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Model Theory – Definite Semantics

  • In most ILP practical systems background theory and hypotheses are restricted to being definite clauses
    • Clause: A disjunction of literals
    • Horn Clause: A clause with at most one positive literal
    • Definite Clause: A Horn clause with exactly one positive literal
  • This setting has the advantage that definite clause theory T has a unique minimal Herbrand model M +( T )
    • Any logical formulae is either true or false in this minimal model (all formulae are decidable and the Closed World Assumption holds)

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