CIS730-Lecture-15-20050928

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Lecture 15 of 42
First-Order Logic 3 of 4 Unification and
Resolution
Wednesday, 28 September 2005 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
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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
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First-Order Satisfiability and ValidityUndecidab
ility and Semi-Decidability
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Skolemization
Adapted from slides by S. Russell, UC Berkeley
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Resolution Theorem Proving
Adapted from slides by S. Russell, UC Berkeley
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ExampleResolution Proof
Adapted from slides by S. Russell, UC Berkeley
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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

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Logic Programming vs. Imperative Programming
Adapted from slides by S. Russell, UC Berkeley
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A Look AheadLogic Programming as Horn Clause
Resolution
Adapted from slides by S. Russell, UC Berkeley
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A Look AheadLogic Programming (Prolog) Examples
Adapted from slides by S. Russell, UC Berkeley
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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

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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