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First-Order Logic Unification and Inference Discussion

Explore first-order logic concepts such as unification, inference, and constraint logic in this lecture. Topics include resolution, Skolemization, and the unification algorithm. Get insights on logic programming and theorem proving in computer science.

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First-Order Logic Unification and Inference Discussion

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  1. Lecture 13 of 42 First-Order Logic: Unification, Inference Discussion: PS3, Constraint Logic Friday, 26 September 2008 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-2008/CIS730 Instructor home page: http://www.cis.ksu.edu/~bhsu Reading for Next Class: Section 9.2 – 9.4, p. 275 – 295, Russell & Norvig 2nd edition CIS 490 / 730: Artificial Intelligence

  2. 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 490 / 730: Artificial Intelligence

  3. First-Order Logic Problems CIS 490 / 730: Artificial Intelligence

  4. Decidability of First-Order Resolution CIS 490 / 730: Artificial Intelligence

  5. Skolemization Adapted from slides by S. Russell, UC Berkeley CIS 490 / 730: Artificial Intelligence

  6. Resolution Theorem Proving Adapted from slides by S. Russell, UC Berkeley CIS 490 / 730: Artificial Intelligence

  7. Example:Resolution Proof Adapted from slides by S. Russell, UC Berkeley CIS 490 / 730: Artificial Intelligence

  8. Offline Exercise:Read-and-Explain Pairs • For Class Participation (PS5) • With Your Assigned Partner(s) • Read: Chapter 10 R&N • By 14 Oct 2006 CIS 490 / 730: Artificial Intelligence

  9. Logic Programming vs. Imperative Programming Adapted from slides by S. Russell, UC Berkeley CIS 490 / 730: Artificial Intelligence

  10. A Look Ahead:Logic Programming as Horn Clause Resolution Adapted from slides by S. Russell, UC Berkeley CIS 490 / 730: Artificial Intelligence

  11. A Look Ahead:Logic Programming (Prolog) Examples Adapted from slides by S. Russell, UC Berkeley CIS 490 / 730: Artificial Intelligence

  12. CIS 490 / 730: Artificial Intelligence

  13. The Unification Algorithm CIS 490 / 730: Artificial Intelligence

  14. The Unification Algorithm [2] CIS 490 / 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 490 / 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 490 / 730: Artificial Intelligence

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