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

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

DOI: 10.1093/jigpal/jzm040

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@article{Finger2007EqualRF, title={Equal Rights for the Cut: Computable Non-analytic Cuts in Cut-based Proofs}, author={Marcelo Finger and Dov M. Gabbay}, journal={Logic Journal of the IGPL}, year={2007}, volume={15}, pages={553-575} }