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2008 | 6 | 3 | 372-383
Tytuł artykułu

On n × m-valued Łukasiewicz-Moisil algebras

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
n×m-valued Łukasiewicz algebras with negation were introduced and investigated in [20, 22, 23]. These algebras constitute a non trivial generalization of n-valued Łukasiewicz-Moisil algebras and in what follows, we shall call them n×m-valued Łukasiewicz-Moisil algebras (or LM n×m -algebras). In this paper, the study of this new class of algebras is continued. More precisely, a topological duality for these algebras is described and a characterization of LM n×m -congruences in terms of special subsets of the associated space is shown. Besides, it is determined which of these subsets correspond to principal congruences. In addition, it is proved that the variety of LM n×m -algebras is a discriminator variety and as a consequence, certain properties of the congruences are obtained. Finally, the number of congruences of a finite LM n×m -algebra is computed.
Wydawca
Czasopismo
Rocznik
Tom
6
Numer
3
Strony
372-383
Opis fizyczny
Daty
wydano
2008-09-01
online
2008-07-02
Twórcy
Bibliografia
  • [1] Balbes R., Dwinger P., Distributive lattices, University of Missouri Press, Columbia, Mo., 1974
  • [2] Boicescu V., Filipoiu A., Georgescu G., Rudeanu S., Łukasiewicz–Moisil algebras, Annals of Discrete Mathematics, 49, North-Holland Publishing Co., Amsterdam, 1991
  • [3] Bulman-Fleming S., Werner H., Equational compactness in quasi-primal varieties, Algebra Universalis, 1977, 7, 33–46 http://dx.doi.org/10.1007/BF02485416
  • [4] Burris S., Sankappanavar H.P., A course in universal algebra, Graduate Texts in Mathematics, 78, Springer-Verlag, New York-Berlin, 1981
  • [5] Cignoli R., Moisil algebras, Notas de Lógica Matemática, 27, Instituto de Matemática, Universidad Nacional del Sur, Bahía Blanca, 1970
  • [6] Cignoli R., Proper n-valued Łukasiewicz algebras as S-algebras of Łukasiewicz n-valued propositional calculi, Studia Logica, 1982, 41, 3–16 http://dx.doi.org/10.1007/BF00373490
  • [7] Cignoli R., D’Ottaviano I., Mundici D., Algebras das logicas de Łukasiewicz, Coleção CLE, 12, Campinas UNICAMP-CLE, 1995
  • [8] Cignoli R., D’Ottaviano I., Mundici D., Algebraic foundations of many-valued reasoning, Trends in Logic-Studia Logica Library, 7, Kluwer Academic Publishers, Dordrecht, 2000
  • [9] Cornish W., Fowler P., Coproducts of De Morgan algebras, Bull. Austral. Math. Soc., 1977, 16, 1–13 http://dx.doi.org/10.1017/S0004972700022966
  • [10] Figallo A.V., Pascual I., Ziliani A., Notes on monadic n-valued Łukasiewicz algebras, Math. Bohem., 2004, 129, 255–271
  • [11] Grigolia R., Algebraic analysis of Łukasiewicz-Tarski’s n-valued logical systems, In: Wójcicki R., Malinowski G. (Eds.), Selected papers on Łukasiewicz sentential calculi, Zaklad Narod. im. Ossolin., Wydawn. Polsk. Akad. Nauk, Wroclaw, 1977, 81–92
  • [12] Iorgulescu A., Connections between MVn algebras and n-valued Łukasiewicz-Moisil algebras IV, Journal of Universal Computer Science, 2000, 6, 139–154
  • [13] Łukasiewicz J., On three-valued logic, Ruch Filozoficzny, 1920, 5, 160–171
  • [14] Moisil Gr.C., Notes sur les logiques non-chrysippiennes, Ann. Sci. Univ. Jassy, 1941, 27, 86–98
  • [15] Moisil Gr.C., Essais sur les logiques non chrysippiennes, Éditions de l’Académie de la République Socialiste de Roumanie, Bucharest, 1972
  • [16] Post E., Introduction to a general theory of elementary propositions, Amer. J. Math., 1921, 43, 163–185 http://dx.doi.org/10.2307/2370324
  • [17] Priestley H., Representation of distributive lattices by means of ordered Stone spaces, Bull. London Math. Soc., 1970, 2, 186–190 http://dx.doi.org/10.1112/blms/2.2.186
  • [18] Priestley H., Ordered topological spaces and the representation of distributive lattices, Proc. London Math. Soc., 1972, 4, 507–530 http://dx.doi.org/10.1112/plms/s3-24.3.507
  • [19] Priestley H., Ordered sets and duality for distributive lattices, Ann. Discrete Math., North-Holland, Amsterdam, 1984, 23, 39–60
  • [20] Sanza C., Algebras de Łukasiewicz matriciales n × m-valuadas con negación, Noticiero de la Unión Matemática Argentina, Rosario (Argentina), 2000
  • [21] Sanza C., Algebras de Łukasiewicz n × m-valuadas con negación, Ph.D. thesis, Universidad Nacional del Sur. Argentina, 2004
  • [22] Sanza C., Notes on n × m-valued Łukasiewicz algebras with negation, Log. J. IGPL, 2004, 12, 499–507 http://dx.doi.org/10.1093/jigpal/12.6.499
  • [23] Sanza C., n × m-valued Łukasiewicz algebras with negation, Rep. Math. Logic, 2006, 40, 83–106
  • [24] Suchoń W., Matrix Łukasiewicz Algebras, Rep. Math. Logic, 1975, 4, 91–104
  • [25] Tarski A., Logic semantics metamathematics, Clarendon Press, Oxford, 1956
  • [26] Werner H., Discriminator-algebras, Algebraic representation and model theoretic properties, Akademie-Verlag, Berlin, 1978
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-008-0035-7
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