A mind of a non-countable set of ideas
DOI:
https://doi.org/10.12775/LLP.2008.003Keywords
propositional logic, superintuitionistic logic, intermediate logic, admissible rule, inference rule, modal logic, multi-valued logic, functional completeness, Boolean functionAbstract
The paper is dedicated to the 80th birthday of the outstanding Russian logician A.V. Kuznetsov. It is addressing a history of the ideas and research conducted by him in non-classical and intermediate logics.References
Bezhanishvili, M.N., Notes on Wajsberg’s proof of separation theorem, Dordrecht/Boston/Lancaster, Martinus Nijhoff Publishers, 1987, pp. 117–128.
Citkin, A.I., “On decidability of the problem of mutual equipotency of two finite logical matrices”, VINITI, #498–75 (1975), 61–73.
Citkin, A.I., “Finite base of quasivariety generated by free cyclic pseudoBoolean algebra”, VINITI, #705–76 (1976), 85–91.
Citkin, A.I., “On structurally complete superintuitionistic logics”, Soviet Math. Dokl. 19 (1978), 4, 816–819.
Citkin, A.I., “On modal logics for reviewing admissible rules of intutionistic logic”, VINITI (1978), 171–187.
Citkin, A.I., “On structural completeness of tabular superintuitionistic logics”, VINITI (1978), 76–97.
Citkin, A.I., “On modal logic of intuitionistic admissibility”, pp. 105–107 in Modal and Tense Logics, Moscow, 1979 (in Russian).
Citkin, A.I., “Finite axiomatizability of locally tabular superintuitionistic logics”, Mathematical Notes 40 (1986), 407–413.
Citkin, A.I., “Towards the question of an error in a well-known paper by M. Wajsberg”, pp. 240-256 in Reaserch on non-classical logics and set theory, Moscow, Nauka, 1979. Translated in Selecta Mathematics Sovietica 7 (1988), 23–36.
Danil’chenko, A.F., “Parametric expressibility of functions of three-valued logic”, Algebra and Logic 16, 4 (1977), 266–280.
Friedman, H., “One hundred and two problems in mathematical logic”, J. Symbolic Logic 40, 3 (1975), 113–130.
Gerčiu, V.Ya., “On finite approximability of superintuitionistic logics”, Math. Issledovaniya 7 (1972), 186–192.
Hosoi, T., and H. Ono, “The intermediate logics on the second slice”, J. Fac. Sci. Univ. Tokyo Sect. I, vol. 17 (1970), 457–461.
Harrop, R., “On the existence or finite models and decision procedures for propositional calculi”, Proc. Camb. Phil. Soc. 54 (1958), 1–13.
Harrop, R., “The finite model property and subsytems of classical propositional calculus”, Zeitschrift für Matematische Logil und Grundlagen der Matematik 5 (1959), 29–32.
Harrop, R., “Concerning formulas of types A › B ? C,A › E(x)B(x) in intuitionistic formal systems”, J. Symbolic Logic 25 (1960), 27–32.
Harrop, R., “Some structure results for proposotional calculi”, J. Symbolic Logic 30 (1965), 271–292.
Iemhoff, R., “On the admissible rules of intuitionistic propositional logic”, J. Symbolic Logic 66 (2001), 281–294.
Jaśkowski, S., “Recherches sur le systeme de la logique intuitioniste”, Actes du Congress Internat. De Philosophie Scient. VI, no. 393, Paris, 1936, pp. 58–61.
Kabziński, J.K., and M. Porębska, “Proof of the separability of the intuitionistic propositional logic by the Wajsberg’s method”, Reports on mathematical Logic 4 (1977), 31–38.
Kirk, R.E., “A result on propositional logics having the disjunction property”, Notre Dame J. of Formal Logic 23 (1982), 71–74.
Kreisel, G., and H. Putnam, “Eine Unableitbarkeitsbeweismethode fur denintuitionistischen Aussagenkalkul”, Archive fur Math. Logik und Grundlagenforschung 3 (1957), 74–78.
Kuznetsov, A.V., On the problems of identity and functional completeness for algebraic systems, Trans. 3rd Math. Congress, 1956, pp. 145–146.
Kuznetsov, A.V., “On non-decidability of general problems of completeness, decidability and equivalency for propositional calculi”, Algebra i Logika 2, 4 (1963), 47–65.
