The classical Hennessy-Milner theorem says that two states of an image-finite transition system are bisimilar if and only if they satisfy the same formulas in a certain modal logic. In this paper we study this type of result in a general context, moving from transition systems to coalgebras and from bisimilarity to coinductive predicates. We formulate when a logic fully characterises a coinductive predicate on coalgebras, by providing suitable notions of adequacy and expressivity, and give sufficient conditions on the semantics. The approach is illustrated with logics characterising similarity, divergence and a behavioural metric on automata.

中文翻译：

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合归纳谓词的表达逻辑

经典的 Hennessy-Milner 定理说，图像有限跃迁系统的两个状态是双相似的，当且仅当它们在某个模态逻辑中满足相同的公式。在本文中，我们在一般背景下研究这种类型的结果，从过渡系统到余代数，从双相似性到共归纳谓词。我们通过提供适当的充分性和表达性概念，并在语义上给出充分条件，从而在逻辑充分表征了余代数上的合归纳谓词时进行公式化。该方法用表征相似性、发散性和自动机行为度量的逻辑进行说明。