.The function putprop assigns properties to an atom .it takes 3 arguments: An object name can atom, a proper or attribute name ,and property or attribute value. For ex: to assign properties to a car, we can assign properties such as make year, color and style with the following statements.Syntax: (putprop object value attribute)Ex: (putprop ‘car ‘ford’ make)=>ford(Putprop ‘car 1988 ‘year)=>1988(Putprop ‘car ‘red’ color)=>redgetprop: to retrieve a property value, such as the color of car we use the function get, which also takes the 2 arguments object and attribute.Syntax: (get object attribute)Ex: (get ‘car ‘ color )=>red(get ‘car ‘ year )=>1998remprop:this function is used to remove the properties .it takes 2 arguments object & attribute .syntax: (remprop object attribute)ex: (remprop ‘car ‘ color)=>red

setf:the new function setf is same as setq except it is more general.it is an assignment function which also takes 2 arguments, the first of which may be either an atom or an access function (CRA,CDR,get) and the second the value to be assigned .arrays: single or multiple dimension arrays may be defined in lisp using the make-array function.the items tored in the array may be any lisp object.(self myarray (make-array(10)))#A(00000000) Mapping functions: Map car: Mapcar is one of several mapping functions provided in lisp to apply some function successively to one or more lists of elements. the first argument of mapcar is a function and the remaining arguments are lists of elements to which the named function is applied. The result of applying the function to successive members of the lists are placed in a new list which is returned.Ex;1-> (map car ‘1+’(5 10 15 20 25)(6 11 16 21 26)->2->(map car ‘+’ (123456)’( 1 2 3 4 ))2 4 6 8 ->lambda functions: LISP provides a method of writing unnamed or anonymous functions that are evaluated only when they are encountered in a program. Such functions are called lambda functions.(lambda (arguments))ex:(lambda (x)(* x x x))(lambda(5) (* 5 5 5))=>125otherwise ->(defun cub_lsit(lst)(map car #’(lambda (x)(for all x x x ))lst))CUBE_LIST->(cube list (1 2 3 4 )(182764)+ to indicate that the following item is a function. This is equivalent to preceding the function with a single quotation mark(‘).

Question PaperArtificial Intelligence (MC321) : January 2008Section A : Basic Concepts (30 Marks)• This section consists of questions with serial number 1 - 30.• Answer all questions.• Each question carries one mark.• Maximum time for answering Section A is 30 Minutes.1. Transition networks are based on(a) The application of directed graphs and finite state automata(b) The application of undirected graphs and finite state automata(c) The application of directed graphs only(d) The application of undirected graphs only(e) The application of only finite state automata.

2. The traveling salesman problem involves n cities with paths connecting the cities. The time taken for traversing through all the cities, without knowing in advance the length of a minimum tour, is(a) O(n)(b) O(n2)(c) O(n!)(d) O(2n)(e) On(log n).

3. The problem space of means-end analysis has(a) An initial state and one or more goal states(b) One or more initial states and one goal state(c) One or more initial states and one or more goal states(d) One initial state and one goal state(e) No goal state.

4. The engineering goal of artificial intelligence is(a) To solve artificial problems(b) To solve real-world problems(c) To solve problems intelligently(d) To explain various sorts of intelligence(e) To extract scientific causes.

5. Applications of artificial intelligence should be judged according to(a) Whether there is a well-defined task(b) An implemented program(c) A set of identifiable principles(d) A set of intelligent people (e) (a), (b) and (c) above.

6. An algorithm A is admissible if,(a) It is not guaranteed to return an optimal solution when one exists(b) It is guaranteed to return an optimal solution when one exists(c) It returns more solutions, but not an optimal one(d) It returns no solutions at all(e) It returns an optimal solution.

7. An algorithm A is optimal over a class of algorithms if(a) A dominates all members of the class(b) A gives optimal solution(c) A equally performs with all members of the class(d) A is dominated by all members of the class(e) A does not give an optimal solution.

8. In informed or directed search,(a) Some information about the problem space is used to compute a preference among the children for exploration and expansion(b) No preference is given for exploration and expansion(c) Preference is given depending on the user interaction(d) Preference is given only to explore but not for expansion(e) Preference is given both to explore and for expansion.

