Expressive Logics for Coinductive Predicates

Expressive Logics for Coinductive Predicates

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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 longboard dancer deck 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 twist e liquid purple no 1 characterising similarity, divergence and a behavioural metric on automata.