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Lecture 15 of 42

Lecture 15 of 42. First-Order Logic: Resolution Discussion: AI Applications 2 of 3. Wednesday, 27 September 2007 William H. Hsu Department of Computing and Information Sciences, KSU KSOL course page: http://snipurl.com/v9v3

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Lecture 15 of 42

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  1. Lecture 15 of 42 First-Order Logic: Resolution Discussion: AI Applications 2 of 3 Wednesday, 27 September 2007 William H. Hsu Department of Computing and Information Sciences, KSU KSOL course page: http://snipurl.com/v9v3 Course web site: http://www.kddresearch.org/Courses/Fall-2007/CIS730 Instructor home page: http://www.cis.ksu.edu/~bhsu Reading for Next Class: Section 9.5 – 9.6, p. 295 - 310, Russell & Norvig 2nd edition CIS 530 / 730: Artificial Intelligence

  2. Lecture Outline • Reading for Next Class: Section 9.5 – 9.6, R&N 2e • Today • Resolution theorem proving • Prolog as related to resolution • Decidability of SAT, VALID • Recursive, Recursive Enumerable, and Co-RE languages • MP4 & 5 preparations • Friday • Logic programming in real life • Industrial-strength Prolog • Lead-in to MP4 • Next Week CIS 530 / 730: Artificial Intelligence

  3. Logical Agents:Review Adapted from slides by S. Russell, UC Berkeley CIS 530 / 730: Artificial Intelligence

  4. Example:Backward Chaining Adapted from slides by S. Russell, UC Berkeley CIS 530 / 730: Artificial Intelligence

  5. Backward Chaining • Question: How Does This Relate to Proof by Refutation? • Answer • Suppose ¬Query, For The Sake Of Contradiction (FTSOC) • Attempt to prove that KB  ¬Query ⊢ CIS 530 / 730: Artificial Intelligence

  6. Resolution Inference Rule Adapted from slides by S. Russell, UC Berkeley CIS 530 / 730: Artificial Intelligence

  7. Conjunctive Normal (akaClausal) Form:Conversion (Nilsson) and Mnemonic • Implications Out • Negations Out • Standardize Variables Apart • Existentials Out (Skolemize) • Universals Made Implicit • Distribute And Over Or (i.e., Disjunctions In) • Operators Out • Rename Variables • A Memonic for Star Trek: The Next Generation Fans • Captain Picard: • I’ll Notify Spock’s Eminent Underground Dissidents On Romulus • I’ll Notify Sarek’s Eminent Underground Descendant On Romulus Adapted from slides by S. Russell, UC Berkeley CIS 530 / 730: Artificial Intelligence

  8. Skolemization Adapted from slides by S. Russell, UC Berkeley CIS 530 / 730: Artificial Intelligence

  9. Resolution Theorem Proving Adapted from slides by S. Russell, UC Berkeley CIS 530 / 730: Artificial Intelligence

  10. Example:Resolution Proof Adapted from slides by S. Russell, UC Berkeley CIS 530 / 730: Artificial Intelligence

  11. Offline Exercise:Read-and-Explain Pairs • For Class Participation (PS5) • With Your Assigned Partner(s) • Read: Chapter 10 R&N • By 13 Oct 2007 CIS 530 / 730: Artificial Intelligence

  12. Logic Programming vs. Imperative Programming Adapted from slides by S. Russell, UC Berkeley CIS 530 / 730: Artificial Intelligence

  13. A Look Ahead:Logic Programming as Horn Clause Resolution Adapted from slides by S. Russell, UC Berkeley CIS 530 / 730: Artificial Intelligence

  14. A Look Ahead:Logic Programming (Prolog) Examples Adapted from slides by S. Russell, UC Berkeley CIS 530 / 730: Artificial Intelligence

  15. Summary Points • From Propositional to First-Order Proofs • Generalized Modus Ponens • Resolution • Unification Problem • Roles in Computer Science • Type inference • Theorem proving • What do these have to do with each other? • Search Patterns • Forward chaining • Backward chaining • Fan-in, fan-out CIS 530 / 730: Artificial Intelligence

  16. Terminology • From Propositional to First-Order Proofs • Generalized Modus Ponens • Resolution • Unification Problem • Most General Unifier (MGU) • Roles in Computer Science • Type inference • Theorem proving • What do these have to do with each other? • Search Patterns • Forward chaining • Backward chaining • Fan-in, fan-out CIS 530 / 730: Artificial Intelligence

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