A realization theorem for the modal logic of transitive closure $\mathsf{K}^+$

Мұқаба

Дәйексөз келтіру

Толық мәтін

Ашық рұқсат Ашық рұқсат
Рұқсат жабық Рұқсат берілді
Рұқсат жабық Тек жазылушылар үшін

Аннотация

We present a justification logic corresponding to the modal logic of transitive closure $\mathsf{K}^+$ and establish a normal realization theorem relating these two systems. The result is obtained by means of a sequent calculus allowing non-well-founded proofs.

Авторлар туралы

Daniyar Shamkanov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow; National Research University Higher School of Economics, Moscow

Хат алмасуға жауапты Автор.
Email: daniyar.shamkanov@gmail.com
Candidate of physico-mathematical sciences, no status

Әдебиет тізімі

  1. E. Antonakos, “Explicit generic common knowledge”, Logical foundations of computer science, Lecture Notes in Comput. Sci., 7734, Springer, Heidelberg, 2013, 16–28
  2. S. N. Artemov, “Explicit provability and constructive semantics”, Bull. Symb. Log., 7:1 (2001), 1–36
  3. S. Artemov, “Justified common knowledge”, Theoret. Comput. Sci., 357:1-3 (2006), 4–22
  4. S. Bucheli, Justification logics with common knowledge, Ph.D. thesis, Univ. Bern, 2012, 219 pp.
  5. S. Bucheli, R. Kuznets, T. Studer, “Two ways to common knowledge”, Proceedings of the 6th workshop on methods for modalities (M4M-6 2009), Electron. Notes Theor. Comput. Sci., 262, Elsevier Science B.V., Amsterdam, 2010, 83–98
  6. S. Bucheli, R. Kuznets, T. Studer, “Justifications for common knowledge”, J. Appl. Non-Class. Log., 21:1 (2011), 35–60
  7. C. Doczkal, G. Smolka, “Constructive completeness for modal logic with transitive closure”, Certified programs and proofs, Lecture Notes in Comput. Sci., 7679, Springer, Berlin, 2012, 224–239
  8. R. Kashima, “Completeness proof by semantic diagrams for transitive closure of accessibility relation”, Advances in modal logic (Moscow, 2010), v. 8, College Publications, London, 2010, 200–217
  9. S. Kikot, I. Shapirovsky, E. Zolin, “Modal logics with transitive closure: completeness, decidability, filtration”, Advances in modal logic (Helsinki, 2020), v. 13, College Publications, London, 2020, 369–388
  10. D. Shamkanov, On structural proof theory of the modal logic $K^+$ extended with infinitary derivations, 2023
  11. Д. С. Шамканов, “Теорема о реализации для логики доказуемости Гeделя–Лeба”, Матем. сб., 207:9 (2016), 171–190

Қосымша файлдар

Қосымша файлдар
Әрекет
1. JATS XML

© Shamkanov D.S., 2025

Согласие на обработку персональных данных

 

Используя сайт https://journals.rcsi.science, я (далее – «Пользователь» или «Субъект персональных данных») даю согласие на обработку персональных данных на этом сайте (текст Согласия) и на обработку персональных данных с помощью сервиса «Яндекс.Метрика» (текст Согласия).