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Resolution Theorem Proving - Artificial Intelligence - Lecture Slides, Slides of Artificial Intelligence

Some concept of Artificial Intelligence are Agents and Problem Solving, Autonomy, Programs, Classical and Modern Planning, First-Order Logic, Resolution Theorem Proving, Search Strategies, Structure Learning. Main points of this lecture are: Resolution Theorem Proving, Implications Out, Negations Out, Standardize Variables Apart, Existentials Out, Universals Made Implicit, Distribute and Over, Operators Out, Rename Variables, Memonic

Typology: Slides

2012/2013

Uploaded on 04/29/2013

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Lecture 14 of 41
Resolution Theorem Proving
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Lecture 14 of 41

Resolution Theorem Proving

Conjunctive Normal ( aka Clausal) 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

Resolution Theorem Proving

Example:

Resolution Proof

Adapted from slides by S. Russell, UC Berkeley

Logic Programming vs. Imperative Programming

Adapted from slides by S. Russell, UC Berkeley

A Look Ahead:

Logic Programming as Horn Clause Resolution

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

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