PP-2000-13: Products, or How to Create Modal Logics of High Complexity

PP-2000-13: Marx, Maarten and Mikulás, Szabolcs (2000) Products, or How to Create Modal Logics of High Complexity. [Report]

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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 \textbf{K}$\times$\textbf{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 \textbf{K}$\times$\textbf{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. Keyword(s): modal logic, computational complexity

Item Type: Report
Report Nr: PP-2000-13
Series Name: Prepublication (PP) Series
Year: 2000
Date Deposited: 12 Oct 2016 14:36
Last Modified: 12 Oct 2016 14:36
URI: https://eprints.illc.uva.nl/id/eprint/40

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