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Logic Programming Basics – Horn Logic

  • Syntactically a LP rule is a First Order Logic Horn Clause
  • The semantics of LP are different form the standard Tarski style FOL semantics (details later)
    • Herbrand semantics differ from FOL smeantics in the structures it considers to be models (details later)
      → Minimal model semantics
  • A FOL Horn clause is a disjunction of literals with one positive literal, with all variables universally quantified:
    • (∀) ¬C1 ∨ … ∨ ¬Cn ∨ H
  • This can be rewritten to closer correspond to a rule-like form:
    • (∀) C1 ∧ … ∧ Cn → H
  • In LP systems usually the following (non First Order Logic) syntax is used:
    • H :- C1,...,Cn
  • Such rules can be evaluated very efficiently , since the resolution of two Horn clauses is a again a Horn clause

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