Reasoning with Global Assumptions in Arithmetic Modal Logics

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9210)


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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of StrathclydeGlasgowUK
  2. 2.Australian National UniversityCanberraAustralia
  3. 3.Friedrich-Alexander Universität Erlangen-NürnbergErlangenGermany

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