9. The action ‘ONTABLE(A)’ of a robot arm means,(a) Put block A on the table(b) Check whether block A is on the table

(c) Block A is on the table(d) Table is on the block A(e) Block A is not on the table.

10. In the matching process,(a) The conditions in the left hand side (LHS) of the rules in the knowledge base are matched against the contents of working memory(b) The conditions in the right hand side (RHS) of the rules in the knowledge base are matched against the contents of working memory(c) The conditions in the left hand side (LHS) of the rules in the knowledge base are matched against the rules of the conflict set(d) The conditions in the right hand side (RHS) of the rules in the knowledge base are matched against the rules of the conflict set(e) Both (a) and (c) above.

11. Logic programming is,(a) A programming language paradigm in which logical assertions are viewed as programs(b) A programming language where the programs are all arranged as logical assertions(c) A procedural language where logic is programmed(d) A procedural language where programs are arranged as logical assertions(e) A procedural language where logical assertions are viewed as programs.

12. A PROLOG program is described as,(a) A series of logical assertions, each of which is a horn clause(b) A series of programming statements, each of which is not a clause(c) A program where each statement is expressed as a logical assertion(d) A program similar to C language(e) A series of programming statements, each of which is a clause.

13. Among the following, which is not a horn clause?(a) p(b) Øp V q (c) p ? q (d) p ? Øq(e) Øp VØq.

14. In the rule selection process,(a) One of the rules is selected from the working memory to execute(b) One of the rules is selected from the conflict set to execute(c) One of the rules is selected from the working memory for verification(d) One of the rules is selected from the conflict set for verification(e) Both (a) and (c) above.

15. Analogy is,(a) Based on previously tested knowledge that bears a strong resemblance to the current situation(b) Based on previously tested knowledge that does not bear any resemblance to the current situation(c) Based on future anticipated knowledge that bears a strong resemblance to the current situation(d) Based on future anticipated knowledge that does not bear any resemblance to the current situation(e) Both (b) and (d) above.

16. In Case grammars case relates to,(a) The syntactic role that a noun phrase plays with respect to verbs and adjectives(b) The semantic role that a noun phrase plays with respect to verbs and adjectives(c) The syntactic role that a noun phrase plays with respect to verbs and adverbs(d) The semantic role that a noun phrase plays with respect to verbs and adverbs(e) The syntactic role that a noun phrase plays with respect to adjectives and adverbs.

17. Semantic grammars(a) Encode semantic information into a syntactic grammar(b) Decode semantic information into a syntactic grammar(c) Encode syntactic information into a semantic grammar(d) Decode syntactic information into a semantic grammar(e) Both (a) and (b) above.

18. Factors which affect the performance of learner system does not include,(a) The representation scheme used(b) The training scenario(c) The type of feedback(d) Good data structures

(e) Learning algorithm.

19. A model of a set of wff’s is,(a) An interpretation that satisfies them(b) An isolation that satisfies them(c) An interpretation that doesn’t satisfy them(d) An isolation that doesn’t satisfy them(e) Both (a) and (b) above.

20. Perception involves(a) Sights, sounds, smell and touch(b) Hitting(c) Dancing(d) Acting(e) Listening.

21. Third component of a planning system is,(a) Detect when a solution has been found(b) Detect when will solution be found(c) Detect whether solution exists or not(d) Detect whether multiple solutions exist(e) Detect whether a single solution exist.

22. Robustness is the measure of,(a) Ease with which the method can be adapted to different domains of application(b) The average time required to construct the target knowledge structures from some specified initial structures(c) A learning system to function with unreliable feedback and with a variety of training examples(d) The overall power of the system(e) A learning system to function with reliable feedback and with a variety of training examples.

23. In Closed World Assumption,(a) If a proposition cannot be proven, it is true(b) If a proposition cannot be proven, it is false(c) If a proposition can be proven, it is false(d) If a proposition can be proven, it does not exist(e) If a proposition cannot be proven it exists.

