Lecture 11 of 41 Propositional Logic Wumpus World

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Lecture 11 of 41 Propositional Logic: Wumpus World Examples & Model Checking (Truth Tables)

Lecture 11 of 41 Propositional Logic: Wumpus World Examples & Model Checking (Truth Tables) William H. Hsu Department of Computer Science, KSU Canvas course redirector: http: //bit. ly/kstate-ai-class Course web site: http: //kdd. cs. ksu. edu/Courses/CIS 530/ Instructor home page: http: //www. cs. ksu. edu/~bhsu Reading for Today: § 7. 5 – 7. 8, p. 249 – 274, Russell & Norvig 3 rd edition Reading for Next Class: § 8. 1 – 8. 2, p. 285 – 300, Russell & Norvig 3 rd edition CIS 530 / 730 Artificial Intelligence Lecture 11 of 41 Part A (1 of 2) Department of computer science Kansas State University

Lecture Outline l Last Class: Intro to KR and Logic, § 7. 1 –

Lecture Outline l Last Class: Intro to KR and Logic, § 7. 1 – 7. 4 (p. 235 – 249), R&N 3 e l Today: Propositional Logic (PL), Proofs, § 7. 5 – 7. 7 (249 – 274), R&N 3 e Propositional calculus aka propositional logic (PL) Syntax: propositions and connectives Semantics: models, truth assignments (relation to Boolean algebra) Proof procedures: enumeration, forward/backward chaining Clausal form (conjunctive normal form, aka CNF) l Properties of sentences: entailment and provability, satisfiability and validity of proof rules: soundness and completeness l Reading for Next Class: § 8. 1 – 8. 2 (p. 285 – 300), R&N 3 e l Coming Weeks: KR/Reasoning in First-Order Logic (Ch. 8 – 10) l This Month: Alternative Knowledge Representations Elements of logic: ontology and epistemology Section III: Propositional (Ch. 7), first-order (8 – 9), temporal logic (10) Section V: Probability (Chapters 13 - 15), fuzzy logic (Chapter 14) CIS 530 / 730 Artificial Intelligence Lecture 11 of 41 Part A (1 of 2) Department of computer science Kansas State University

Where we Are Today CIS 530 / 730 Artificial Intelligence Lecture 11 of 41

Where we Are Today CIS 530 / 730 Artificial Intelligence Lecture 11 of 41 Part A (1 of 2) Department of computer science Kansas State University

Wumpus World Example: Review P? B OK P? OK Adapted from slides © 2004

Wumpus World Example: Review P? B OK P? OK Adapted from slides © 2004 -2010 S. Russell & P. Norvig. Reused with permission. CIS 530 / 730 Artificial Intelligence Lecture 11 of 41 Part A (1 of 2) Department of computer science Kansas State University

Wumpus Models [1] – [2]: Review KB {Rules} Breeze (1, 1) Breeze (2, 1)

Wumpus Models [1] – [2]: Review KB {Rules} Breeze (1, 1) Breeze (2, 1) Adapted from slides © 2004 -2010 S. Russell & P. Norvig. Reused with permission. CIS 530 / 730 Artificial Intelligence Lecture 11 of 41 Part A (1 of 2) Department of computer science Kansas State University

Wumpus Models [3] KB {Rules} Breeze (2, 1) Excludes possible world where neither (2,

Wumpus Models [3] KB {Rules} Breeze (2, 1) Excludes possible world where neither (2, 2) nor (3, 1) has a pit Adapted from slide © 2004 -2010 S. Russell & P. Norvig. Reused with permission. CIS 530 / 730 Artificial Intelligence Lecture 11 of 41 Part A (1 of 2) Department of computer science Kansas State University

Wumpus Models [4] Adapted from slides © 2004 -2010 S. Russell & P. Norvig.

Wumpus Models [4] Adapted from slides © 2004 -2010 S. Russell & P. Norvig. Reused with permission. CIS 530 / 730 Artificial Intelligence Lecture 11 of 41 Part A (1 of 2) Department of computer science Kansas State University

Inference © 2004 -2010 S. Russell & P. Norvig. Reused with permission. CIS 530

Inference © 2004 -2010 S. Russell & P. Norvig. Reused with permission. CIS 530 / 730 Artificial Intelligence Lecture 11 of 41 Part A (1 of 2) Department of computer science Kansas State University

Propositional Logic: Syntax © 2004 -2010 S. Russell & P. Norvig. Reused with permission.

Propositional Logic: Syntax © 2004 -2010 S. Russell & P. Norvig. Reused with permission. CIS 530 / 730 Artificial Intelligence Lecture 11 of 41 Part A (1 of 2) Department of computer science Kansas State University

Propositional Logic: Semantics © 2004 -2010 S. Russell & P. Norvig. Reused with permission.

Propositional Logic: Semantics © 2004 -2010 S. Russell & P. Norvig. Reused with permission. CIS 530 / 730 Artificial Intelligence Lecture 11 of 41 Part A (1 of 2) Department of computer science Kansas State University

Truth Tables for Connectives © 2004 -2010 S. Russell & P. Norvig. Reused with

Truth Tables for Connectives © 2004 -2010 S. Russell & P. Norvig. Reused with permission. CIS 530 / 730 Artificial Intelligence Lecture 11 of 41 Part A (1 of 2) Department of computer science Kansas State University

Wumpus World Sentences © 2004 -2010 S. Russell & P. Norvig. Reused with permission.

Wumpus World Sentences © 2004 -2010 S. Russell & P. Norvig. Reused with permission. CIS 530 / 730 Artificial Intelligence Lecture 11 of 41 Part A (1 of 2) Department of computer science Kansas State University

Truth Tables for Inference © 2004 -2010 S. Russell & P. Norvig. Reused with

Truth Tables for Inference © 2004 -2010 S. Russell & P. Norvig. Reused with permission. CIS 530 / 730 Artificial Intelligence Lecture 11 of 41 Part A (1 of 2) Department of computer science Kansas State University

Inference by Enumeration © 2004 -2010 S. Russell & P. Norvig. Reused with permission.

Inference by Enumeration © 2004 -2010 S. Russell & P. Norvig. Reused with permission. CIS 530 / 730 Artificial Intelligence Lecture 11 of 41 Part A (1 of 2) Department of computer science Kansas State University

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