Abstract
We establish a generic upper bound \(\textsc {ExpTime} \) for reasoning with global assumptions in coalgebraic modal logics. Unlike earlier results of this kind, we do not require a tractable set of tableau rules for the instance logics, so that the result applies to wider classes of logics. Examples are Presburger modal logic, which extends graded modal logic with linear inequalities over numbers of successors, and probabilistic modal logic with polynomial inequalities over probabilities. We establish the theoretical upper bound using a type elimination algorithm. We also provide a global caching algorithm that offers potential for practical reasoning.
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Acknowledgements
We wish to thank Erwin R. Catesbeiana for remarks on unsatisfiability. Work of the first author forms part of the DFG project GenMod2 (SCHR 1118/5-2).
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Kupke, C., Pattinson, D., Schröder, L. (2015). Reasoning with Global Assumptions in Arithmetic Modal Logics. In: Kosowski, A., Walukiewicz, I. (eds) Fundamentals of Computation Theory. FCT 2015. Lecture Notes in Computer Science(), vol 9210. Springer, Cham. https://doi.org/10.1007/978-3-319-22177-9_28
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DOI: https://doi.org/10.1007/978-3-319-22177-9_28
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