24. In Dempster-Shafer theory, the relation between belief and plausibility is given as,(a) Pl(s) = 1 + Bel(Øs)(b) Pl(s) = 1 – Bel(s)(c) Pl(s) = 1 + Bel(s)(d) Pl(s) = 1 – Bel(Øs)(e) P1(s) = 1 * Bel(s).

25. Circumscription states that,(a) All objects that have some property P are the only objects that satisfy P(b) All objects that have some property P are the only objects that does not satisfy P(c) All objects that have some property P are the only objects that validate P(d) All objects that have some property P are the only objects that does not validate P(e) Both (a) and (c) above.

26. Completion formulas are,(a) Axioms which are added to a Knowledge Base to allow the applicability of specific predicates(b) Axioms which are added to a Knowledge Base to restrict the applicability of specific predicates(c) Constant rules which are added to a Knowledge Base to allow the applicability of specific predicates(d) Constant rules which are added to a Knowledge Base to restrict the applicability(e) Both (a) and (c) above.

27. Knowledge-based systems get their power from the expert knowledge that has been coded into(a) Facts(b) Rules(c) Heuristics(d) Procedures(e) Relations.

28. A good system for the representation of knowledge in a particular domain should possess the properties(a) Representational Adequacy(b) Inferential Adequacy(c) Inferential Efficiency(d) Acquisitional Efficiency(e) All of the above.

29. A horn clause is,(a) A clause that has at least one positive literal(b) A clause that has at most one negative literal(c) A clause that has at most one positive literal(d) A clause that has at least one negative literal(e) A clause that has only one positive literal.

30. Identify the true statement.(a) Neural networks store information in the working memory(b) Neural networks store information in the strengths of the interconnections(c) Neural networks store information in the RAM(d) Neural networks store information in the secondary memory(e) Neural networks store information in the cache memory.

END OF SECTION A

Section B : Problems (50 Marks)

• This section consists of questions with serial number 1 – 5 .• Answer all questions. • Marks are indicated against each question.• Detailed workings should form part of your answer. • Do not spend more than 110 - 120 minutes on Section B. 1. a. Define Agent and state its characteristics. ( 5 marks)

b. What is a Learning Agent? Explain the role of the Learning Agent in Artificial Intelligence. ( 5 marks) 2. a. Briefly explain Uniform Cost Search. ( 3 marks)

b. Explain in detail the A* Search algorithm. ( 5 marks) c. Explain the relationship between the A* algorithm and the Uniform Cost Search algorithm. ( 2 marks) 3. Consider the following facts:• Abhaya and Dishna are married.• Bimal and Chintha are siblings. (i.e. bother and sister)• Chintha’s mother is Dishna.• Abhaya’s son is Bimal.

a. Convert the above knowledge into predicate logic sentences. ( 3 marks) b. Give additional predicate logic sentences which the system would need to successfully make inferences about the domain concerned. ( 3 marks) c. Show how the resolution algorithm will answer questions of the following kind given the above facts:• Is Abhaya, Chintha’s father?• Who is Bimal’s father? ( 4 marks) 4. a. The following figure shows a typical ECG image.

A computer vision system is needed to be developed to identify abnormalities in ECG patterns. With regard to this vision system, identify a suitable processing technique for each of the processing stages given in the following table and complete the table. ( 7 marks)

b. In many computer vision systems, image segments are used as useful features for providing interpretations about the contents of an image. Give two techniques which can be used to extract segments of an image. ( 3 marks) 5. a. If the start state is 1 and the goal state is 7 in the diagram given below, describe the search path pursued by a breadth first search algorithm, uniform cost search algorithm and a depth-first search algorithm. The value given on a link that connects two nodes describes the cost to travel between the two nodes.( 5 marks)

b. Compare the depth-first search and breadth-first search algorithms by writing out their advantages and disadvantages. ( 5 marks)

END OF SECTION B

Section C : Applied Theory (20 Marks)

• This section consists of questions with serial number 6 - 7 .

