Modal Tableaux with Propagation Rules and Structural Rules
Castilho, Marcos and Farinas del Cerro, Luis and Gasquet, Olivier and Herzig, Andreas
Abstract:
In this paper we generalize the existing tableau methods
for modal logics.
First of all, while usual modal tableaux are based on trees, our basic
structures are rooted directed acyclic graphs (RDAG). This allows
natural tableau rules for some modal logics that are difficult to
capture in the usual way (such as those having an accessibility
relation that is dense or confluent).
Second, tableau rules rewrite patterns, which are (schemas of) parts
of a RDAG. A particular case of these rules are the single-step rules
recently proposed by Massacci. This allows in particular
tableau rule presentations for K5, KD5, K45, KD45, and S5 that respect
the subformula property.
Third, we divide modal tableau rules into propagation rules and
structural rules. Structural rules construct new edges and nodes
(without adding formulas to nodes), while propagation rules add
formulas to nodes. This distinction allows to prove completeness in a
modular way.
Bibtex-entry:
@Article{CaFaGaHe-FI97,
author = "Castilho, M. and Fari{\~{n}}as del Cerro, L. and Gasquet, O. and Herzig, A." ,
title = "Modal Tableaux with Propagation Rules and Structural Rules",
journal = "Fundamenta Informaticae",
year = "1997",
volume = "32",
number = "3/4",
pages = "",
}
https://www.irit.fr/~Olivier.Gasquet