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Strong cut-elimination in sequent calculus using Klop's ι-translation and perpetual reductions

Published online by Cambridge University Press:  12 March 2014

Morten Heine Sørensen  and
PaweŁ Urzyczyn
Morten Heine Sørensen
Affiliation:
Formalit, Byenden 32, 4660 Store Heddinge, Denmark, E-mail: mhs@formalit.dk
PaweŁ Urzyczyn
Affiliation:
University of Warsaw, Institute of Informatics, Banacha2, 02-097 Warszawa, Poland, E-mail: urzy@mimuw.edu.pl
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Abstract

There is a simple technique, due to Dragalin. for proving strong cut-elimination for intuitionistic sequent calculus, but the technique is constrained to certain choices of reduction rules, preventing equally natural alternatives. We consider such a natural, alternative set of reduction rules and show that the classical technique is inapplicable. Instead we develop another approach combining two of our favorite tools—Klop's ι-translation and perpetual reductions.

These tools are of independent interest and have proved useful in a variety of settings; it is therefore natural to investigate, as we do here, what they have to offer the field of sequent calculus.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 3 , September 2008 , pp. 919 - 932
Copyright
Copyright © Association for Symbolic Logic 2008

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