A meta-modal logic for bisimulations

[2507.15117] A meta-modal logic for bisimulations Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Logic in Computer Science arXiv:2507.15117 (cs) [Submitted on 20 Jul 2025 ( v1 ), last revised 11 Apr 2026 (this version, v3)] Title: A meta-modal logic for bisimulations Authors: Alfredo Burrieza , Fernando Soler-Toscano , Antonio Yuste-Ginel View a PDF of the paper titled A meta-modal logic for bisimulations, by Alfredo Burrieza and Fernando Soler-Toscano and Antonio Yuste-Ginel View PDF HTML (experimental) Abstract: We propose a modal study of the notion of bisimulation. Our contribution is threefold. First, we extend the basic modal language with a new modality $\nbi$, whose intended meaning is universal quantification over all states that are bisimilar to the current one. We show that bisimulations are definable in this object language via frame correspondence. Second, we provide a sound and complete axiomatisation of the class of all pairs of Kripke models that are bisimulation-related. Third, we show that the satisfiability problem of our logic is decidable and PSPACE-complete via a translation to standard modal logic $K$ under a simple frame condition. All our results are encoded and verified by Isabelle/HOL. Comments: 27 pages Subjects: Logic in Computer Science (cs.LO) ; Logic (math.LO) MSC classes: 03B45 ACM classes: F.4.0 Cite as: arXiv:2507.15117 [cs.LO] (or arXiv:2507.15117v3 [cs.LO] for this version) https://doi.org/10.48550/arXiv.2507.15117 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Antonio Yuste-Ginel [ view email ] [v1] Sun, 20 Jul 2025 20:32:14 UTC (19 KB) [v2] Wed, 15 Oct 2025 11:06:15 UTC (25 KB) [v3] Sat, 11 Apr 2026 07:44:11 UTC (21 KB) Full-text links: Access Paper: View a PDF of the paper titled A meta-modal logic for bisimulations, by Alfredo Burrieza and Fernando Soler-Toscano and Antonio Yuste-Ginel View PDF HTML (experimental) TeX Source view license Current browse context: cs.LO < prev | next > new | recent | 2025-07 Change to browse by: cs math math.LO References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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