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Discrete Duality for Tense Łukasiewicz–Moisil Algebras

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Języki publikacji
EN
Abstrakty
EN
In 2007, tense Łukasiewicz–Moisil algebras were introduced by Diaconescu and Georgescu as an algebraic counterpart of tense n–valued Moisil logic. These algebras constitute a generalization of tense algebras. In this paper we describe a discrete duality for tense Łukasiewicz– Moisil algebras bearing in mind the results indicated by Dzik, Orłowska and van Alten in 2006, for De Morgan algebras.
Wydawca
Rocznik
Strony
317--329
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
  • Instituto de Ciencias Básicas Universidad Nacional de San Juan San Juan, Argentina
autor
  • Instituto de Ciencias Básicas Universidad Nacional de San Juan San Juan, Argentina
Bibliografia
  • [1] V. Boicescu, A. Filipoiu, G. Georgescu and S. Rudeanu, Łukasiewicz - Moisil Algebras, Annals of Discrete Mathematics 49, North - Holland, 1991.
  • [2] M. Botur, I. Chajda, R. Halaˇs and M. Kolaˇrik, Tense operators on Basic Algebras, Internat. J. Theoret. Phys., 50 (12), 3737–3749, (2011).
  • [3] M.Botur, J.Paseka, Tense MV–algebras, arXiv: 1305.3406 [math.AC].
  • [4] J. Burges, Basic tense logic. In: Gabbay, D.M., Günter, F. (eds) Handbook of Philosophical Logic, vol. II, pp. 89–139. Reidel, Dordrecht (1984).
  • [5] I. Chajda, Algebraic axiomatization of tense intuitionistic logic, Cent. Eur. J. Math., 9 (5), 1185–1191, (2011).
  • [6] I. Chajda and J. Paseka, Dynamic effect algebras and their representations, Soft Computing, 16 (10), 1733–1741, (2012).
  • [7] I. Chajda and M. Kolařik, Dynamic Effect Algebras, Math. Slovaca 62 (3), 379–388, (2012).
  • [8] C. Chirită, Tense θ–valued Moisil propositional logic, Int. J. of Computers, Communications and Control, 5, 642–653, (2010).
  • [9] C. Chirită, Tense θ–valued Łukasiewicz–Moisil algebras, J. Mult. Valued Logic Soft Comput., 17, (1), 1–24,
  • [10] C. Chirită, Polyadic tense θ–valued Łukasiewicz–Moisil algebras, Soft Computing, 16,(6), 979–987, (2012).
  • [11] D. Diaconescu and G. Georgescu, Tense operators on MV -algebras and Łukasiewicz-Moisil algebras, Fund. Inform. 81 (4), 379–408, (2007).
  • [12] W. Dzik, E. Orłowska and C. van Alten, Relational representation theorems for general lattices with negations, Relations and Kleene algebra in computer science, 162–176, Lecture Notes in Comput. Sci., 4136, Springer, Berlin, 2006.
  • [13] A. V. Figallo and G. Pelaitay, Note on tense SHn–algebras, An. Univ. Craiova Ser. Mat. Inform., 38 (4), 24–32, (2011).
  • [14] A. V. Figallo and G. Pelaitay, Tense Operators on De Morgan Algebras, to appear in Log. J. IGPL.
  • [15] A. V. Figallo and Pelaitay, Tense operators on SHn-algebras, Pioneer J. of Algebra, Number Theory and Appl. 1,33–41, (2011).
  • [16] B. Jónsson and A. Tarski, Boolean algebras with operators I, American Journal of Mathematics 73, 891–939, (1951).
  • [17] T. Kowalski, Varieties of tense algebras, Rep. Math. Logic, 32, 53–95, (1998).
  • [18] Gr. C. Moisil, Recherches sur les logiques non-chrysippiennes, Ann. Sci. Univ. Iassy, 26, 1940, 431–466.
  • [19] E. Orłowska and I. Rewitzky, Duality via Truth: Semantic frameworks for lattice–based logics, Log. J. IGPL., 13 (2005), 467–490.
  • [20] E. Orłowska and I. Rewitzky, Discrete duality and its applications to reasoning with incomplete information. In: M. Kryszkiewicz, J.F. Peters, H. Rybiński, A. Skowron (eds.) Rough Sets and Intelligent Systems Paradigms, Lecture Notes in Artificial Intelligence, vol. 4585, pp. 51–56. Springer–Verlag, Heidelberg (2007)
  • [21] J.Paseka, Operators on MV–algebras and their representations, Fuzzy Sets and Systems, 232, 62-73, (2013), 10.101/j.fss.2013.02.010.
  • [22] H. A. Priestley, Representation of distributive lattices by means of ordered Stone spaces, Bull. London Math. Soc., 2, 186–190, (1970).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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