Expressive Logics for Coinductive Predicates

Authors Clemens Kupke, Jurriaan Rot

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Author Details

Clemens Kupke
  • Strathclyde University, United Kingdom
Jurriaan Rot
  • University College London, United Kingdom and Radboud University, The Netherlands


We would like to thank Bart Jacobs for useful discussions and the anonymous referees for their very constructive and helpful feedback.

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Clemens Kupke and Jurriaan Rot. Expressive Logics for Coinductive Predicates. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
  • Theory of computation → Categorical semantics
  • Coalgebra
  • Fibration
  • Modal Logic


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