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CIS 730 (Introduction to Artificial Intelligence) Lecture 14 of 30

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CIS 730: Introduction to Artificial Intelligence. Lecture 14 ... Conversion (Nilsson) and Mnemonic. Implications Out. Negations Out. Standardize Variables Apart ... – PowerPoint PPT presentation

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Title: CIS 730 (Introduction to Artificial Intelligence) Lecture 14 of 30


1
Lecture 14 of 41
Resolution Theorem Proving
Monday, 27 September 2004 William H.
Hsu Department of Computing and Information
Sciences, KSU http//www.kddresearch.org http//ww
w.cis.ksu.edu/bhsu Reading Chapter 9, Russell
and Norvig 2e Handout, Nilsson and Genesereth
2
Conjunctive Normal (aka Clausal) FormConversion
(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
  • Ill Notify Spocks Eminent Underground
    Dissidents On Romulus
  • Ill Notify Sareks Eminent Underground
    Descendant On Romulus

Adapted from slides by S. Russell, UC Berkeley
3
Skolemization
Adapted from slides by S. Russell, UC Berkeley
4
Resolution Theorem Proving
Adapted from slides by S. Russell, UC Berkeley
5
ExampleResolution Proof
Adapted from slides by S. Russell, UC Berkeley
6
Offline ExerciseRead-and-Explain Pairs
  • For Class Participation (PS3)
  • With Your Term Project Partner or Assigned
    Partner(s)
  • Read Chapter 10 RN
  • By Fri 08 Oct 2004

7
Logic Programming vs. Imperative Programming
Adapted from slides by S. Russell, UC Berkeley
8
A Look AheadLogic Programming as Horn Clause
Resolution
Adapted from slides by S. Russell, UC Berkeley
9
A Look AheadLogic Programming (Prolog) Examples
Adapted from slides by S. Russell, UC Berkeley
10
Summary Points
  • Previously Logical Agents and Calculi, FOL in
    Practice
  • Today Resolution Theorem Proving
  • Conjunctive Normal Form (clausal form)
  • Inference rule
  • Single-resolvent form
  • General form
  • Proof procedure refutation
  • Decidability properties
  • FOL-SAT
  • FOL-NOT-SAT (language of unsatisfiable sentences
    complement of FOL-SAT)
  • FOL-VALID
  • FOL-NOT-VALID
  • Thursday
  • More Prolog
  • Implementing unification

11
Terminology
  • Properties of Knowledge Bases (KBs)
  • Satisfiability and validity
  • Entailment and provability
  • Properties of Proof Systems
  • Soundness and completeness
  • Decidability, semi-decidability, undecidability
  • Normal Forms CNF, DNF, Horn Clauses vs. Terms
  • Resolution
  • Refutation
  • Satisfiability, Validity
  • Unification
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