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MODAL LOGICS WITH THE COMPLEMENT MODALITY
- Authors: Zolin E.E.1
-
Affiliations:
- Lomonosov Moscow State University
- Issue: Vol 525, No 1 (2025)
- Pages: 31-39
- Section: MATHEMATICS
- URL: https://ogarev-online.ru/2686-9543/article/view/356782
- DOI: https://doi.org/10.7868/S3034504925050046
- ID: 356782
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Abstract
Modal logic with two operators, one for the accessibility relation on a Kripke model and the other for its complement, was studied first by Humberstone in 1983 [5], who axiomatized it using an infinite number of axioms. In this paper we suggest a finite axiomatization of this logic, and also axiomatize the corresponding logics of some natural classes of Kripke frames.
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About the authors
E. E. Zolin
Lomonosov Moscow State University
Email: vshehtman@gmail.com
Moscow, Russia
References
- Золин Е.Е. Модальные логики с модальностью пересечения // Доклады Российской Академии Наук. Математика, информатика, процессы управления. 2025. Т. 521. С. 107—123.
- Chagrov A., Zakharyaschev M. Modal logic. Oxford, 1997.
- Goranko V., Vakarelov D. Modal Logic and Universal Algebra I: Modal Axiomatizations of Structures // Advances in Modal Logic / ed. by M. Kracht [et al.]. CSLI Publications, 1998. P. 265—292.
- Hemaspaandra E. The Price of Universality // Notre Dame Journal of Formal Logic. 1996. V. 37. No. 2. P. 174—203. https://doi.org/10.1305/ndjfl/1040046086
- Humberstone I.L. Inaccessible worlds // Notre Dame Journal of Formal Logic. 1983. July. V. 24. No. 3. P. 346—352. https://doi.org/10.1305/ndjfl/1093870378
- Lutz C., Sattler U. The Complexity of Reasoning with Boolean Modal Logics // Advances in Modal Logic. 2000. V. 3. P. 329—348.
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