A realization theorem for the modal logic of transitive closure $\mathsf{K}^+$
- Authors: Shamkanov D.S.1,2
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Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
- National Research University Higher School of Economics, Moscow
- Issue: Vol 89, No 2 (2025)
- Pages: 189-212
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/303953
- DOI: https://doi.org/10.4213/im9598
- ID: 303953
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Abstract
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.
About the authors
Daniyar Salkarbekovich Shamkanov
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow; National Research University Higher School of Economics, Moscow
Author for correspondence.
Email: daniyar.shamkanov@gmail.com
Candidate of physico-mathematical sciences, no status
References
- E. Antonakos, “Explicit generic common knowledge”, Logical foundations of computer science, Lecture Notes in Comput. Sci., 7734, Springer, Heidelberg, 2013, 16–28
- S. N. Artemov, “Explicit provability and constructive semantics”, Bull. Symb. Log., 7:1 (2001), 1–36
- S. Artemov, “Justified common knowledge”, Theoret. Comput. Sci., 357:1-3 (2006), 4–22
- S. Bucheli, Justification logics with common knowledge, Ph.D. thesis, Univ. Bern, 2012, 219 pp.
- 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
- S. Bucheli, R. Kuznets, T. Studer, “Justifications for common knowledge”, J. Appl. Non-Class. Log., 21:1 (2011), 35–60
- 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
- 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
- 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
- D. Shamkanov, On structural proof theory of the modal logic $K^+$ extended with infinitary derivations, 2023
- Д. С. Шамканов, “Теорема о реализации для логики доказуемости Гeделя–Лeба”, Матем. сб., 207:9 (2016), 171–190
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