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Products, or How to Create Modal Logics of High Complexity
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| Citations: | 4 - 0 self |
BibTeX
@MISC{Marx_products,or,
author = {Maarten Marx and Szabolcs Mikulas},
title = {Products, or How to Create Modal Logics of High Complexity},
year = {}
}
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Abstract
The aim of this paper is to exemplify the complexity of the satisability 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 satisability problem of the product KK.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 KK-satisability 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 ltration and selective generation techniques from modal logic. We put products of modal logics into an historic perspective and review the most important results. Keywords: modal logic, computational complexity 1 Introduction Taking products of modal logics is one of the most straightforward ways to combine two or more modal logics. The construction is dened as ...
Keyphrases
modal logic high complexity satisability problem product kk important result computational complexity main goal full language modal depth non-elementary decision procedure tight complexity bound main open problem nondeterministic exponential time straightforward way new proof matching upper bound historic perspective combine ltration modest contribution selective generation technique introduction taking product
