Hennessy-Milner Theorems via Galois Connections

Authors Harsh Beohar, Sebastian Gurke, Barbara König, Karla Messing

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Author Details

Harsh Beohar
  • University of Sheffield, UK
Sebastian Gurke
  • Universität Duisburg-Essen, Germany
Barbara König
  • Universität Duisburg-Essen, Germany
Karla Messing
  • Universität Duisburg-Essen, Germany


We want to thank Jonas Forster, Lutz Schröder and Paul Wild for several interesting discussions on the topics of this paper.

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Harsh Beohar, Sebastian Gurke, Barbara König, and Karla Messing. Hennessy-Milner Theorems via Galois Connections. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


We introduce a general and compositional, yet simple, framework that allows to derive soundness and expressiveness results for modal logics characterizing behavioural equivalences or metrics (also known as Hennessy-Milner theorems). It is based on Galois connections between sets of (real-valued) predicates on the one hand and equivalence relations/metrics on the other hand and covers a part of the linear-time-branching-time spectrum, both for the qualitative case (behavioural equivalences) and the quantitative case (behavioural metrics). We derive behaviour functions from a given logic and give a condition, called compatibility, that characterizes under which conditions a logically induced equivalence/metric is induced by a fixpoint equation. In particular, this framework allows to derive a new fixpoint characterization of directed trace metrics.

Subject Classification

ACM Subject Classification
  • Theory of computation → Concurrency
  • Theory of computation → Modal and temporal logics
  • behavioural equivalences and metrics
  • modal logics
  • Galois connections


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