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Artificial Intelligence in the 21 st Century S. Lucci / D. Kopec Chapter 5: Logic in Artificial Intelligence

Artificial Intelligence in the 21 st Century S. Lucci / D. Kopec Chapter 5: Logic in Artificial Intelligence. A Typical Wumpus World. Logic in general. What is a logic?. A formal language Syntax – what expressions are legal Semantics – what legal expressions mean

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Artificial Intelligence in the 21 st Century S. Lucci / D. Kopec Chapter 5: Logic in Artificial Intelligence

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  1. Artificial Intelligence in the 21st Century S. Lucci / D. Kopec Chapter 5:Logic in Artificial Intelligence

  2. A Typical Wumpus World

  3. Logic in general

  4. What is a logic? • A formal language • Syntax – what expressions are legal • Semantics – what legal expressions mean • Proof system – a way of manipulating syntactic expressions to get other syntactic expressions (which will tell us something new) • Why proofs? Two kinds of inferences an agent might want to make: • Multiple percepts  conclusions about the world • Current state & operator  properties of next state

  5. Entailment

  6. Types of logic

  7. 5.1 – Logic & Representation • Induction puzzles • Logic puzzles solved via identification and subsequent elimination of perhaps a series of obvious cases • A well known example of an induction puzzle is “The King’s Wise Men”

  8. The King’s Wise Men Three men facing each other are blindfolded and each is wearing either a blue or white hat

  9. The King’s Wise Men / cont. • King tells the three men that each has either a blue or white hat and at least one is blue • Whoever guesses their hat color first will be the king’s next wise man • Predicate logic can be used to solve this puzzle • Allows each state to be denoted by a distinct expression • Predicate WM_I( ) denotes that wise man I has a hat of some color

  10. The King’s Wise Men / cont. ( WM_1(B) ∧ WM_2(W) ∧WM_3(W) ) (1) ( WM_1(W) ∧ WM_2(B) ∧ WM_3(W) ) (2) ( WM_1(W) ∧ WM_2(W) ∧ WM_3(B) ) (3) ( WM_1(B) ∧ WM_2(B) ∧WM_3(W) ) (4) ( WM_1(W) ∧ WM_2(B) ∧WM_3(B) ) (5) ( WM_1(B) ∧ WM_2(W) ∧WM_3(B) ) (6) ( WM_1(B) ∧ WM_2(B) ∧WM_3(B) ) (7) Table 5.1: The seven distinct cases for The King’s Wise Men Problem.

  11. 5.2 – Propositional Logic • With propositional logic, wise man one having a blue hat can be represented with the variable p • If wise man one has a white hat, then a different variable, such as q, must be used • Although propositional logic is less expressive than predicate logic, it is easier to work with and is a convenient place to begin our discussion of logic

  12. 5.2.1 – Propositional Logic - Basics • A statement (or logical expression) in propositional logic is similar to a sentenceused in the English language • It is a sentence that can be categorized with a truth value of true or false • Lower-case letters from the middle of the alphabet such as p, q, and r are used to denote propositional logic variables • These variables are the primitives, or basic building blocks in this logic

  13. Basics / cont. Table 5.2: Compound expressions formed by using logical connectives

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