Kuznetsov, A.V., “Analogs of Sheffer’s stroke in constructivist logic”, Doklady AN SSSR 160 (1965), 274–277.
Kuznetsov, A.V., and V.Ya. Gerčiu, “Superintuitionistic logics and finite approximability”, Doklady AN SSSR 195 (1970), 1029–1032.
Kuznetsov, A.V., “On functional expressibility in superintuitionistic logics”, Mathematical Researches, Chishineu, 1971, pp. 75–122.
Kuznetsov, A.V., “On finitely generated pseudo-Boolean algebras and finite approximable varieties”, XII All Union algebraic colloquium, 1973, 281.
Kuznetsov, A.V., “On superintuitionistic logics”, pp. 243–249 in Proceedings of the 17th International Congress of Mathematicians, Vancouver, 1974.
Kuznetsov, A.V., “On the tools for detecting nondeducibility or inexpressibility”, pp. 5–53 in Logical Derivation, Nauka, Moscow, 1979.
Łukasiewicz, J., Aristotelian Syllogistics from the Standpoint of Modern Formal Logic, Clarendon Press, Oxford, 1951.
Maksimova, L.L., “On maximal intermediate logics with the disjunction property”, Studia Logica 45 (1986), 69–75.
Maksimova, L.L., “Pre-tabular superintuitionist logics”, Algebra and Logic 11 (1972), 558–570.
Mal’cev, A.I., “On Homomorphisms on finite groups”, Ivanovski Gos. Ped. Institute Uchenie Zapiski 18 (1958), 49–60.
McKinsey, J.C.C., “The decision problem for some classes of senteces without quantifiers”, J. Symbolic Logic 8 (1943), 61–76.
Mints, G.E., “Derivability of admissible rules”, J. of Soviet Mathematics 6, #4 (1976), 417–421.
Pogorzelski, W.A., “Structural completeness of the propositional calculus”, Bull. Acad. Polon. Sci. Ser. Math. And Phys. 19 (1971), 349–351.
Shehtman, V.B., “Undecidable superintuitionistic propositional calculus”, Doklady AN SSSR 240, #3 (1978), 542–545.
Smiley, T., “The independence of connectives”, J. Symbolic Logic 27 (1962), 426–436.
Ratsa, M.F., “Criterion of functional completeness in intuitionistic propositional logic”, Doklady AN SSSR 102 (1971), 794–797.
Ratsa, M.F., Expressibility in Propositional Calculi, Chishinau, Shtiinca, 1991.
Rose, G.F., “Jaśkowski’s truth-tables and realizability”, PhD Thesis Univ. of Wiskonsin, 1952.
Roziere, P., “Admissible and derivable rules”, Math. Sruct. in Comp. Science 3 (1993), 129–136.
Rybakov, V.V., “A criterion for admissibility of rules in modal system S4 and intuitionistic logic”, Algebra and Logic 23, 5 (1984), 369–384.
Rybakov, V.V., Addmissibility of Logical Inference Rules, Elsevier, 1997.
Umezawa, T., “On logic intermediate between intuitionistic and classical predicate logic”, J. Symbolic Logic 24, 2 (1959), 141–153.
Visser, A., “Rules and Arithmetics”, Notre Dame Journal of Formal Logic 40, 1 (1999), 116–139.
Wajsberg, M., “On A. Heyting’s propositional calculus”, pp. 132–171 in Logical Works, Warszawa, 1977.
Yankov, V.A., “Constructing a sequence of strongly independent superintuitionistic calculi”, Doklady AN SSSR 151 (1968), 806–807.
Yankov, V.A., “The relationship between deducibility in the intuitionistic propositional logic and finite implicational structures”, Doklady AN SSSR 151 (1963), 1203–1204.
Yankov, V.A., “Conjunction irreducible formulas in propositional calculi”, Izv. Akad. Nauk SSSR, Ser. Mat. 33 (1968), 18–38.
Yanovskaya, S.A., “Mathematical logic, and foundations of mathematics”, pp. 13–120 in Mathematics in the USSR during 40 Years, ch. 13, NAUKA Publishers, Moscow, 1959 (in Russian).
Zygmunt, J. “An application of the Lindenbaum method in the domain of strongly finite sentencial calculi”, Acta Universitayis Wratislaviensis 517, Logika 8 (1983), 59–68.
Downloads
Published
How to Cite
Issue
Section
Stats
Number of views and downloads: 526
Number of citations: 0
