An efficient approach to nominal equalities in hybrid logic tableaux

Journal of Applied Non-Classical Logics 20 (1-2):39-61 (2010)
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Abstract

Basic hybrid logic extends modal logic with the possibility of naming worlds by means of a distinguished class of atoms (called nominals) and the so-called satisfaction operator, that allows one to state that a given formula holds at the world named a, for some nominal a. Hence, in particular, hybrid formulae include “equality” assertions, stating that two nominals are distinct names for the same world. The treatment of such nominal equalities in proof systems for hybrid logics may induce many redundancies. This paper introduces an internalized tableau system for basic hybrid logic, significantly reducing such redundancies. The calculus enjoys a strong termination property: tableau construction terminates without relying on any specific rule application strategy, and no loop-checking is needed. The treatment of nominal equalities specific of the proposed calculus is briefly compared to other approaches. Its practical advantages are demonstrated by empirical results obtained by use of implemented systems. Finally, it is briefly shown how to extend the calculus to include the global and converse modalities.

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Citations of this work

Decision procedures for some strong hybrid logics.Andrzej Indrzejczak & Michał Zawidzki - 2013 - Logic and Logical Philosophy 22 (4):389-409.
Nominal Substitution at Work with the Global and Converse Modalities.Serenella Cerrito & Marta Cialdea Mayer - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 59-76.

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References found in this work

Modal Logic: Graph. Darst.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - New York: Cambridge University Press. Edited by Maarten de Rijke & Yde Venema.
Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
Modal logic.Yde Venema - 2000 - Philosophical Review 109 (2):286-289.
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.

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