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Semantics – Some Informal Definitions

  • Given the truth values of all symbols in a sentence, it can be “evaluated” to determine its truth value (True or False)

  • A model for a KB is a “possible world” (assignment of truth values to propositional symbols) in which each sentence in the KB is True

  • A valid sentence or tautology is a sentence that is True under all interpretations, no matter what the world is actually like or how the semantics are defined (example: “It’s raining or it’s not raining”)

  • An inconsistent sentence or contradictio n is a sentence that is False under all interpretations (the world is never like what it describes, as in “It’s raining and it’s not raining”)

  • P entails Q , written P ⊧ Q, means that whenever P is True, so is Q; in other words, all models of P are also models of Q

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