Expressive Logics for Coinductive Predicates

The classical Hennessy-Milner theorem says that two Soldering Tools 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 Serving Platter logics characterising similarity, divergence and a behavioural metric on automata.