CS 414 ARTIFICIAL INTELLIGENCE ASSIGN AND SIMPLIFY EXAMPLE

SATISFIABILITY EXAMPLE • F = (x 1 V x 2) (x 1 V x

TRY THIS • Given a sentence find the satisfiability search tree 13

KNOWLEDGE BASE • A knowledge base KB is a set of sentences. Example KB:

NATURAL DEDUCTION • Proof is a sequence of sentences First ones are premises (KB)

And-introduction T T F F F T F F KB : is true

And-elimination T T F F F T F F KB : is true

NATURAL DEDUCTION EXAMPLE Prove S Step Formula Derivation 1 P Q Given 2 P

NATURAL DEDUCTION EXAMPLE • KB: . 1 Jerry. Giving. Lecture (Today. Is. Tuesday Today.

Step Formula Derivation 1 Jerry. Giving. Lecture (Today. Is. Tuesday Today. Is. Thursday( Given

Unit Resolution rule T T F T F F T F KB :

RESOLUTION TREE • • KB : (A C D) (A D E) (A C)

Slides: 52

Download presentation

CS 414 ARTIFICIAL INTELLIGENCE

ASSIGN AND SIMPLIFY EXAMPLE 2

SEARCH EXAMPLE 3

SEARCH EXAMPLE 4

SEARCH EXAMPLE 5

SEARCH EXAMPLE 6

SEARCH EXAMPLE 7

SEARCH EXAMPLE 8

SEARCH EXAMPLE 9

SEARCH EXAMPLE 10

SATISFIABILITY EXAMPLE • F = (x 1 V x 2) (x 1 V x 3 V x 4 V x 5) ( x 2) (x 2 V x 5) ( x 1) (x 1) 12

TRY THIS • Given a sentence find the satisfiability search tree 13

KNOWLEDGE BASE • A knowledge base KB is a set of sentences. Example KB: Jerry. Giving. Lecture (Today. Is. Tuesday Today. Is. Thursday( Jerry. Giving. Lecture • It is equivalent to a single long sentence: the conjunction of all sentences (Jerry. Giving. Lecture (Today. Is. Tuesday Today. Is. Thursday)) Jerry. Giving. Lecture 14

NATURAL DEDUCTION • Proof is a sequence of sentences First ones are premises (KB) Then, you can write down on line j the result of applying an inference rule to previous lines When is on a line, you know KB If inference rules are sound, then KB Modus ponens Modus tolens Andintroduction Andelimination 15

Modus ponens T T F F F T T F F T KB : is true KB : is true So that has to be true 16

Modus tolens T T T F F T T F F T T T KB : is true So that has to be true 17

And-introduction T T F F F T F F KB : is true So that has to be true 18

And-elimination T T F F F T F F KB : is true So that , has to be true 19

NATURAL DEDUCTION EXAMPLE Prove S Step Formula Derivation 1 P Q Given 2 P R Given 3 (Q R) S Given 20

NATURAL DEDUCTION EXAMPLE • KB: . 1 Jerry. Giving. Lecture (Today. Is. Tuesday Today. Is. Thursday(. 2 Jerry. Giving. Lecture Prove: Today. Is. Tuesday 21

Step Formula Derivation 1 Jerry. Giving. Lecture (Today. Is. Tuesday Today. Is. Thursday( Given 2 Jerry. Giving. Lecture Given 3 Jerry. Giving. Lecture (Today. Is. Tuesday Today. Is. Thursday( 4 )Today. Is. Tuesday Today. Is. Thursday) Jerry. Giving. Lecture 5 Jerry. Giving. Lecture (Today. Is. Tuesday Today. Is. Thursday ( Biconditional elimination to 1. Contrapositive to 4. 22

PROPOSITIONAL RESOLUTION 23

g g Resolution rule g g g T T T F F T T F T T T F F T F F T T F F F T F KB : is true KB : g is true So that g has to be true 24

Unit Resolution rule T T F T F F T F KB : is true So that has to be true 25

PROPOSITIONAL RESOLUTION EXAMPLE 26

RESOLUTION TREE • • KB : (A C D) (A D E) (A C) Prove : (D E) Negated conclusion : (D E) Convert KB in the CNF, So we have KB: 1. ( A C D) 2. (A D E) 3. ( A C) 4. D 5. E 27

RESOLUTION TREE 28

RESOLUTION TREE 29

RESOLUTION TREE 30

RESOLUTION TREE 31

RESOLUTION TREE 32