Journal of Symbolic Logic

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

Morten Heine Sørensen and Paweł Urzyczyn

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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.

Article information

Source
J. Symbolic Logic, Volume 73, Issue 3 (2008), 919-932.

Dates
First available in Project Euclid: 27 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1230396755

Digital Object Identifier
doi:10.2178/jsl/1230396755

Mathematical Reviews number (MathSciNet)
MR2444276

Zentralblatt MATH identifier
1168.03041

Citation

Heine Sørensen, Morten; Urzyczyn, Paweł. Strong cut-elimination in sequent calculus using Klop’s ι-translation and perpetual reductions. J. Symbolic Logic 73 (2008), no. 3, 919--932. doi:10.2178/jsl/1230396755. https://projecteuclid.org/euclid.jsl/1230396755


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