Expressive Logics for Coinductive Predicates

Clemens Kupke, Jurriaan Rot, Michael Wagner
2020 Annual Conference for Computer Science Logic  
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
more » ... cient conditions on the semantics. The approach is illustrated with logics characterising similarity, divergence and a behavioural metric on automata. ACM Subject Classification Theory of computation → Modal and temporal logics; Theory of computation → Categorical semantics Acknowledgements We would like to thank Bart Jacobs for useful discussions and the anonymous referees for their very constructive and helpful feedback.
doi:10.4230/lipics.csl.2020.26 dblp:conf/csl/KupkeR20 fatcat:fxdsbiiedrgshgqbeyasc7gina