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Proofs (cont’)

  • The concept of provability is important because it suggests how we can automate the determination of logical entailment

    • Starting from a set of premises Δ, we enumerate conclusions from this set

    • If a sentence φ appears, then it is provable from Δ and is, therefore, a logical consequence

    • If the negation of φ appears, then ¬φ is a logical consequence of Δ and φ is not logically entailed (unless Δ is inconsistent)

    • Note that it is possible that neither φ nor ¬φ will appear

Speaker notes:

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