Beohar H, Gurke S, König B, Messing K, Forster J, Schröder L, Wild P (2024)
Publication Type: Conference contribution
Publication year: 2024
Publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Book Volume: 289
Conference Proceedings Title: Leibniz International Proceedings in Informatics, LIPIcs
Event location: Clermont-Ferrand, FRA
ISBN: 9783959773119
DOI: 10.4230/LIPIcs.STACS.2024.10
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).
APA:
Beohar, H., Gurke, S., König, B., Messing, K., Forster, J., Schröder, L., & Wild, P. (2024). Expressive Quantale-Valued Logics for Coalgebras: An Adjunction-Based Approach. In Olaf Beyersdorff, Mamadou Moustapha Kante, Orna Kupferman, Daniel Lokshtanov (Eds.), Leibniz International Proceedings in Informatics, LIPIcs. Clermont-Ferrand, FRA: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing.
MLA:
Beohar, Harsh, et al. "Expressive Quantale-Valued Logics for Coalgebras: An Adjunction-Based Approach." Proceedings of the 41st International Symposium on Theoretical Aspects of Computer Science, STACS 2024, Clermont-Ferrand, FRA Ed. Olaf Beyersdorff, Mamadou Moustapha Kante, Orna Kupferman, Daniel Lokshtanov, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2024.
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