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Important Properties for Inference

  • Soundness: If KB ⊢ Q then KB ⊧ Q

    • If Q is derived from a set of sentences KB using a set of inference rules, then Q is entailed by KB

    • Hence, inference produces only real entailments, or any sentence that follows deductively from the premises is valid

    • Only sentences that logically follow will be derived

  • Completeness: If KB ⊧ Q then KB ⊢ Q

    • If Q is entailed by a set of sentences KB, then Q can also be derived from KB using the rules of inference

    • Hence, inference produces all entailments, or all valid senteces can be proved from the premises

    • All the sentences that logically follow can be derived


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