### Decision procedures for some strong hybrid logics

Andrzej Indrzejczak, Michał Zawidzki

DOI: http://dx.doi.org/10.12775/LLP.2013.022

#### 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 TH(@,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 SH(@,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; modal logics; tableau calculi; sequent calculi; decision procedures; automated reasoning

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ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)