Logic and Logical Philosophy 22 (4):389-409 (2013)

Authors
Michał Zawidzki
University of Lodz
Abstract
Hybrid logics are extensions of standard modal logics, which significantly increase the expressive power of the latter. Since most of hybrid logics are known to be decidable, decision procedures for them is a widely investigated field of research. So far, several tableau calculi for hybrid logics have been presented in the literature. In this paper we introduce a sound, complete and terminating tableau calculus T H(@,E,D, ♦ −) for hybrid logics with the satisfaction operators, the universal modality, the difference modality and the inverse modality as well as the corresponding sequent calculus S H(@,E,D, ♦ −) . They not only uniformly cover relatively wide range of various hybrid logics but they are also conceptually simple and enable effective search for a minimal model for a satisfiable formula. The main novelty is the exploitation of the unrestricted blocking mechanism introduced as an explicit, sound tableau rule
Keywords hybrid logics  tableau calculi  decision procedures  modal logics  automated reasoning  sequent calculi
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DOI 10.12775/LLP.2013.022
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References found in this work BETA

Terminating Tableau Systems for Hybrid Logic with Difference and Converse.Mark Kaminski & Gert Smolka - 2009 - Journal of Logic, Language and Information 18 (4):437-464.
Lightweight Hybrid Tableaux.Guillaume Hoffmann - 2010 - Journal of Applied Logic 8 (4):397-408.
Nominal Substitution at Work with the Global and Converse Modalities.Serenella Cerrito & Marta Cialdea Mayer - 2010 - In Lev Beklemishev, Valentin Goranko & Valentin Shehtman (eds.), Advances in Modal Logic, Volume 8. CSLI Publications. pp. 59-76.

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Citations of this work BETA

Simple Cut Elimination Proof for Hybrid Logic.Andrezj Indrzejczak - 2016 - Logic and Logical Philosophy 25 (2):129-141.

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