(Metric) Bisimulation Games and Real-Valued Modal Logics for Coalgebras
(Metric) Bisimulation Games and Real-Valued Modal Logics for Coalgebras
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DOI：
10.4230/lipics.concur.2018.37
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发表时间：
2017-05
期刊：
影响因子：
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通讯作者：
Barbara König;Christina Mika-Michalski
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文献类型：
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作者：
Barbara König;Christina Mika-Michalski
行为等价可以通过互模拟、模态逻辑和破坏者-防御者博弈来表征。在本文中，我们回顾了这三个角度在一个coalgebraic设置，这使我们能够概括从特定的分支类型的过渡系统。我们感兴趣的定性概念（经典互模拟）以及定量概念（互模拟度量）。我们的第一个贡献是在经典的情况下，介绍了一个破坏者-防御者互模拟游戏的余代数。其次，我们介绍了这种游戏的度量的情况下，并进一步定义了一个实值模态共代数逻辑，从中我们可以得出的策略的扰流板。对于这个逻辑，我们展示了Hennessy-Milner定理的一个定量版本。
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.