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Validity checking

  • Approach: To determine whether a set of sentences

    { φ1,…,φn }

    logically entails a sentence j, form the sentence

    ( φ1 ∧…∧ φn → φ )

    and check that it is valid.

  • To see how this method works, consider the previous example and write the tentative conclusion as shown below.

    (lovesAmyPat → lovesAmyQuincy) ∧ (ismonday → lovesAmyPat ∨ lovesAmyQuincy) → (ismonday → lovesAmyQuincy)

  • Then, form a truth table for our language with an added column for this sentence and check its satisfaction under each of the possible interpretations for our logical constants

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