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1993 | 28 | 1 | 51-66
Tytuł artykułu

Polyadic algebras over nonclassical logics

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)'s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Łukasiewicz, modal logics that admit the rule of necessitation, BCK logic, etc.
Rocznik
Tom
28
Numer
1
Strony
51-66
Opis fizyczny
Daty
wydano
1993
Twórcy
autor
  • Department of Mathematics, Iowa State University, Ames, Iowa 50011, U.S.A.
  • Dip. Informatica, University of Pisa, Corso Italia 40, I-56125 Pisa, Italy
Bibliografia
  • [1] H. P. Barendregt, The Lambda Calculus. Its Syntax and Semantics, revised edition, Stud. Logic Found. Math. 103, North-Holland, Amsterdam 1985.
  • [2] W. J. Blok and D. Pigozzi, Algebraizable logics, Mem. Amer. Math. Soc. 396 (1989).
  • [3] Z. B. Diskin, Polyadic algebras for non-classical logics, I,II,III,IV, Latv. Mat. Ezhegodnik (in Russian), to appear.
  • [4] J. .Freedman, Algebraic semantics for modal predicate logic, Z. Math. Logik Grundlag. Math. 22 (1976), 523-552.
  • [5] G. Georgescu, A representation theorem for tense polyadic algebras, Mathematica (Cluj), 21 (1979), 131-138.
  • [6] G. Georgescu, Modal polyadic algebras, Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 23 (1979), 49-64.
  • [7] G. Georgescu, A representation theorem for polyadic Heyting algebras, Algebra Universalis 14 (1982), 197-209.
  • [8] P. Halmos, Homogeneous locally finite polyadic Boolean algebras of infinite degree, Fund. Math. 43 (1956), 255-325; see also [9], pp. 97-166.
  • [9] P. Halmos, Algebraic Logic, Chelsea, New York 1962.
  • [10] L. Henkin, An algebraic characterization of quantifiers, Fund. Math. 37 (1950), 63-74.
  • [11] L. Henkin, J. D. Monk and A. Tarski, Cylindric Algebras, Parts I and II, North-Holland, Amsterdam 1971 and 1985.
  • [12] J. Kotas and A. Pieczkowski, On a generalized cylindrical algebra and intuitionistic logic, Studia Logica 17 (1966), 73-80.
  • [13] A. R. Meyer, What is a model of the lambda calculus?, Inform. Control 52 (1982), 87-122.
  • [14] D. Monk, Polyadic Heyting algebras, Notices Amer. Math. Soc. 7 (1960), 735.
  • [15] A. Mostowski, Proofs of non-deducibility in intuitionistic functional calculus, J. Symbolic Logic 13 (1948), 204-207.
  • [16] I. Németi, Algebraizations of quantifier logics. An introductory overview, Studia Logica 50 (1991), 485-569.
  • [17] D. Pigozzi and A. Salibra, The abstract variable-binding calculus, manuscript.
  • [18] D. Pigozzi and A. Salibra, An introduction to lambda abstraction algebras, manuscript.
  • [19] H. Rasiowa, An Algebraic Approach to Non-Classical Logics, North-Holland, Amsterdam 1974.
  • [20] H. Rasiowa and R. Sikorski, The Mathematics of Metamathematics, PWN, Warszawa 1963.
  • [21] D. Schwartz, Polyadic MV-algebras, Z. Math. Logik Grundlag. Math. 26 (1980), 561-564.
  • [22] A. Wroński, BCK-algebras do not form a variety, Math. Japon. 28 (1983), 211-213.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv28z1p51bwm
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