Year: 2020
Type: preprint
Abstract: We define a new logic-induced notion of bisimulation (called $ρ$-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 $ρ$-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 \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 $ρ$.
Source: arXiv (Cornell University)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3080169480