A Note on Calculi for Non-deterministic Many-valued Logics

• Autorzy: Kaminski Michael

Identyfikatory

DOI

10.3233/FI-222123

• Języki publikacji: EN

Abstrakty

EN

We present two deductively equivalent calculi for non-deterministic many-valued log ics. One is defined by axioms and the other – by rules of inference. The two calculi are obtained from the truth tables of the logic under consideration in a straightforward manner. We prove soundness and strong completeness theorems for both calculi and also prove the cut elimination theorem for the calculi defined by rules of inference.

Słowa kluczowe

EN

computer science; logic in computer science

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2022
• Tom: Vol. 186, nr 1-4
• Strony: 143--153
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Kaminski Michael

• Department of Computer Science Technion – Israel Institute of Technology Haifa 3200003, Israel

Bibliografia

• [1] Avron A, and Konikowska B. Multi-valued calculi for logics based on non-determinism. Logic Journal of IGPL, 2005. 13(4):365-387. doi:10.1093/jigpal/jzi030.
• [2] Avron A, and Lev I. Non-deterministic multiple-valued structures. Journal of Logic and Computation, 2005. 15(3):241-261. doi:10.1093/logcom/exi001
• [3] Avron A, and Zamansky A. Non-deterministic semantics for logical systems. In D.M. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, Springer 2011 pages 227-304. doi:10.1007/978-94-007-0479-4 4.
• [4] Baaz M, Fermüller CG, and Zach R. Systematic construction of natural deduction systems for many-valued logics. In Proceedings of the 23rd IEEE International Symposium on Multiple-Valued Logic, IS-MVL, pages 208-213. IEEE Computer Society, 1993. doi:10.1109/ISMVL.1993.289558.
• [5] Baaz M, Lahav O, and Zamansky A. Finite-valued semantics for canonical labelled calculi. Journal of Automated Reasoning, 2013. 51:401-430. doi:10.1007/s10817-013-9273-x.
• [6] Francez N, and Kaminski M. On poly-logistic natural-deduction for finitely-valued propositional logics. Journal of Applied Logic, 2019. 6:255-289. doi:10.1007/s11787-019-00219-z.
• [7] Hanazawa M, and Takano M. On intuitionistic many-valued logics. Journal of the Mathematical Society of Japan, 1986. 38:409-419.
• [8] Kaminski M. Nonstandard connectives of intuitionistic propositional logic. Notre Dame Journal of Formal Logic, 1988. 29:309-331. doi:10.1305/ndjfl/1093637931.
• [9] Kaminski M, and Francez N. Calculi for many-valued logics. Logica Universalis, 2021. 15:193-226. doi:10.1007/s11787-021-00274-5.
• [10] Roussenau G. Sequents in many valued logic I. Fundamenta Mathematicae, 1967. 60:23-33. doi:10.4064/FM-67-1-125-131.
• [11] Roussenau G. Sequents in many valued logic II. Fundamenta Mathematicae, 67:125-131, 1970. doi:10.4064/ fm-67-1-125-131.
• [12] Takahashi M. Many-valued logics of extended Gentzen style I. Science Reports of the Tokyo Kyoiku Daigaku, Section A, 1968. 9:271-292. URL https://www.jstor.org/stable/43699119.
• [13] Takahashi M. Many-valued logics of extended Gentzen style II. Journal of Symbolic Logic, 1970. 35:493-528. doi:10.2307/2271438.