Expressive logics for coinductive predicates

Kupke, Clemens and Rot, Jurriaan (2021) Expressive logics for coinductive predicates. Logical Methods in Computer Science. ISSN 1860-5974 (In Press)

[thumbnail of Kupke-etal-LMCS-2021-Expressive-logics-for-coinductive-predicates]
Text. Filename: Kupke_etal_LMCS_2021_Expressive_logics_for_coinductive_predicates.pdf
Accepted Author Manuscript
License: Creative Commons Attribution 4.0 logo

Download (509kB)| Preview


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.