A quasipolynomial cut-elimination procedure in deep inference via atomic flows and threshold formulae

Authors:
Paola Bruscoli;Alessio Guglielmi;Tom Gundersen;Michel Parigot
Affiliations:
University of Bath, UK and LORIA & INRIA Nancy-Grand Est, France;University of Bath, UK and LORIA & INRIA Nancy-Grand Est, France;University of Bath, UK and LORIA & INRIA Nancy-Grand Est, France;Laboratoire PPS, UMR, CNRS & Université Paris 7, France
Venue:
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Year:
2010

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Abstract

Jeřábek showed in 2008 that cuts in propositional-logic deepinference proofs can be eliminated in quasipolynomial time. The proof is an indirect one relying on a result of Atserias, Galesi and Pudlák about monotone sequent calculus and a correspondence between this system and cut-free deep-inference proofs. In this paper we give a direct proof of Jeřábek's result: we give a quasipolynomial-time cut-elimination procedure in propositional-logic deep inference. The main new ingredient is the use of a computational trace of deep-inference proofs called atomic flows, which are both very simple (they trace only structural rules and forget logical rules) and strong enough to faithfully represent the cutelimination procedure.