• Answer all questions. • Marks are indicated against each question.• Do not spend more than 25 - 30 minutes on Section C. 6. a. Consider the following table of distances between cities in an imaginary country:Route Between Cities Distance Route Between Cities DistanceA to Z 75 A to T 118T to L 111 L to M 70M to D 75 D to C 120C to P 138 P to B 101B to U 85 U to H 98A to S 140 S to F 99F to B 211 S to R 80R to P 97 Suppose it is necessary to travel from City A to City B. Also assume that straight line distance to City B from other cities can be found using a scaled map of these cities. Using the straight line distances (given below), describe a simple best-first search strategy known as greedy search to reach City B. Give the total distance traveled by using this algorithm.Straight line distance between City B and other cities: A(366), C(160), D(242), F(178), H(151), L(244), M(241), P(98), R(193), S(253), T(329), U(80), Z(374).b. Explain whether the heuristic function in the answer to c (i) above can identify the shortest path between City A and City B. Describe how this heuristic function can be improved to make it optimal and complete. What is the optimal path given by this modified algorithm? ( 10 marks)

7. Animals can be divided into various categories such as mammals and birds. Mammals have hair. They give milk too. Birds can fly and lay eggs. Animals who eat meat, are known as carnivore. These carnivore animals have pointed teeth, claws and forward eyes. Mammals who have hoofs or chew cud are known as ungulate. Cheetah is a mammal as well as a carnivore. It has tawny color and dark spots. Giraffe is an ungulate. It has a long neck, long legs and dark spots. Zebra is also an ungulate with black stripes. Although a Penguin is a bird, it cannot fly, but it can swim. It is colored black and white. Represent the above information using a semantic network. ( 10 marks)

END OF SECTION C

END OF QUESTION PAPER

Suggested AnswersArtificial Intelligence (MC321) : January 2008Section A : Basic ConceptsAnswer Reason 1. A Transition networks are based on the application of directed graphs and finite state automata. < TOP >

2. C The time taken for traversing through all the cities, without knowing in advance the length of a minimum tour, is O(n!). < TOP >

3. A The problem space of means-end analysis has an initial state and one or more goal states. < TOP >

4. B The engineering goal of artificial intelligence is to solve real-world problems. < TOP >

5. E Applications of artificial intelligence should be judged according to Whether there is a well-defined task, an implemented program and a set of identifiable principles. < TOP >

6. B An algorithm A is admissible if, It is guaranteed to return an optimal solution when one exists. < TOP >

7. A An algorithm A is optimal over a class of algorithms if A dominates all members of the class. < TOP >

8. A In informed or directed search, some information about the problem space is used to compute a preference among the children for exploration and expansion. < TOP >

9. C The action ‘ONTABLE(A)’ of a robot arm means Block A is on the table. < TOP >

10. A In the matching process, the conditions in the left hand side (LHS) of the rules in the knowledge base are matched against the contents of working memory. < TOP >

11. A Logic programming is a programming language paradigm in which logical assertions are viewed as programs. < TOP >

12. A A PROLOG program is described as, a series of logical assertions, each of which is a horn clause. < TOP >

13. D p ? Øq is not a horn clause. < TOP >

14. B In the rule selection process one of the rules is selected from the conflict set to execute. < TOP >

15. A Analogy is based on previously tested knowledge that bears a strong resemblance to the current situation. < TOP >

16. B In Case grammars case relates to the semantic role that a noun phrase plays with respect to verbs and adjectives. < TOP >

17. A Semantic grammars encode semantic information into a syntactic grammar. < TOP >

18. D Factors which affect the performance of learner system does not include good data structures. < TOP >

19. A A model of a set of wff’s is an interpretation that satisfies them. < TOP >

20. A Perception involves Sights, sounds, smell and touch. < TOP >

21. A Third component of a planning system is, to detect when a solution has been found. < TOP >

22. C Robustness is the measure of a learning system to function with unreliable feedback and with a variety of training examples. < TOP >

23. B In Closed World Assumption ,If a proposition cannot be proven, it is false. < TOP >

24. D In Dempster-Shafer theory, the relation between belief and plausibility is given as, Pl(s) = 1 – Bel(Øs). < TOP >

25. A Circumscription states that all objects that have some property P are the only objects that satisfy P. < TOP >

26. B Completion formulas are axioms which are added to a Knowledge Base to restrict the applicability of specific predicates. < TOP >

