Chapter 17 Advanced Knowledge Representation

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Chapter 17

Advanced Knowledge Representation

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Chapter 17 Contents (1)

The Blackboard Architecture Scripts The Copycat Architecture Nonmonotonic Reasoning The Modal Operator M Default Reasoning Truth Maintenance Systems Closed-World Assumption

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Chapter 17 Contents (2)

Circumscription Abductive Reasoning The Dempster-Shafer Theory MYCIN and Certainty Factors Temporal Logic Event Calculus Mental Situation Calculus Knowledge Engineering Case-Based Reasoning

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The Blackboard Architecture (1)

A method for structured knowledge representation.

Uses opportunistic reasoning – decides whether to use forward or backward reasoning as appropriate.

Allows knowledge from a range of experts to be combined together and used in one system.

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The Blackboard Architecture (2) Information from the various knowledge sources

(experts) is written on the blackboard, which is a shared data store.

When a knowledge source sees some data on the blackboard that it can use, it derives a conclusion and adds this as a new fact to the blackboard.

The opportunistic model means experts do not need to take turns, but can add data whenever they want.

Typically there is a control mechanism that determines when knowledge sources can add data to the blackboard, but this is not essential.

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Scripts (1)

A script is a structured representation of a situation, such as buying dinner in a restaurant or going shopping.

A script has a set of preconditions called entry conditions that determine when it can be used.

Running a script generates an output called a result.

Scripts are designed to enable us to reason about motivations or reasons – why did he do that?

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Scripts (2)

A script is presented with a story, and attempts to match elements of the story with its scripted elements.

Scripts are encoded with a great deal of domain knowledge, and so are able to answer questions that are not explicitly answered in the story.

Scripts include roles, which define types of people – for a restaurant the roles might be waiter, chef and customer.

The individuals named in a story are matched with these roles to assist with understanding the story.

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The Copycat Architecture (1)

A system for solving analogies such as:abc => abd

Hence, tuv => ? Uses a non-deterministic approach, meaning

running it multiple times on the same problem may generate different answers.

The above problem has several possible answers, such as:tuwtud

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The Copycat Architecture (2)

The architecture consists of the following components: The Workspace The Coderack The Slipnet

The workspace is a working memory, similar to the blackboard architecture.

The coderack contains a number of relationships between objects. These are encoded as codelets. For example:

the b in abc is the successor of a

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The Copycat Architecture (3)

Each concept in the slipnet has an activation level which shows how relevant it is to the current problem.

Concepts within the slipnet show relationships between other concepts – the example above shows the way the slipnet records the idea that “first” is “opposite” to “last”.

A simplified version of the slipnet is shown here.

The slipnet is the long-term memory.

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The Copycat Architecture (4)

The system uses temperature to represent how far it is from a solution.

The higher the temperature, the more random its codelets are allowed to be.

Copycat works by building rules that explain the relationships between the letters in the example it is given, and then by applying those rules to the problem.

As the system runs, the temperature is gradually lowered until it hits a threshold at which point it has found a solution, and stops.

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Nonmonotonic Reasoning

In a monotonic logical system, if conclusion C can be derived from premises, P, then adding additional facts to P cannot cause C to become false.

Propositional and predicate logics are monotonic. We will now examine some logical systems that

are not monotonic. These can be useful, particularly as the real world does not usually behave in a monotonic way: We often find ourselves changing our beliefs

and conclusions as we learn new facts. This is nonmonotonic reasoning.

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The Modal Operator M

Predicate calculus can be extended with the modal operator M.

M represents the idea that a concept is consistent with our beliefs.

For example:x bird (x) Λ M flies (x) flies (x)

“for all x, if x is a bird and it is consistent with our beliefs to believe that x can fly, then x can fly”

(I.e.: “most birds can fly”) Our beliefs can change – for example, when we

realise that dead birds cannot fly.

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Default Reasoning

Another form of nonomonotonic reasoning:Car (x) Λ :Has_Driver (x) Has_Driver (x)

This can be read “if x is a car and we have no reason to believe that x does not have a driver, then we can conclude that x does have a driver.”

This allows us to set up default rules. The defaults can be overridden by new facts.

If you saw the driver jump out a few seconds before, or you know it’s a new driverless car, then you’d know that in this case the car did not have a driver.

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Truth Maintenance Systems (1)

A TMS is used to store beliefs and information about how those beliefs were derived.

The JTMS (Justification-based TMS) stores reasons for each belief.

For example, belief Q might have the following reason:

({P, R}, {¬S}) If P and R are both true, and ¬S is false, then we can

deduce that Q is true. If we use this reason to conclude that Q is true, and

later discover that ¬S is true, then we must retract our earlier conclusion.

