From frame properties to hypersequent rules in modal logics

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Abstract

We provide a general method for generating cut-free and/or analytic hyper sequent Gent Zen-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.

Original languageEnglish
Article number6571573
Pages (from-to)408-417
Number of pages10
JournalProceedings - Symposium on Logic in Computer Science
DOIs
StatePublished - 2013
Event2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2013 - New Orleans, LA, United States
Duration: 25 Jun 201328 Jun 2013

Keywords

  • cut-Admissibility
  • frame properties
  • hypersequent calculi
  • modal logic
  • proof theory

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