Semantic cut elimination in the intuitionistic sequent calculus

Authors:
Olivier Hermant
Affiliations:
Projet LogiCal, Pôle Commun de Recherche en Informatique du plateau de Saclay, CNRS, École Polytechnique, INRIA, Université Paris-Sud
Venue:
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Year:
2005

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Abstract

Cut elimination is a central result of the proof theory. This paper proposes a new approach for proving the theorem for Gentzen's intuitionistic sequent calculus LJ, that relies on completeness of the cut-free calculus with respect to Kripke Models. The proof defines a general framework to extend the cut elimination result to other intuitionistic deduction systems, in particular to deduction modulo provided the rewrite system verifies some properties. We also give an example of rewrite system for which cut elimination holds but that doesn't enjoys proof normalization.