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2014 Nested Sequents for Intuitionistic Logics
Melvin Fitting
Notre Dame J. Formal Logic 55(1): 41-61 (2014). DOI: 10.1215/00294527-2377869

Abstract

Relatively recently nested sequent systems for modal logics have come to be seen as an attractive deep-reasoning extension of familiar sequent calculi. In an earlier paper I showed that there was a strong connection between modal nested sequents and modal prefixed tableaux. In this paper I show that the connection continues to intuitionistic logic, both standard and constant domain, relating nested intuitionistic sequent calculi to intuitionistic prefixed tableaux. Modal nested sequent machinery generalizes one-sided sequent calculi—intuitionistic nested sequents similarly generalize two-sided sequents. It is noteworthy that the resulting system for constant domain intuitionistic logic is particularly simple. It amounts to a combination of intuitionistic propositional rules and classical quantifier rules, a combination that is known to be inadequate when conventional intuitionistic sequent systems are used.

Citation

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Melvin Fitting. "Nested Sequents for Intuitionistic Logics." Notre Dame J. Formal Logic 55 (1) 41 - 61, 2014. https://doi.org/10.1215/00294527-2377869

Information

Published: 2014
First available in Project Euclid: 20 January 2014

zbMATH: 1327.03006
MathSciNet: MR3161411
Digital Object Identifier: 10.1215/00294527-2377869

Subjects:
Primary: 03B20
Secondary: 03B44, 03B60, 68T15

Rights: Copyright © 2014 University of Notre Dame

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Vol.55 • No. 1 • 2014
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