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arXiv · 2008.09238

Logic-Induced Bisimulations

Jim de Groot·Helle Hvid Hansen·Alexander Kurz
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Abstract

We define a new logic-induced notion of bisimulation (called $\rho$-bisimulation) for coalgebraic modal logics given by a logical connection, and investigate its properties. We show that it is structural in the sense that it is defined only in terms of the coalgebra structure and the one-step modal semantics and, moreover, can be characterised by a form of relation lifting. Furthermore we compare $\rho$-bisimulations to several well-known equivalence notions, and we prove that the collection of bisimulations between two models often forms a complete lattice. The main technical result is a Hennessy-Milner type theorem which states that, under certain conditions, logical equivalence implies $\rho$-bisimilarity. In particular, the latter does \emph{not} rely on a duality between functors $\mathsf{T}$ (the type of the coalgebras) and $\mathsf{L}$ (which gives the logic), nor on properties of the logical connection $\rho$.

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Jim de Groot, Helle Hvid Hansen, Alexander Kurz. 2020-08-21. Logic-Induced Bisimulations. https://arxiv.org/abs/2008.09238

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