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Logic Journal of IGPL Advance Access published online on October 17, 2007
Logic Journal of IGPL, doi:10.1093/jigpal/jzm040
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

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

Marcelo Finger

University of Sao Paulo, Brazil. E-mail: mfinger{at}ime.usp.br

Dov Gabbay

King's College, London. E-mail: dg{at}dcs.kcl.ac.uk


  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.

Key Words: Proof Theory • non-analytic cuts • sequent calculus • tableaux


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