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lecture11

# lecture11 - Artificial Intelligence Knowledge...

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Knowledge Representation and Reasoning; page 1 of 42 Artificial Intelligence Knowledge Representation and Reasoning Russell and Norvig - Chapters 7, 8 Nilsson - Chapters 13, 14, 15 (Logic)

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Knowledge Representation and Reasoning; page 2 of 42 Breeze Breeze Breeze Breeze Breeze Stench Stench Breeze PIT PIT PIT 1 2 3 4 1 2 3 4 START Gold Stench “wumpus world” knowledge representation languages should be expressive, concise, unambiguous, independent of context, effective
Knowledge Representation and Reasoning; page 3 of 42 Agents are given knowledge about the world. Knowledge Representation: How can facts about the world be represented? Reasoning: How can the agent infer new facts from the given ones?

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Knowledge Representation and Reasoning; page 4 of 42 representation world sentences facts sentences facts entail entail have interpretation have interpretation = represent = represent (“meaning”) (“meaning”) computer
Knowledge Representation and Reasoning; page 5 of 42 arithmetic Is “1 > 2” a well-formed formula? Is “x + * y 5 >” a well-formed formula? syntax semantics When is “x + 2 = 5” true?

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Knowledge Representation and Reasoning; page 6 of 42 propositional logic = sentences represent whole propositions “2 is prime.” “I ate breakfast today.” P Q
Knowledge Representation and Reasoning; page 7 of 42 syntax = how a sentence looks like Sentence -> AtomicSentence | ComplexSentence AtomicSentence -> T(RUE) | F(ALSE) | Symbols ComplexSentence -> ( Sentence ) | NOT Sentence | Connective -> AND | OR | IMPLIES | EQUIV(ALENT) Sentence Connective Sentence Symbols -> P | Q | R | ... Precedence: NOT AND OR IMPLIES EQUIVALENT conjunction disjunction implication equivalence negation

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Knowledge Representation and Reasoning; page 8 of 42 syntax = how a sentence looks like The constants T(RUE) and F(ALSE) are sentences. The symbols P, Q, R, ... are sentences. If S is a sentence, then (S) is a sentence. If S1 and S2 are sentences, then S1 EQUIV S2 is a sentence. If S1 and S2 are sentences, then S1 IMPLIES S2 is a sentence. If S1 and S2 are sentences, then S1 OR S2 is a sentence. If S1 and S2 are sentences, then S1 AND S2 is a sentence. If S is a sentence, then NOT S is a sentence. Examples: P, T, P IMPLIES NOT T, P AND (Q OR S)
Knowledge Representation and Reasoning; page 9 of 42 semantics = what a sentence means interpretation: assigns each symbol a truth value, either t(rue) or f(alse) the truth value of T(RUE) is t(rue) the truth value of F(ALSE) is f(alse) truth tables (“compositional semantics”) A t t f f B t f t f NOT A f t A AND B t f f f A OR B t t t f A IMPLIES B t f t t A EQUIV B t f f t the meaning of a sentence is a function of the meaning of its parts

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Knowledge Representation and Reasoning; page 10 of 42 examples either I go to the movies or I go swimming A t t f f B t f t f A OR B t t t f A XOR B f t t f (inclusive OR) (exclusive OR) (inclusive versus exclusive OR - our OR is inclusive) Read “A IMPLIES B” as “if A then B” Read “A EQUIV B” as “if and only if A then B” or “A and B have the same truth value”
Knowledge Representation and Reasoning; page 11 of 42 examples

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lecture11 - Artificial Intelligence Knowledge...

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