CUT-FREE COMPLETENESS FOR MODULAR HYPERSEQUENT CALCULI FOR MODAL LOGICS K, T, AND D
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Published:2020-07-21
Issue:4
Volume:14
Page:910-929
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ISSN:1755-0203
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Container-title:The Review of Symbolic Logic
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language:en
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Short-container-title:The Review of Symbolic Logic
Author:
BURNS SAMARA,ZACH RICHARD
Abstract
AbstractWe investigate a recent proposal for modal hypersequent calculi. The interpretation of relational hypersequents incorporates an accessibility relation along the hypersequent. These systems give the same interpretation of hypersequents as Lellman’s linear nested sequents, but were developed independently by Restall for S5 and extended to other normal modal logics by Parisi. The resulting systems obey Došen’s principle: the modal rules are the same across different modal logics. Different modal systems only differ in the presence or absence of external structural rules. With the exception of S5, the systems are modular in the sense that different structural rules capture different properties of the accessibility relation. We provide the first direct semantical cut-free completeness proofs for K, T, and D, and show how this method fails in the case of B and S4.
Publisher
Cambridge University Press (CUP)
Subject
Logic,Philosophy,Mathematics (miscellaneous)
Cited by
1 articles.
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1. Cut Elimination for Extended Sequent Calculi;Bulletin of the Section of Logic;2023-09-25