Studia Logica

, Volume 41, Issue 1, pp 3–16 | Cite as

Proper n-valued Łukasiewicz algebras as S-algebras of Łukasiewicz n-valued prepositional calculi

  • Roberto Cignoli


Proper n-valued Łukasiewicz algebras are obtained by adding some binary operators, fulfilling some simple equations, to the fundamental operations of n-valued Łukasiewicz algebras. They are the s-algebras corresponding to an axiomatization of Łukasiewicz n-valued propositional calculus that is an extention of the intuitionistic calculus.


Mathematical Logic Binary Operator Computational Linguistic Propositional Calculus Simple Equation 
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  1. [1]
    R. Balbes and P. Dwinger, Distributive Lattices, University of Missouri Press, Columbia, Mo., 1974.Google Scholar
  2. [2]
    G. Birkhoff, Lattice Theory, 3rd Ed., American Mathematical Society, Providence, R. I., 1967.Google Scholar
  3. [3]
    L. Borkowski (Editor), Selected Works of J. Łukasiewicz, North-Holland, Amsterdam, 1970.Google Scholar
  4. [4]
    R. Cignoli, Moisil algebras, Notas de Lógica Matemática No 27, Universidad Nacional del Sur, Bahía Blanca, 1970.Google Scholar
  5. [5]
    R. Cignoli, Some algebraic aspects of many-valued logics. In: A. I. Arruda, N. C. A. da Costa and A. M. Sette (editors), Proceedings of the Third Brazilian Conference on Mathematical Logic, Sociedade Brasileira de Lógica, São Paulo, 1980, pp. 49–68.Google Scholar
  6. [6]
    G. Epstein and A. Horn, P-algebras, an abstraction from Post algebras, Algebra Universalis, 4 (1974), pp. 195–206.Google Scholar
  7. [7]
    R. Grigolia, Algebraic analysis of Łukasiewicz — Tarski n-valued logical systems. In: R. Wójcicki and G. Malinowski (Editors), Selected Papers on Łukasiewicz Sentential Calculi, Ossolineum, Wrocław and Warsaw, 1977, pp. 81–92.Google Scholar
  8. [8]
    L. Iturrioz, Łukasiewicz and Symmetrical Heyting algebras, Zeitschrift für Mathematische Logik und Grundlagen den Mathematik, 23 (1977), pp. 131–136.Google Scholar
  9. [9]
    J. Łukasiewicz, Philosophische Bemerkungem zu mehrwertigen Systemen des Aussagenkalküls, Comptes Rendus des Seances de la Société des Sciences et des Lettres de Varsovie, classe III, 23 (1930), 51–77. An English version is published in [3], pp. 153–178.Google Scholar
  10. [10]
    R. Mc Naughton, A theorem about infinite-valued sentential logic, The Journal of Symbolic Logic, 16 (1951), pp. 1–3.Google Scholar
  11. [11]
    H. Rasiowa, An Algebraic Approach to Non-Classical Logics, North-Holland, Amsterdam, 1974.Google Scholar
  12. [12]
    J. B. Rosser and A. Turquette, Many-Valued Logics, North-Holland, Amsterdam, 1952.Google Scholar
  13. [13]
    W. Suchoń, Définition des foncteurs modaux de Moisil dans le calcull n-valent des propositions de Łukasiewicz avec implication et négation, Reports on Mathematical Logic, 2 (1974), pp. 43–47.Google Scholar

Copyright information

© Polish Academy of Sciences 1982

Authors and Affiliations

  • Roberto Cignoli
    • 1
  1. 1.Instituto de MatemáticaUniversidade Estadual de CampinasCampinas-S.P.Brazil

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