Expressive logics for coinductive predicates

Kupke, Clemens and Rot, Jurriaan (2020) Expressive logics for coinductive predicates. In: Computer Science Logic, 2020-01-13 - 2020-01-16.

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    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.