27. E Knowledge-based systems get their power from the expert knowledge that has been coded in relations. < TOP >

28. E Representational Adequacy,Inferential Adequacy, Inferential Efficiency, Acquisitional efficiency. < TOP >

29. C A Horn clause is a clause that has at most one positive literal. < TOP >

30. B Neural networks store information in the strengths of the interconnections. < TOP >

Section B : Problems

1. a. A simple agent program can be defined mathematically as an agent function which maps every possible percepts sequence to a possible action the agent can perform or to a coefficient, feedback element, function or constant that affects eventual actions:f:P * - > AThe program agent, instead, maps every possible percept to an action.It is possible to group agents into five classes based on their degree of perceived intelligence and capability:simple reflex agents; model-based reflex agents; goal-based agents; utility-based agents; learning agents. 1. Simple reflex agentsSimple reflex agents acts only on the basis of the current percept. The agent function is based on the condition-action rule:if condition then action ruleThis agent function only succeeds when the environment is fully observable. Some reflex agents can also contain information on their current state which allows them to disregard conditions whos actuators are already triggered.2. Model-based reflex agentsModel-based agents can handle partially observable environments. Its current state is stored inside the agent maintaining some kind of structure which describes the part of the world which cannot be seen. This behavior requires information on how the world behaves and works. This additional information completes the “World View” model.3. Goal-based agentsGoal-based agents are model-based agents which store information regarding situations that are desirable. This allows the agent a way to choose among multiple possibilities, selecting the one which reaches a goal state.4. Utility-based agentsGoal-based agents only distinguish between goal states and non-goal states. It is possible to define a measure of how desirable a particular state is. This measure can be obtained through the use of a utility function which maps a state to a measure of the utility of the state.b. Learning agentsIAs are also referred to as autonomous intelligent agents, which means they act independently, and will learn and adapt to changing circumstances. IA systems should exhibit the following characteristics:• learn and improve through interaction with the environment .• adapt online and in real time • learn quickly from large amounts of data • accommodate new problem solving rules incrementally • have memory based exemplar storage and retrieval capacities • have parameters to represent short and long term memory, age, forgetting, etc. • be able to analyze itself in terms of behavior, error and success. To actively perform their functions, Intelligent Agents today are normally gathered in a hierarchical structure containing many “sub-agents”. Intelligent sub-agents process and perform lower level functions. Taken together, the intelligent agent and sub-agents create a compete system that can accomplish difficult tasks or goals with behaviors and responses that display a form of intelligence.Some of the sub-agents (not already mentioned in this treatment) that may be a part of an Intelligent Agent or a complete Intelligent Agent in themselves are:1. Temporal Agents (for time-based decisions); 2. Spatial Agents (that relate to the physical real-world);

3 Input Agents (that process and make sense of sensor inputs - example neural network based agents neural network); 4. Processing Agents (that solve a problem like speech recognition); 5. Decision Agents (that are geared to decision making); 6. Learning Agents (for building up the data structures and database of other Intelligent agents); 7. World Agents (that incorporate a combination of all the other classes of agents to allow autonomous behaviors). < TOP >

