Beohar, H. orcid.org/0000-0001-5256-1334, Gurke, S., König, B. et al. (4 more authors) (2024) Expressive quantale-valued logics for coalgebras: an adjunction-based approach. In: Beyersdorff, O., Kanté, M.M., Kupferman, O. and Lokshtanov, D., (eds.) 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024), 12-14 Mar 2024, Clermont-Ferrand, France. Leibniz International Proceedings in Informatics (LIPIcs), 289 . Schloss Dagstuhl – Leibniz-Zentrum für Informatik , 10:1-10:19.
Abstract
We address the task of deriving fixpoint equations from modal logics characterizing behavioural equivalences and metrics (summarized under the term conformances). We rely on an earlier work that obtains Hennessy-Milner theorems as corollaries to a fixpoint preservation property along Galois connections between suitable lattices. We instantiate this to the setting of coalgebras, in which we spell out the compatibility property ensuring that we can derive a behaviour function whose greatest fixpoint coincides with the logical conformance. We then concentrate on the linear-time case, for which we study coalgebras based on the machine functor living in Eilenberg-Moore categories, a scenario for which we obtain a particularly simple logic and fixpoint equation. The theory is instantiated to concrete examples, both in the branching-time case (bisimilarity and behavioural metrics) and in the linear-time case (trace equivalences and trace distances).
Metadata
Item Type: | Proceedings Paper |
---|---|
Authors/Creators: |
|
Editors: |
|
Copyright, Publisher and Additional Information: | © Harsh Beohar, Sebastian Gurke, Barbara König, Karla Messing, Jonas Forster, Lutz Schröder, and Paul Wild; licensed under Creative Commons License CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/) |
Keywords: | modal logics; coalgebras; behavioural equivalences; behavioural metrics; linear-time semantics; Eilenberg-Moore categories |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 21 Jun 2024 11:46 |
Last Modified: | 23 Jun 2024 01:29 |
Status: | Published |
Publisher: | Schloss Dagstuhl – Leibniz-Zentrum für Informatik |
Series Name: | Leibniz International Proceedings in Informatics (LIPIcs) |
Refereed: | Yes |
Identification Number: | 10.4230/LIPIcs.STACS.2024.10 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:213738 |