(Metric) Bisimulation Games and Real-Valued Modal Logics for Coalgebras

Authors Barbara König, Christina Mika-Michalski

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Barbara König
  • Universität Duisburg-Essen, Germany
Christina Mika-Michalski
  • Universität Duisburg-Essen, Germany

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Barbara König and Christina Mika-Michalski. (Metric) Bisimulation Games and Real-Valued Modal Logics for Coalgebras. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 37:1-37:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Behavioural equivalences can be characterized via bisimulations, modal logics and spoiler-defender games. In this paper we review these three perspectives in a coalgebraic setting, which allows us to generalize from the particular branching type of a transition system. We are interested in qualitative notions (classical bisimulation) as well as quantitative notions (bisimulation metrics). Our first contribution is to introduce a spoiler-defender bisimulation game for coalgebras in the classical case. Second, we introduce such games for the metric case and furthermore define a real-valued modal coalgebraic logic, from which we can derive the strategy of the spoiler. For this logic we show a quantitative version of the Hennessy-Milner theorem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Concurrency
  • Theory of computation → Logic and verification
  • coalgebra
  • bisimulation games
  • spoiler-defender games
  • behavioural metrics
  • modal logic


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