Cardinality of sets of closed functional classes in weak 3-valued logics
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09.04.2013
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Аннотация
This paper proves that sets of closed functional classes in 3-valued logics of Bochvar $B_3$ and Hallden $H_3$ contains a continuum of different closed classes. It is also proven that both of these logics contain a closed functional class which has no basis.
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Преловский Н. Cardinality of sets of closed functional classes in weak 3-valued logics // Логические исследования / Logical Investigations. 2013. Т. 19. C. 334-343.
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Литература
Karpenko A.S., Development of Multivalued Logic. М.: URSS, 2010 (in Russian).
Karpenko A.S., Continuality of 3-Valued Logics: Problems and Hypotheses, Logical Investigations 16:127–133, 2010. (in Russian)
Muchnik A.A., Yanov Yu. I., On Existence of k-valued Closed Classes, Which Have no Finite Bases, Proceedings of Academy of Sciences USSR 127(1):44–46, 1959 (in Russian).
Ratsa M.F., On Functional Completeness of Propositional Intuitionistic Logic, Problems of Cybernetics 39:107–150, 1982 (in Russian).
Ratsa M.F., Iterative Chain Classes of Pseudo-boolean Functions. Kishinev, 1990 (in Russian).
Finn V.K., On Criterion of Functional Completeness for B3, Researches in Formal Languages and Non-classical Logics, М.: Nauka, 1974, pp. 194–199 (in Russian).
Finn V.K., Axiomatization of Some 3-valued Propositional Calculi and Their Algebras, Philosophy in Modern World. Philosophy and Logic, М.: Nauka, 1974, pp. 398–438 (in Russian).
Hallden S., The Logic of Nonsense, Uppsala Universitets Arsskrift, 1949.
Lau D., Function Algebras on Finite Sets, Springer-Verlag, BerlinHeidelberg-New York, 2006.
Post E.L., The two-valued iterative systems of mathematical logic, Annals of Mathematical Studies 5, Princeton University Press, 1941.
Karpenko A.S., Continuality of 3-Valued Logics: Problems and Hypotheses, Logical Investigations 16:127–133, 2010. (in Russian)
Muchnik A.A., Yanov Yu. I., On Existence of k-valued Closed Classes, Which Have no Finite Bases, Proceedings of Academy of Sciences USSR 127(1):44–46, 1959 (in Russian).
Ratsa M.F., On Functional Completeness of Propositional Intuitionistic Logic, Problems of Cybernetics 39:107–150, 1982 (in Russian).
Ratsa M.F., Iterative Chain Classes of Pseudo-boolean Functions. Kishinev, 1990 (in Russian).
Finn V.K., On Criterion of Functional Completeness for B3, Researches in Formal Languages and Non-classical Logics, М.: Nauka, 1974, pp. 194–199 (in Russian).
Finn V.K., Axiomatization of Some 3-valued Propositional Calculi and Their Algebras, Philosophy in Modern World. Philosophy and Logic, М.: Nauka, 1974, pp. 398–438 (in Russian).
Hallden S., The Logic of Nonsense, Uppsala Universitets Arsskrift, 1949.
Lau D., Function Algebras on Finite Sets, Springer-Verlag, BerlinHeidelberg-New York, 2006.
Post E.L., The two-valued iterative systems of mathematical logic, Annals of Mathematical Studies 5, Princeton University Press, 1941.