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Logic Programming – Semantics

  • A Herbrand Model M is a Herbrand Interpretation which makes every formula true, so:
    • Every fact from the program is in M
    • For every rule in the program: If every positive literal in the body is in M, then the literal in the head is also in M
  • The model of a Logic Program P is the minimal Herbrand Model
    • This least Herbrand Model is the intersection of all Herbrand Models
    • Every program has a Herbrand Model. Thus every model also has a minimal Herbrand Model.
    • This model is uniquely defined only for programs without negation
    ⇒ A very intuitive and easy way to capture the semantics of LP
  • As soon as negation is allowed a unique minimal model is not guaranteed anymore

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