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Entailment and Derivation

  • Entailment: KB ⊧ Q

    • Entailment is a relation that is concerned with the semantics of statements

    • Q is entailed by KB (a set of premises or assumptions) if and only if there is no logically possible world in which Q is false while all the premises in KB are true

    • Stated positively: Q is entailed by KB if and only if the conclusion is true in every possible world in which all the premises in KB are true

  • Provability: KB ⊢ Q

    • Provability is a syntactic relation

    • We can derive Q from KB if there is a proof consisting of a sequence of valid inference steps starting from the premises in KB and resulting in Q

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