Logical reasoning 21.1.13

Unit IILogical Reasoning

V.SaranyaAP/CSE

Sri Vidya College of Engineering and Technology,

Virudhunagar

Logical AgentsKnowledge based AgentsThe Wumpus WorldLogic

February 20, 2006 AI: Chapter 7: Logical Agents 3

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


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”



• 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





• 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


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


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


Wumpus World


Wumpus World


Wumpus World


Wumpus World


Wumpus World


Wumpus World


Wumpus World


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.


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”

Education

Logical reasoning 21.1.13