Confluence of Cut-Elimination Procedures for the Intuitionistic Sequent Calculus

Authors:
Kentaro Kikuchi
Affiliations:
RIEC, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan
Venue:
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Year:
2007

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Abstract

We prove confluence of two cut-elimination procedures for theimplicational fragment of a standard intuitionistic sequentcalculus. One of the cut-elimination procedures uses global prooftransformations while the other consists of local ones. Both ofthem include permutation of cuts to simulateβ-reduction in an isomorphic image of theλ-calculus. We establish the confluence propertiesthrough a conservativity result on the cut-eliminationprocedures.