Logic-induced Bisimulations

Jim de Groot, Helle Hvid Hansen, Alexander Kurz

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We define a new logic-induced notion of bisimulation (called ρ-bisimulation) for coal-
gebraic 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 coalge-
bra structure and the one-step modal semantics and, moreover, can be characterised
by a form of relation lifting. Furthermore we compare ρ-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 ρ-bisimilarity. In particular, the latter does not rely on a duality
between functors T (the type of the coalgebras) and L (which gives the logic), nor on
properties of the logical connection ρ.
Original languageEnglish
Title of host publicationAdvances in Modal Logic
EditorsNicola Olivetti, Rineke Verbrugge, Sara Negri, Gabriel Sandu
PublisherCollege Publications
ISBN (Print)978-1-84890-341-8
Publication statusPublished - 2020
Externally publishedYes
EventAdvances in Modal Logic 2020 - University of Helsinki, Helsinki, Finland
Duration: 24-Aug-202028-Aug-2020


ConferenceAdvances in Modal Logic 2020
Abbreviated titleAiML
Internet address

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