LJQ: a strongly focused calculus for intuitionistic logic

Authors:
Roy Dyckhoff;Stéphane Lengrand
Affiliations:
School of Computer Science, University of St Andrews, St Andrews, Fife, Scotland;School of Computer Science, University of St Andrews, St Andrews, Fife, Scotland
Venue:
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Year:
2006

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Abstract

LJQ is a focused sequent calculus for intuitionistic logic, with a simple restriction on the first premisss of the usual left introduction rule for implication. We discuss its history (going back to about 1950, or beyond), present the underlying theory and its applications both to terminating proof-search calculi and to call-by-value reduction in lambda calculus.