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Model Theory – Non-monotonic Semantics (5)

  • Example setting:
    • An acceptable hypothesis H1 would be
          flies(X) ← bird(X)
    • It is acceptable because if fulfills the completeness and consistency criteria of the definite semantics
    • This realizes can inductive leap because flies(oliver) is true in
          M + ( B ∪ H ) = { bird(tweety), bird(oliver), flies(tweety), flies(oliver) }
  • Non-monotonic setting:
    • H1 is not a solution since there exists a substitution {X oliver} which makes the clause false in M +( B’ ) (the validity criteria is violated:
          M + ( B’ ) = { bird(tweety), bird(oliver), flies(tweety) }
          {X ← oliver}: flies(oliver) ← bird(oliver)
          {X ← tweety}: flies(tweety) ← bird(tweety)

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