PP-2000-09: Local Variations on a Loose Theme: Modal Logic and Decidability

PP-2000-09: Marx, Maarten and Venema, Yde (2000) Local Variations on a Loose Theme: Modal Logic and Decidability. [Report]

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This chapter is about the satisfiability problem for modal logics and related formalisms. We discuss and explain the good computational behaviour of many modal systems. We show how finite and other simple structures are used in the proofs of various decidability and complexity results. In doing so, we introduce some of the most important proof methods that are used in establishing these results. Concerning the first theme, we single out some principles of the basic modal logic that determine its computational properties. The most important of these is the {\em looseness principle} which says that any satisfiable modal formula is satisfiable on a loose model; but we will also discuss two {\em locality principles} which are two formalizations of the intuition that the truth of a modal formula at a state of a model only depends on a small, local part of the model. Concerning the second theme, we give detailed expositions of the selection of points method, the method of filtration and the mosaic method. The chapter starts with a general introduction to modal logic, and then focuses on a detailed proof of the decidability of the basic modal system. After that, decidability is discussed for some variations of this basic modal system, and the picture is refined by taking complexity issues into account. Finally, the observation that modal logic is nothing but a nice, decidable fragment of first-order logic, is employed to generalize this to larger parts of first-order logic, such as the guarded and packed fragments. Keyword(s): modal logic, decidability, complexity, guarded fragments

Item Type: Report
Report Nr: PP-2000-09
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/36

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