From Frame Properties to Hypersequent Rules in Modal Logics

We provide a general method for generating cutfree and/or analytic hypersequent Gentzen-type calculi for a variety of normal modal logics. The method applies to all modal logics characterized by Kripke frames, transitive Kripke frames, or symmetric Kripke frames satisfying some properties, given by...

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Bibliographic Details
Published in:2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 408 - 417
Main Author: Lahav, Ori
Format: Conference Proceeding
Language:English
Published: IEEE 01.06.2013
Subjects:
Calculus
Computer science
Context
cut-admissibility
Educational institutions
frame properties
hypersequent calculi
modal logic
proof theory
Semantics
Syntactics
ISBN:1479904139, 9781479904136
ISSN:1043-6871
Online Access:Get full text
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Summary:We provide a general method for generating cutfree and/or analytic hypersequent Gentzen-type calculi for a variety of normal modal logics. The method applies to all modal logics characterized by Kripke frames, transitive Kripke frames, or symmetric Kripke frames satisfying some properties, given by first-order formulas of a certain simple form. This includes the logics KT, KD, S4, S5, K4D, K4.2, K4.3, KBD, KBT, and other modal logics, for some of which no Gentzen calculi was presented before. Cut-admissibility (or analyticity in the case of symmetric Kripke frames) is proved semantically in a uniform way for all constructed calculi. The decidability of each modal logic in this class immediately follows.
ISBN:1479904139
9781479904136
ISSN:1043-6871
DOI:10.1109/LICS.2013.47