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 $\rho$.

中文翻译：

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逻辑诱导互模拟

我们为由逻辑连接给出的合代数模态逻辑定义了一个新的逻辑诱导的互模拟概念（称为 $\rho$-bisimulation），并研究了它的性质。我们表明它是结构性的，因为它仅根据代数结构和单步模态语义来定义，而且可以通过关系提升的形式来表征。此外，我们将 $\rho$-bisimulations 与几个众所周知的等价概念进行比较，并且我们证明了两个模型之间的互模拟集合通常形成一个完整的格子。主要的技术结果是 Hennessy-Milner 类型定理，该定理指出，在某些条件下，逻辑等价意味着 $\rho$-双相似性。特别是，