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Deductive (proof) systems

  • Semantic methods for checking logical entailment have the merit of being conceptually simple; they directly manipulate interpretations of sentences

  • Unfortunately, the number of interpretations of a language grows exponentially with the number of logical constants.

    • When the number of logical constants in a propositional language is large, the number of interpretations may be impossible to manipulate.

  • Deductive (proof) systems provide an alternative way of checking and communicating logical entailment that addresses this problem

    • In many cases, it is possible to create a “proof” of a conclusion from a set of premises that is much smaller than the truth table for the language;

    • Moreover, it is often possible to find such proofs with less work than is necessary to check the entire truth table

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