Products, or how to create modal logics of high complexity

Marx, M. and Mikulas, Szabolcs (2001) Products, or how to create modal logics of high complexity. Logic Journal of the IGPL 9 (1), pp. 71-82. ISSN 1367-0751.

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Official URL: https://doi.org/10.1093/jigpal/9.1.71

Abstract

The aim of this paper is to exemplify the complexity of the satisfiability problem of products of modal logics. Our main goal is to arouse interest for the main open problem in this area: a tight complexity bound for the satisfiability problem of the product K x K. At present, only non-elementary decision procedures for this problem are known. Our modest contribution is two-fold. We show that the problem of deciding K x K-satisfiability of formulas of modal depth two is already hard for nondeterministic exponential time, and provide a matching upper bound. For the full language, a new proof for decidability is given which combines filtration and selective generation techniques from modal logic. We put products of modal logics into an historic perspective and review the most important results.

Metadata

Item Type:	Article
School:	Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
Depositing User:	Sarah Hall
Date Deposited:	13 Jul 2021 14:54
Last Modified:	09 Aug 2023 12:51
URI:	https://eprints.bbk.ac.uk/id/eprint/45078

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