License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2023.12
URN: urn:nbn:de:0030-drops-174735
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17473/
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Beohar, Harsh ; Gurke, Sebastian ; König, Barbara ; Messing, Karla

Hennessy-Milner Theorems via Galois Connections

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LIPIcs-CSL-2023-12.pdf (0.7 MB)

Abstract

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.

BibTeX - Entry

@InProceedings{beohar_et_al:LIPIcs.CSL.2023.12,
  author =	{Beohar, Harsh and Gurke, Sebastian and K\"{o}nig, Barbara and Messing, Karla},
  title =	{{Hennessy-Milner Theorems via Galois Connections}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{12:1--12:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17473},
  URN =		{urn:nbn:de:0030-drops-174735},
  doi =		{10.4230/LIPIcs.CSL.2023.12},
  annote =	{Keywords: behavioural equivalences and metrics, modal logics, Galois connections}
}

Keywords: behavioural equivalences and metrics, modal logics, Galois connections
Collection: 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)
Issue Date: 2023
Date of publication: 01.02.2023

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