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Admissibility of structural rules for contraction-free systems of intuitionistic logic

Published online by Cambridge University Press:  12 March 2014

Roy Dyckhoff  and
Sara Negri
Roy Dyckhoff
Affiliation:
School of Computer Science, St Andrews University, St Andrews. Fife KY16 9SS. Scotland, E-mail:rd@dcs.st-and.ac.uk
Sara Negri
Affiliation:
Department of Philosophy, PL 24. Unioninkatu 40 B, 00014University of Helsinki, Finland, E-mail:negri@helsinki.fi
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Abstract

We give a direct proof of admissibility of cut and contraction for the contraction-free sequent calculus G4ip for intuitionistic propositional logic and for a corresponding multi-succedent calculus: this proof extends easily in the presence of quantifiers, in contrast to other, indirect, proofs, i.e., those which use induction on sequent weight or appeal to admissibility of rules in other calculi.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 4 , December 2000 , pp. 1499 - 1518
Copyright
Copyright © Association for Symbolic Logic 2000

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