Notes 9: Inference in Firstorder logic

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Notes 9Inference in First-order logic

• ICS 171 Fall 2006

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Unification

• To unify Knows(John,x) and Knows(y,z),
• ? y/John, x/z or ? y/John, x/John,
  z/John
  
• The first unifier is more general than the
  second.
  
• There is a single most general unifier (MGU) that
  is unique up to renaming of variables.
  
• MGU y/John, x/z

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The unification algorithm
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The unification algorithm
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Logic programming Prolog

• Algorithm Logic Control
• Basis backward chaining with Horn clauses
  bells whistles
• Widely used in Europe, Japan (basis of 5th
  Generation project)
• Compilation techniques ? 60 million LIPS
• Program set of clauses head - literal1,
  literaln.
  
• criminal(X) - american(X), weapon(Y),
  sells(X,Y,Z), hostile(Z).
  
• Depth-first, left-to-right backward chaining
• Built-in predicates for arithmetic etc., e.g., X
  is YZ3
• Built-in predicates that have side effects (e.g.,
  input and output
  
• predicates, assert/retract predicates)
• Closed-world assumption ("negation as failure")
• e.g., given alive(X) - not dead(X).
• alive(joe) succeeds if dead(joe) fails

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Prolog

• Appending two lists to produce a third
• append(,Y,Y).
• append(XL,Y,XZ) - append(L,Y,Z).
• query append(A,B,1,2) ?
• answers A B1,2
• A1 B2
• A1,2 B

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