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Nested Sequents for Intuitionistic Logics Melvin Fitting

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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 there was a strong connection between modal nested sequents and modal prefixed tableaux. In this paper I show 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

Topics: intuitionistic logic, constant domain logic, nested sequent, prefixed tableau Classification Codes, 03B20, 03B44, 03B60, 68T15
Year: 2012
OAI identifier: oai:CiteSeerX.psu:10.1.1.360.1885
Provided by: CiteSeerX
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