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ON FITTING’S MODIFICATION OF KRIPKE’S THEORY OF TRUTH
- Authors: Speranski S.O1
-
Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Issue: Vol 526, No 1 (2025)
- Pages: 36-39
- Section: MATHEMATICS
- URL: https://medbiosci.ru/2686-9543/article/view/364247
- DOI: https://doi.org/10.7868/S3034504925060068
- ID: 364247
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Abstract
In [3], inspired by some ideas from logic programming, Melvin Fitting proposed his own modification of Kripke’s theory of truth. Let J* denote the corresponding monotone operator. We show that: 1) the closure ordinal of J* is ω1 СК, i.e. the least non-constructive ordinal; 2) the collection of all sentences true according to J* is Π1 1-complete.
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About the authors
S. O Speranski
Steklov Mathematical Institute of Russian Academy of Sciences
Email: katze.tail@gmail.com
Moscow, Russia
References
- Belnap N.D., Jr. A useful four-valued logic // Modern Uses of Multiple-Valued Logic / Eds. Dunn J.M., Epstein G.D. Reidel, 1977. P. 8–37.
- Burgess J.P. The truth is never simple // Journal of Symbolic Logic. 1986. V. 51.№4. P. 663–681.
- Fitting M. A theory of truth that prefers falsehood // Journal of Philosophical Logic. 1997. V. 26.№5. P. 477–500.
- Fitting M. Bilattice basics // Journal of Applied Logics — IfCoLog Journal. 2020. V. 7. № 6. P. 975–1018.
- Gelfond M., Lifschitz V. The stable model semantics for logic programming // Logic Programming: Proceedings of the Fifth International Conference and Symposium / Eds. Kowalski R., Bowen K. MIT Press, 1988. P. 1070–1080.
- Kripke S. Outline of a theory of truth // The Journal of Philosophy. 1975. V. 72. № 19. P. 690–716.
- Sacks G.E. Higher Recursion Theory. Springer, 1990.
- Speranski S.O. Notes on the computational aspects of Kripke’s theory of truth // Studia Logica. 2017. V. 105.№2. P. 407–429.
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