2. a. Breadth first search finds the shallowest goal state and that this will be the cheapest solution so long as the path cost is a function of the depth of the solution. However, if this is not the case, then breadth first search is not guaranteed to find the best (i.e. cheapest) solution. Uniform cost search remedies this. It works by always expanding the lowest cost node on the fringe, where the cost is the path cost, g(n).In fact, breadth first search is a uniform cost search with g(n) = DEPTH(n).b. A* (pronounced “A star”) is a graph/tree search algorithm that finds a path from a given initial node to a given e(or one passing a given goal test). It employs a “heuristic estimate” h(x) that ranks each node x by an estimate of the best route that goes through that node. It visits the nodes in order of this heuristic estimate. The A* algorithm is therefore an example of best-first search.Generally speaking, Depth-first search and breadth-first search are two special cases of A* algorithm. Dijkstra’s algorithm as another example of a best-first search algorithm, is the special case of A* where h(x) = 0 for all x. For depth-first search, we may consider that there is a global counter C initialized with a very big value. Every time, we process a node, we assign C to all of its newly discovered neighbors. After each single assignment, we decrease the counter C by one. Thus the earlier a node is discovered, the higher its h(x) value.Consider the problem of route finding, for which A* is commonly used. A* incrementally builds all routes leading from the starting point until it finds one that reaches the goal. But, like all informed search algorithms, it only builds routes that appear to lead towards the goal.To know which routes will likely lead to the goal, A* employs a heuristic estimate of the distance from any given point to the goal. In the case of route finding, this may be the straight-line distance, which is usually an approximation of road distance.What sets A* apart from greedy best-first search is that it also takes the distance already travelled into account. This makes A* complete and optimal, i.e., A* will always find the shortest route if any exists and if h(x) was chosen correctly. While optimal in arbitrary graphs, it is not guaranteed to perform better than simpler search algorithms that are more informed about the problem domain. In a maze-like environment, the only way to reach the goal might be to first travel one way (away from the goal) and eventually turn around. In this case trying nodes closer to your destination first may cost you time.PropertiesLike breadth-first search, A* is complete in the sense that it will always find a solution if there is one.If the heuristic function h is admissible, meaning that it never overestimates the actual minimal cost of reaching the goal, then A* is itself admissible (or optimal) if we do not use a closed set. If a closed set is used, then h must also be monotonic (or consistent) for A* to be optimal. This means that it never overestimates the cost of getting from a node to its neighbor. Formally, for all paths x,y where y is a successor of x:A* is also optimally efficient for any heuristic h, meaning that no algorithm employing the same heuristic will expand fewer nodes than A*, except when there are several partial solutions where h exactly predicts the cost of the optimal path.A* is admissible and computationally optimalA* is both admissible and considers fewer nodes than any other admissible search algorithm with the same heuristic, because A* works from an “optimistic” estimate of the cost of a path through every node that it considers — optimistic in that the true cost of a path through that node to the goal will be at least as great as the estimate. But, critically, as far as A* “knows”, that optimistic estimate might be achievable.When A* terminates its search, it has, by definition, found a path whose actual cost is lower than the estimated cost of any path through any open node. But since those estimates are optimistic, A* can safely ignore those nodes. In other words, A* will never overlook the possibility of a lower-cost path and so is admissible.Suppose now that some other search algorithm A terminates its search with a path whose actual cost is not less than the estimated cost of a path through some open node. Algorithm A cannot rule out the possibility, based on the heuristic information it has, that a path through that node might have a lower cost. So while A might consider fewer nodes than A*, it cannot be admissible. Accordingly, A* considers the fewest nodes of any admissible search algorithm that uses a no more accurate heuristic estimate.ComplexityThe time complexity of A* depends on the heuristic. In the worst case, the number of nodes expanded is exponential in the length of the solution (the shortest path), but it is polynomial when the heuristic function h meets the following condition:| h(x) - h * (x) | = O(logh * (x)) where h * is the optimal heuristic, i.e. the exact cost to get from x to the goal. In other words, the error of h should not grow faster than the logarithm of the “perfect heuristic” h * that returns the true distance from x to the goal .More problematic than its time complexity is A*’s memory usage. In the worst case, it must also remember an exponential number of nodes. Several variants of A* have been developed to cope with this, including iterative deepening A* (IDA*), memory-bounded A* (MA*) and simplified memory bounded A* (SMA*) and recursive best-first search (RBFS).c. Uniform cost search minimises the cost g(n) of the path up to node n. Uniform cost search is both optimal and complete but can be very inefficient. We combine this evaluation function, g(n), with a heuristic evaluation, h(n) to give the evaluation function for the A* algorithm, i.e. f(n) = g(n) + h(n) As g(n) gives the path cost from the start node to node n and h(n) gives the estimated cost of the cheapest path from node n to the goal, we have f(n) = estimated cost of the cheapest solution through node n. A* is both optimal and complete if the heuristic is admissible (i.e. does not overestimate the cost to the goal). It also, in the worst case, has the same time and space complexity as uniform cost search. < TOP >

