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Journal of Logic and Computation Advance Access originally published online on August 12, 2006
Journal of Logic and Computation 2006 16(6):737-763; doi:10.1093/logcom/exl008
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© The Author, 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

Tableau-based Decision Procedures for Hybrid Logic

Thomas Bolander

Informatics and Mathematical Modelling, Richard Petersens Plads, Building 322, Technical University of Denmark, DK-2800 Lyngby, Denmark.

Torben Braüner

Department of Computer Science, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark. E-mail: torben{at}ruc.dk

E-mail: tb{at}imm.dtu.dk


  Abstract

Hybrid logics are a principled generalization of both modal logics and description logics. It is well known that various hybrid logics without binders are decidable, but decision procedures are usually not based on tableau systems, a kind of formal proof procedure that lends itself to computer implementation. In this article, we give four different tableau-based decision procedures for a very expressive hybrid logic including the universal modality; three of the procedures are based on different tableau systems, and one procedure is based on a Gentzen system. The decision procedures make use of so-called loop-checks, which is a standard technique used in connection with tableau systems for other logics, namely, prefixed tableau systems for transitive modal logics as well as for certain description logics. The loop-checks used in our four decision procedures are similar, but the four proof systems on which the procedures are based constitute a spectrum of different systems: prefixed and internalized systems, tableau and Gentzen systems.

Keywords: Hybrid logic; modal logic; universal modality; tableau systems; decision procedures


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