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    Modal decision problems

    Wolter, F. and Zakharyaschev, Michael (2007) Modal decision problems. In: Blackburn, P. and van Benthem, J.F.A.K. and Wolter, F. (eds.) Handbook of Modal Logic. Studies in logic and practical reasoning 3. North-Holland, pp. 427-489. ISBN 9780444516909.

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    This chapter analyzes the development of modal logic within the research framework formulated for a historical analysis of mathematical modal logic. Modal logic is decidable when interpreted on the class of all models. By changing the interpreting class of models, the logical validities can be changed, and decidability is typically lost when the structural conditions come too close to “danger zones” such as tiling patterns, arithmetic, or other structures allowing for Turing machine computation. The chapter examines how the properties as decidability, the finite model property, and finite axiomatizability are distributed across the lattice of normal modal logics. The emphasis is on providing general results and drawing attention to important open questions. Thomason's explication of the semantical part of the research programme is discussed. The appropriate refinement of the syntactical part of the research programme for normal modal logics and solutions to it given by Chagrov and Thomason are described. The logics axiomatized by formulas satisfying certain syntactical constraints, in particular, Sahlqvist formulas, uniform formulas, and modal reduction principles are considered. The Big Research Programme for the class of all tense logics of linear flows of time is also described.


    Item Type: Book Section
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Sarah Hall
    Date Deposited: 25 Oct 2021 16:48
    Last Modified: 09 Aug 2023 12:52


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