Reasoning with Global Assumptions in Arithmetic Modal Logics [chapter]

Clemens Kupke, Dirk Pattinson, Lutz Schröder
2015 Lecture Notes in Computer Science  
We establish a generic upper bound 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
more » ... oretical upper bound using a type elimination algorithm. We also provide a global caching algorithm that offers potential for practical reasoning.
doi:10.1007/978-3-319-22177-9_28 fatcat:ggkvnu5drjahtp4cdtwq24x7hu