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An Efficient Approach to Nominal Equalities in Hybrid Logic Tableaux
| Citations: | 5 - 4 self |
BibTeX
@MISC{Cerrito_anefficient,
author = {Serenella Cerrito and Marta Cialdea Mayer and Lab Ibisc and Université D’evry Val D’essonne},
title = {An Efficient Approach to Nominal Equalities in Hybrid Logic Tableaux},
year = {}
}
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Abstract
This is a draft version of a paper published on the Journal of Applied Non-Classical Logics. It should not be cited, quoted or reproduced. 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 loopchecking 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. 1
Keyphrases
nominal equality hybrid logic tableau efficient approach draft version applied non-classical logic so-called satisfaction operator hybrid logic internalized tableau system converse modality distinct name practical advantage strong termination property basic hybrid logic nominal equality specific many redundancy equality assertion specific rule application strategy tableau construction empirical result implemented system hybrid formula distinguished class proof system
