Equal Rights for the Cut: Computable Non-analytic Cuts in Cut-based Proofs

Logic Journal of the IGPL 15 (5-6):553-575 (2007)
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Abstract

This work studies the structure of proofs containing non-analytic cuts in the cut-based system, a sequent inference system in which the cut rule is not eliminable and the only branching rule is the cut. Such sequent system is invertible, leading to the KE-tableau decision method. We study the structure of such proofs, proving the existence of a normal form for them in the form of a comb-tree proof. We then concentrate on the problem of efficiently computing non-analytic cuts. For that, we study the generalisation of techniques present in many modern theorem provers, namely the techniques of conflict-driven formula learning

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Dov Gabbay
Hebrew University of Jerusalem

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