Expressive Logics for Coinductive Predicates

Abstract

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