Transcript
Unit IILogical Reasoning
V.SaranyaAP/CSE
Sri Vidya College of Engineering and Technology,
Virudhunagar
Logical AgentsKnowledge based AgentsThe Wumpus WorldLogic
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Logical Agents• Humans can know “things” and “reason”
– Representation: How are the things stored?– Reasoning: How is the knowledge used?
• To solve a problem…• To generate more knowledge…
• Knowledge and reasoning are important to artificial agents because they enable successful behaviors difficult to achieve otherwise– Useful in partially observable environments
• Can benefit from knowledge in very general forms, combining and recombining information
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Knowledge-Based Agents
• Central component of a Knowledge-Based Agent is a Knowledge-Base– A set of sentences in a formal language
• Sentences are expressed using a knowledge representation language
• Two generic functions:– TELL - add new sentences (facts) to the KB
• “Tell it what it needs to know”– ASK - query what is known from the KB
• “Ask what to do next”
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Knowledge-Based Agents
• The agent must be able to:– Represent states and actions– Incorporate new percepts– Update internal representations of the world– Deduce hidden properties of the world– Deduce appropriate actions
Inference Engine
Knowledge-Base
Domain-Independent Algorithms
Domain-Specific Content
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Knowledge-Based Agents
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Knowledge-Based Agents
• Declarative – You can build a knowledge-based agent simply by
“TELLing” it what it needs to know
• Procedural– Encode desired behaviors directly as program
code• Minimizing the role of explicit representation and
reasoning can result in a much more efficient system
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Wumpus World• Performance Measure
– Gold +1000, Death – 1000– Step -1, Use arrow -10
• Environment– Square adjacent to the Wumpus are smelly– Squares adjacent to the pit are breezy– Glitter iff gold is in the same square– Shooting kills Wumpus if you are facing it– Shooting uses up the only arrow– Grabbing picks up the gold if in the same square– Releasing drops the gold in the same square
• Actuators– Left turn, right turn, forward, grab, release, shoot
• Sensors– Breeze, glitter, and smell
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Wumpus World• Characterization of Wumpus World– Observable
• partial, only local perception– Deterministic
• Yes, outcomes are specified– Episodic
• No, sequential at the level of actions– Static
• Yes, Wumpus and pits do not move– Discrete
• Yes – Single Agent
• Yes
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Wumpus World
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Wumpus World
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Wumpus World
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Wumpus World
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Wumpus World
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Wumpus World
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Wumpus World
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Wumpus World
LOGIC
Syntax:– Knowledge base consists of sentences– These sentences are expressed according to the
syntax.Ex: “x + y=4” is a well formed sentence.
Semantic: • Meaning of the sentence.• Mention the truth of each sentence.
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Logic
• Entailment means that one thing follows logically from anothera |= b
• a |= b iff in every model in which a is true, b is also true
• if a is true, then b must be true
• the truth of b is “contained” in the truth of a
Example• “X+Y=4” is true where X is 2 – And Y is 2
• But false where x is 1 and y is 1.• (every sentence must be true or false in each
possible world.)
Entailment
• Relation of logical element.• A sentence follows logically from another
sentence.• Notation : αl= β– Means sentence a entails(require, need, improve,
demand) β– If every word of α is true and β is also true.– (simply if α is true then β must be true)
Logic in Wumpus world
• The agent detecting nothing in [1,1]
• The agent is interested in whether the adjacent squares [1,2] & [2,2] and [3,1].
• Each of these squares may or may not contain a pit.
• So 23 = 8 possible models.
No pit in [1,2]
• No pit in [2,2]
Conclusion• α1 : there is no pit in [1,2]• α2 : there is no pit in [2,2]• KB is false in any model in which [1,2]
contains pit ,because there is no breeze in [1,1]
We know if KB is true α1 is also true.Hence KB is not equal to α1
in some models, if KB is true α2 is falseKB V α2 so the agent cannot conclude that
there is no pit in [2,2]
Inference (assumption or conclusion)
• The inference algorithm I can be derive from KB, then
•KB |-i a
• a is derived from KB by i” (or)• “ i derives a from KB”
Sound• An inference algorithm derives only entailed sentences is called
“Sound or Truth Preserving”.• Soundness is highly desirable property.
Correspondence between world and representation
entailssentences sentence
Representation
World
Aspects of the real world
Aspects of the real world
semantics
semantics
Illustration Sentences are physical configuration of the
agent.Reasoning is the process of constructing new
physical configurations from old ones.If any connection between logical reasoning
process and the real environment in which the agent exists is called “grounding”
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