Мақаланы E-mail арқылы жіберу MODAL LOGICS OF ALMOST SURE VALIDITIES AND ZERO-ONE LAWS IN HORN CLASSES
- Авторлар: Sliusarev V.V1
-
Мекемелер:
- Moscow Institute of Physics and Technology
- Шығарылым: Том 519, № 1 (2024)
- Беттер: 57-64
- Бөлім: MATHEMATICS
- URL: https://journals.rcsi.science/2686-9543/article/view/275220
- DOI: https://doi.org/10.31857/S2686954324050115
- EDN: https://elibrary.ru/XDHERO
- ID: 275220
Дәйексөз келтіру
Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Аннотация
In this paper we develop a method to study Horn classes of Kripke frames from a probabilistic perspective. We consider the uniform distribution on the set of all 𝑛-point Kripke frames. A formula is almost surely valid in a Horn class F if the probability that it is valid in the F-closure of a random 𝑛-point frame tends to 1 as 𝑛 → ∞. Such formulas constitute a normal modal logic. We show that for pseudotransitive and pseudoeuclidean closures this logic equals S5, and the zero-one law holds.
Негізгі сөздер
Авторлар туралы
V. Sliusarev
Moscow Institute of Physics and Technology
Email: vnvdvc@gmail.com
Moscow, Russia
Әдебиет тізімі
- Глебский Ю. В., Коган Д. И., Легонький М. И., Таланов В. А. Область и степень реализуемости формул ограниченного исчисления предикатов. Кибернетика, 5:142–154, 1969.
- Fagin Ronald Probabilities on finite models. Journal of Symbolic Logic, 41(1):50–58, 1976.
- Halpern Joseph Y., Kapron Bruce Zero-one laws for modal logic. Annals of Pure and Applied Logic, 69(2):157–193, 1994.
- Le Bars Jean-Marie. The 0-1 law fails for frame satisfiability of propositional modal logic. Proceedings — Symposium on Logic in Computer Science, pages 225–234, 02 2002.
- Verbrugge Rineke. Zero-one laws for provability logic: Axiomatizing validity in almost all models and almost all frames. In 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2021, Proceedings Symposium on Logic in Computer Science. IEEE Xplore, June 2021.
- Halpern Joseph Y., Kapron Bruce. Erratum to “zeroone laws for modal logic”. Annals of Pure and Applied Logic APAL, 121:281–283, 06 2003.
- Le Bars Jean-Marie. The 0-1 law fails for frame satisfiability of propositional modal logic. Proceedings Symposium on Logic in Computer Science, pages 225 – 234, 02 2002.
- Le Bars Jean-Marie. Counterexamples of the 0-1 law for fragments of existential second-order logic: An overview. Bulletin of Symbolic Logic, 6, 03 2000.
- Popova Svetlana, Zhukovskii Maksim. Existential monadic second order logic of undirected graphs: a disproof of the Le Bars conjecture. Annals of Pure and Applied Logic, 170:505–514, 2019.
- Gaifman Haim. Concerning measures in first order calculi. Israel Journal of Mathematics, 2:1–18, 1964.
- Goranko Valentin, Kapron Bruce. The modal logic of the countable random frame. Archive for Mathematical Logic, 42, 10 2001.
- Goranko Valentin. The modal logic of almost sure frame validities in the finite. In AiML, 2020.
- Ebbinghaus Heinz-Dieter, Flum Jörg. Finite Model Theory. Perspectives in Mathematical Logic. Springer Berlin Heidelberg, 1999.
- Blackburn Patrick, de Rijke Maarten, Venema Yde. Modal logic. Studia Logica, 76(1):142–148, 2001.
Қосымша файлдар
