From frame properties to hypersequent rules in modal logics

Ori Lahav

doi:10.1109/LICS.2013.47

From frame properties to hypersequent rules in modal logics

Ori Lahav

School of Computer Science

Tel Aviv University

Research output: Contribution to journal › Conference article › peer-review

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 language	English
Article number	6571573
Pages (from-to)	408-417
Number of pages	10
Journal	Proceedings - Symposium on Logic in Computer Science
DOIs	https://doi.org/10.1109/LICS.2013.47
State	Published - 2013
Event	2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2013 - New Orleans, LA, United States Duration: 25 Jun 2013 → 28 Jun 2013

Keywords

cut-Admissibility
frame properties
hypersequent calculi
modal logic
proof theory

All Science Journal Classification (ASJC) codes

Software
General Mathematics

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10.1109/LICS.2013.47

Cite this

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From frame properties to hypersequent rules in modal logics

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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