Possibilistic Computation Tree Logic: Decidability and Complete Axiomatization

[2510.23075] Possibilistic Computation Tree Logic over Finitely-Valued Kripke Structures: Decidability and Complete Axiomatization Skip to main content Search Submit Donate Log in Computer Science > Logic in Computer Science arXiv:2510.23075 (cs) [Submitted on 27 Oct 2025 ( v1 ), last revised 19 Sep 2026 (this version, v3)] Title: Possibilistic Computation Tree Logic over Finitely-Valued Kripke Structures: Decidability and Complete Axiomatization Authors: Yongming Li View PDF HTML (experimental) Abstract: Possibilistic computation tree logic (PoCTL) is a branching-time temporal logic for specifying and verifying systems whose behavior is described by possibility theory. Although the model-checking problem for PoCTL has been investigated, its satisfiability problem and proof-theoretic foundations, particularly the development of a sound and complete axiomatization,remain largely unexplored. We investigate these problems over normalized possibilistic Kripke structures whose transition possibilities take finitely many values; their state spaces may be countably infinite. A counterexample shows that unrestricted countable structures do not have the finite-model property, thereby distinguishing the semantic scope of the present results. For the finitely-valued class, we extract a finite threshold scale from the input formula and define canonical admissible transitions by the set $D(s,t)$. Independent eventuality ranks guide the selection of local witnesses. Finite supported fragments are then spliced cyclically to obtain a model, without requiring the ranks of different eventualities to decrease simultaneously. This yields a finite-model property. Satisfiability for the unbounded language over this class is EXPTIME-complete, and the tableau procedure runs in time $2^{O(n^2)}$. Bounded operators are handled by explicit finite unfolding, with complexity measured after this preprocessing. Finally, we establish a sound and weakly complete finitary axiomatization by translating tableau deletion into formal refutations. Subjects: Logic in Computer Science (cs.LO) Cite as: arXiv:2510.23075 [cs.LO] (or arXiv:2510.23075v3 [cs.LO] for this version) https://doi.org/10.48550/arXiv.2510.23075 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yongming Li [ view email ] [v1] Mon, 27 Oct 2025 07:24:52 UTC (31 KB) [v2] Tue, 25 Aug 2026 09:51:43 UTC (32 KB) [v3] Sat, 19 Sep 2026 02:54:55 UTC (39 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.LO < prev | next > new | recent | 2025-10 Change to browse by: cs References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation 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)

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