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

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 Kings Wise Men 7

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

9. The Kings 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 kings 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 9

10. The Kings Wise Men / cont. Table 5.1: The seven distinct cases for The Kings Wise Men Problem. 10 ( 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)

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 11

12. 5.2.1 – Propositional Logic - Basics A statement (or logical expression) in propositional logic is similar to a sentence used 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 12

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