3. a. 1. married(abhaya, dishna).2. sibling(bimal, chintha).3. mother(dishna, chintha).4. son(bimal, abhaya).b. 5. On father-son relationship : father(X,Y) :- son(Y, X).6. On the sibling relationship : sibling(X, Y) :- sibling(Y, X).7. On the father-sibling relationship: father(X, Y) :- father(X, Z), sibling(Y, Z).8 . On mother-sibling relationship: mother(X,Y) :- mother(X, Z), sibling(Y, Z).c. ~father(abhaya, chintha) + father(X,Y) à~(father(abhaya, Z), sibling(Z, chintha)) --- rule 7

father(abhaya, Z) + father(X, Z) à son(Z, abhaya) --- rule 5son(Z, abhaya) + son(bimal, abhaya) à NULL --- fact 4~sibling(bimal, chintha) + sibling(bimal, chintha) à NULL --- rule 6Hence ~father(abhaya, chintha) is contradicted. i.e. abhaya IS the father of chintha.~father(bimal, X) + father(bimal, X) à ~(son(X, bimal)) --- rule 5~son(X, bimal) + son(abhaya, bimal) à NULL --- fact 4 < TOP >

4. a. Processing stage TechniqueImage capturing Flat-bed Scanner can be used to capture the image.Preprocessing The image can be enhanced using sharpening, smoothing and histogram equalization techniques selecting the appropriate techniques.Feature extraction The ECG pattern should be extracted from the background. This could be done using threshold based segmentation since the signal is darker than the background.Feature representationThe extracted ECG signal pattern can be given as1s and background as 0s in a binary image.Interpretation of the ECG pattern Neural network based techniques can be used to train the system for normal ECG patterns and abnormal patterns can be identified by the system.b. (i) Image segmentation by thresholding. The grey-level histogram can be used as an aid to identify the thresholds required to segment the image into meaningful segments.(ii) Pixel aggregation and region growing. < TOP >

5. a. Breadth-first Search: 1, 2, 3, 4, 5, 6, 7Uniform Cost Search: 1, 4, 3, 2, 8, 9, 7, 6, 5Depth first Search: 1, 2, 5, 6, 3, 7b. Depth First SearchAdvantages1) Needs little memory (only nodes in current path need to be stored)2) May arrive at solutions without examining much of search space.Disadvantages1) May explore a single unfruitful path for a long time (forever if loop exists)2) May settle for a non-optimal solutionBreadth First SearchAdvantages1) Will not go down a blind alley for solution.2) Optimal solutions are always found; multiple solutions found early.Disadvantages1) The entire tree generated must be stored in memory.2) If solution path is long, the whole tree must be searched up to that depth. < TOP >

Section C: Applied Theory

6. Greedy search uses a heuristic function h(n) as follows:h(n) = estimated cost of the cheapest path from the state at node n to a goal stateh(n) could be any function such that h(n) = 0 if n is the goal state. Since the straight line distance from City X to City Y is 0 if X=Y, it is possible to consider the straight line distance between cities and the goal state (city B) to estimate the value for h(n).Traversal Path:A to S (since S(253), T(329), Z(374))S to F (since F(178), R(193)), A(366))F to B (since B(0), S(253))Total = 140+99+211 =450.b) No, it is not possible since distance along the path (A to S, S to R, R to P and P to B) is 418, but the distance along the path given in answer c (i) is 450.By integrating the path cost g(n), the cost from the start node to node n, the heuristic function in the greedy search, can be improved.f(n) = h(n) + g(n)In other words, f(n) is the estimated cost of the cheapest solution through n. f(n) is optimal and complete.A to S (S(253+140), T(329+118), Z(374+75))S to R (F(178+140+99), R(193+140+80), A(366+140+140))R to P (P(98+140+80+97), S(253+140+80+80))P to B (B(0+140+80+97+101), C(160+140+80+97+138))= 418 < TOP >