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Truth Maintenance Systems (2)

The JTMS stores beliefs and reasons in a network of nodes. It does not understand the beliefs or reason about them, it

simply stores them. A problem solving system reasons about the beliefs and modifies the JTMS.

Each node is either in (believed to be true) or out (believed to be false).

If a new belief is added which contradicts another belief, dependency directed backtracking is used to work back from the contradictory node to find the assumptions that led to it.

Contradictions are retracted until no contradictions remain.

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Closed-World Assumption

Also known as negation by failure – used by PROLOG and STRIPS

Assumes that any fact that is not specified is false.

ADL uses the open world assumption – any fact not stated to be false is assumed to be true.

Systems that use the closed-world (or open-world) assumption must be able to reason nonmonotonically.

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Circumscription

A nonmonotonic reasoning method designed to deal with facts which are not explicitly stated or denied.

The circumscription of predicate P in an expression E is written:E(Φ) Λ x (Φ(x) P(x)) x (P(x) Φ(x))

Where Φ(x) is the result of substituting all occurrences of P with Φ in E.

Circumscription provides a way to modify a FOPL expression so that it expresses that no facts are true other than those specified.

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Abductive Reasoning

Abductive reasoning is based on the following rule, which is not logically sound:

B A → B A Hence if B is true, and we know that A implies B,

then it is reasonable to assume that A is true. This does not guarantee to provide correct

solutions, but can be used to give a “good enough” explanation for an observed phenomenon, which can later be corrected if new evidence arises.

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The Dempster-Shafer Theory (1)

Used to describe the degree of belief in a statement.

Bel (A) is used to express the degree to which we believe A to be true.

Note that Bel (A) + Bel (¬A) does not have to equal 1.

For example, we might feel fairly sure that it is raining: Bel (rain) = 0.9; we might have no reason at all to believe that it is not raining: Bel (¬rain) = 0.

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The Dempster-Shafer Theory (2)

The plausibility of x is written:Pl (x) = 1 – Bel (¬x)

So, if Bel (x) = 0.9 and Bel (¬x) = 0:Pl (x) = 1

We can now write this as a range:[0.9, 1]

The fact that this range is narrow tells us we are fairly sure about our belief.

A belief range of [0,1] means we know nothing at all about the statement.

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MYCIN and Certainty Factors (1)

MYCIN: an expert system used for medical diagnosis.

Uses backward chaining and abductive reasoning to determine which bacteria is most likely to be causing the symptoms.

Certainty factors are used to express degrees of belief:

MB(H|E) is the measure of belief of hypothesis H, given evidence E.

MD(H|E) is the measure of disbelief of hypothesis H, given evidence E.

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MYCIN and Certainty Factors (2)

The certainty factor is written:

CF (H|E) = MB(H|E) – MD(H|E) If CF (H|E) = 1 this means that evidence

E gives a strong confidence that H is true.

If CF (H|E) = 0 this means that evidence E gives a strong confidence that H is false.

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Temporal Logic (1)

Extends first order predicate logic with two modal operators:P means from now on, P will be trueP means that at some point in the

future P will be true Other modal operators for dealing with time

include the following:QP means that Q is true until P is true

P means that P will be true in the next time interval

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Temporal Logic (2)

Temporal logic systems have the following factors which define its behavior:

1. Safety conditions define behaviorrs which can never occur.

2. Liveness conditions specify what the system should do; how it should behave.

3. Fairness conditions define the behaviour of the system in nondeterministic situations. For example, deciding what an elevator should do if two people call it at the same time from different floors.

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Event Calculus (1)

An event takes place in space and time:

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Event Calculus (2)

An extension of situation calculus that deals with events.

An event is a bounded period of time. Uses predicates such as:

Happens (e, t)

Starts (e, f, t)

Ends (e, f, t)

Where f is a fluent, e is an event and t is a variable of time.

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Mental Situation Calculus

Allows us to reason about beliefs of an agent, and how they are affected by actions and the environment.

Uses functions such as:Holds (P, S) means that P holds in situation SBelieves (P) means that the agent believes P

Hence, we might write:Holds (Believes (Fly (Pigs)), S)

This means that it is true in situation S that the agent believes that pigs can fly.

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Knowledge Engineering

Systems based on logic rely on knowledge. Knowledge engineering is:

The process of gathering knowledge for such a system, and of converting it into a form suitable for the system.

Knowledge engineering involves selecting the correct predicates, functions and constants to represent knowledge appropriately.

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Case-Based Reasoning

A case-based system stores solutions to problems, along with information about whether these solutions worked or not.

When presented with a new solution, a case-based system identifies similar problems it has solved in the past, and uses their solutions to devise a solution for the new problem.