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Abstrakty
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
Czasopismo
Rocznik
Tom
Strony
317--329
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
- 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).
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Bibliografia
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