A Hypersequent Calculus with Clusters for Linear Frames

Abstract : The logic Kt4.3 is the basic modal logic of linear frames. Along with its extensions, it is found at the core of linear-time temporal logics and logics on words. In this paper, we consider the problem of designing proof systems for these logics, in such a way that proof search yields decision procedures for validity with an optimal complexity—coNP in this case. In earlier work, Indrzejczak has proposed an ordered hypersequent calculus that is sound and complete for Kt4.3 but does not yield any decision procedure. We refine his approach, using a hypersequent structure that corresponds to weak rather than strict total orders, and using annotations that reflect the model-theoretic insights given by small models for Kt4.3. We obtain a sound and complete calculus with an associated coNP proof search algorithm. These results extend naturally to the cases of unbounded and dense frames, and to the complexity of the two-variable fragment of first-order logic over total orders.
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Communication dans un congrès
Guram Bezhanishvili; Giovanna D'Agostino; George Metcalfe; Thomas Studer. Twefth Conference on Advances in Modal Logic, Jul 2018, Bern, Switzerland. College Publications, 12, pp.36--55, 2018, Advances in Modal Logic
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Contributeur : Sylvain Schmitz <>
Soumis le : mardi 31 juillet 2018 - 17:02:08
Dernière modification le : lundi 10 septembre 2018 - 11:46:37

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  • HAL Id : hal-01756126, version 2

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David Baelde, Anthony Lick, Sylvain Schmitz. A Hypersequent Calculus with Clusters for Linear Frames. Guram Bezhanishvili; Giovanna D'Agostino; George Metcalfe; Thomas Studer. Twefth Conference on Advances in Modal Logic, Jul 2018, Bern, Switzerland. College Publications, 12, pp.36--55, 2018, Advances in Modal Logic. 〈hal-01756126v2〉

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