What trends in non-classical logic were anticipated by Nikolai Vasiliev?
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Published:
09.04.2013
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Abstract
In this paper we discuss a question about the trends in non-classical logic that were exactly anticipated by Niko- lai Vasiliev. We show the influence of Vasiliev’s Imaginary logic on paraconsistent logic. Metatheoretical relations between Vasiliev’s logical systems and many-valued predicate logics are established. We also make clear that Vasiliev has developed a sketch of original system of intensional logic and expressed certain ideas of modal and temporal logics.
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How to Cite
Markin V. What trends in non-classical logic were anticipated by Nikolai Vasiliev? // Logicheskie Issledovaniya / Logical Investigations. 2013. VOL. 19. C. 122-135.
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Papers
References
Vasiliev, N.A., Imaginary logic. Selected works, Moscow: Science, 1989 (in Russian).
Kostyuk, T.P., N.A. Vasiliev’s N dimensional logic: modern reconstruction, Logical investigations 7:261–268, 2000 (in Russian).
Kostyuk, T.P., and V.I. Markin, Formal reconstraction of imaginary logic of N.A. Vasiliev, Modern logic: theory, history, and applications in science, proceedings of V all-Russian scientific conference, St. Petersburg: Publishing House of St. Petersburg State University, 1998, pp. 154–159 (in Russian).
Markin, V.I., Modal interpretation of imaginary logic of N.A. Vasiliev, Modern logic: theory, history, and applications in science, proceedings of V all-Russian scientific conference, St. Petersburg: Publishing House of St. Petersburg State University, 1998, pp. 208–214 (in Russian).
Markin, V.I., Embedding of N.A. Vasiliev’s imaginary logic into quantifier three-valued logic, Logical investigations 7:252–260, 2000 (in Russian).
Markin, V.I., Singular extensions of Lukasiewicz syllogistic, Logical investigations 17:173–190, 2011 (in Russian).
Arruda, A.I., On the imaginary logic of N.A. Vasil’ev, Proceedings of Fourth Latin-American Symposium on Mathematical Logic. NorthHolland, 1979, pp. 1–41.
Markin, V.I., and D.V. Zaitsev, Imaginary logic-2: formal reconstruction of the unnoticed Nikolai Vasiliev’s logical system, Logique et Analyse 45(177–178):39–54, 2002.
Kostyuk, T.P., N.A. Vasiliev’s N dimensional logic: modern reconstruction, Logical investigations 7:261–268, 2000 (in Russian).
Kostyuk, T.P., and V.I. Markin, Formal reconstraction of imaginary logic of N.A. Vasiliev, Modern logic: theory, history, and applications in science, proceedings of V all-Russian scientific conference, St. Petersburg: Publishing House of St. Petersburg State University, 1998, pp. 154–159 (in Russian).
Markin, V.I., Modal interpretation of imaginary logic of N.A. Vasiliev, Modern logic: theory, history, and applications in science, proceedings of V all-Russian scientific conference, St. Petersburg: Publishing House of St. Petersburg State University, 1998, pp. 208–214 (in Russian).
Markin, V.I., Embedding of N.A. Vasiliev’s imaginary logic into quantifier three-valued logic, Logical investigations 7:252–260, 2000 (in Russian).
Markin, V.I., Singular extensions of Lukasiewicz syllogistic, Logical investigations 17:173–190, 2011 (in Russian).
Arruda, A.I., On the imaginary logic of N.A. Vasil’ev, Proceedings of Fourth Latin-American Symposium on Mathematical Logic. NorthHolland, 1979, pp. 1–41.
Markin, V.I., and D.V. Zaitsev, Imaginary logic-2: formal reconstruction of the unnoticed Nikolai Vasiliev’s logical system, Logique et Analyse 45(177–178):39–54, 2002.