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Logic Programming - Negation

  • How do we handle negation in Logic Programs?
  • Horn Logic only permits negation in limited form
    • Consider (∀) ¬C1 ∨ … ∨ ¬Cn ∨ H
  • Special solution: Negation-as-failure (NAF):
    • Whenever a fact is not entailed by the knowledge base, its negation is entailed
    • This is a form of “Default reasoning”
    • This introduces non-monotonic behavior (previous conclusions might need to be revised during the inference process)
  • NAF is not classical negation and pushes LP beyond classical First Order Logic
  • This allows a form of negation in rules:
    • (∀) C1 ∧ … ∧ Ci ∧ not Cn → H
    • H :- B1, … Bi, not Bn

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