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A Topological Approach to Tense LMn×m-Algebras

dc.contributor.authorFigallo, Aldo V.
dc.contributor.authorPascual, Inés
dc.contributor.authorPelaitay, Gustavo
dc.date.accessioned2021-05-05T15:52:36Z
dc.date.available2021-05-05T15:52:36Z
dc.date.issued2020-03-30
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/35370
dc.description.abstractIn 2015, tense n × m-valued Lukasiewicz–Moisil algebras (or tense LMn×m-algebras) were introduced by A. V. Figallo and G. Pelaitay as an generalization of tense n-valued Łukasiewicz–Moisil algebras. In this paper we continue the study of tense LMn×m-algebras. More precisely, we determine a Priestley-style duality for these algebras. This duality enables us not only to describe the tense LMn×m-congruences on a tense LMn×m-algebra, but also to characterize the simple and subdirectly irreducible tense LMn×m-algebras.en
dc.language.isoen
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl
dc.relation.ispartofseriesBulletin of the Section of Logic;1en
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0
dc.subjectPriestley-style topological dualityen
dc.subjectPriestley spacesen
dc.subjecttense De Morgan algebrasen
dc.subjectTense LMn×m-algebrasen
dc.titleA Topological Approach to Tense LMn×m-Algebrasen
dc.typeOther
dc.page.number13–51
dc.contributor.authorAffiliationFigallo, Aldo V. - Universidad Nacional de San Juan, Instituto de Ciencias Básicasen
dc.contributor.authorAffiliationPascual, Inés - Universidad Nacional de San Juan, Instituto de Ciencias Básicasen
dc.contributor.authorAffiliationPelaitay, Gustavo - Universidad Nacional de San Juan, Instituto de Ciencias Básicasen
dc.identifier.eissn2449-836X
dc.references[1] V. Boicescu, A. Filipoiu, G. Georgescu and S. Rudeanu, Łukasiewicz–Moisil Algebras, Annals of Discrete Mathematics, Vol. 49 (1991), North-Holland.en
dc.references[2] M. Botur, I. Chajda, R. Halaš and M. Kolařík, Tense operators on Basic Algebras, International Journal of Theoretical Physics, Vol. 50, No. 12 (2011), pp. 3737–3749.en
dc.references[3] M. Botur, J. Paseka, On tense MV -algebras, Fuzzy Sets and Systems, Vol. 259 (2015), pp. 111–125.en
dc.references[4] J. Burges, Basic tense logic, [in:] D. M. Gabbay, F. Günter (eds.), Handbook of Philosophical Logic, Vol. II, Reidel, Dordrecht (1984), pp. 89–139.en
dc.references[5] I. Chajda, Algebraic axiomatization of tense intuitionistic logic, Central European Journal of Mathematics, Vol. 9, No. 5 (2011), pp. 1185–1191.en
dc.references[6] I. Chajda and J. Paseka, Dynamic effect algebras and their representations, Soft Computing, Vol. 16, No. 10 (2012), pp. 1733–1741.en
dc.references[7] I. Chajda and M. Kolařík, Dynamic Effect Algebras, Mathematica Slovaca, Vol. 62, No. 3 (2012), pp. 379–388.en
dc.references[8] C. Chiriţă, Tense θ-valued Moisil propositional logic, International Journal of Computers Communications and Control, Vol. 5 (2010), pp. 642–653.en
dc.references[9] C. Chiriţă, Tense θ-valued Łukasiewicz–Moisil algebras, Journal of Multiple-Valued Logic and Soft Computing, Vol. 17, No. 1 (2011), pp. 1–24.en
dc.references[10] R. Cignoli, Moisil Algebras, Notas de Lógica Matemática, Vol. 27 (1970), Instituto de Matemática, Universidad del Sur, Bahía Blanca.en
dc.references[11] W. Cornish and P. Fowler, Coproducts of De Morgan algebras, Bulletin of the Australian Mathematical Society, Vol. 16 (1977), pp. 1–13.en
dc.references[12]D. Diaconescu and G. Georgescu, Tense operators on MV -algebras and Łukasiewicz–Moisil algebras, Fundamenta Informaticae, Vol. 81, No. 4 (2007), pp. 379–408.en
dc.references[13] A. V. Figallo, G. Pelaitay, n × m-valued Łukasiewicz–Moisil algebras with two modal operators, South American Journal of Logic, Vol. 1, No. 1 (2015), pp. 267–281.en
dc.references[14] A. V. Figallo, I. Pascual, G. Pelaitay, A topological duality for tense LMn-algebras and applications, Logic Journal of the IGPL, Vol. 26, No. 4 (2018), pp. 339–380.en
dc.references[15] A. V. Figallo and G. Pelaitay, Note on tense SHn-algebras, Analele Universitatii din Craiova. Seria Matematica-Informatica, Vol. 38, No. 4 (2011), pp. 24–32.en
dc.references[16] A. V. Figallo and G. Pelaitay, Tense operators on De Morgan algebras, Logic Journal of the IGPL, Vol. 22, No. 2, (2014), pp. 255–267.en
dc.references[17] A. V. Figallo and G. Pelaitay, A representation theorem for tense n × m-valued Łukasiewicz–Moisil algebras, Mathematica Bohemica, Vol. 140, No. 3 (2015), pp. 345–360.en
dc.references[18] A. V. Figallo and G. Pelaitay, Discrete duality for tense Łukasiewicz–Moisil algebras, Fundamenta Informaticae, Vol. 136, No. 4 (2015), pp. 317–329.en
dc.references[19] T. Kowalski, Varieties of tense algebras, Reports on Mathematical Logic, Vol. 32 (1998), pp. 53–95.en
dc.references[20] Gr. C. Moisil, Recherches sur les logiques non-chrysippiennes, Annales scientifiques de l'Université de Jassy, Vol. 26 (1940), pp. 431–466.en
dc.references[21] J. Paseka, Operators on MV-algebras and their representations, Fuzzy Sets and Systems, Vol. 232 (2013), pp. 62–73.en
dc.references[22] H. A. Priestley, Representation of distributive lattices by means of ordered Stone spaces, Bulletin of the London Mathematical Society, Vol. 2 (1970), pp. 186–190.en
dc.references[23] A. V. Figallo and C. Sanza, Álgebras de Łukasiewicz matriciales n × m-valuadas con negación, Noticiero de la Unión Matemática Argentina, Vol. 93 (2000).en
dc.references[24] A. V. Figallo and C. Sanza, The NSn × m-propositional calculus, Bulletin of the Section of Logic, Vol. 35, No. 2 (2008), pp. 67–79.en
dc.references[25] A. V. Figallo and C. Sanza, Monadic n × m-valued Łukasiewicz–Mosil algebras, Mathematica Bohemica, Vol. 137, No. 4 (2012), pp. 425–447.en
dc.references[26] A. V. Figallo and G. Pelaitay, A representation theorem for tense n × m-valued Łukasiewicz–Moisil algebras, Mathematica Bohemica, Vol. 140, No. 3 (2015), pp. 345–360.en
dc.references[27] A. V. Figallo, I. Pascual, G. Pelaitay, A new topological duality for n × m-valued Łukasiewicz–Moisil algebras, Asian–European Journal of Mathematics (2019).en
dc.references[28] C. Gallardo, C. Sanza and A. Ziliani, F-multipliers and the localization of LMn × m-algebras, Analele Stiintice ale Universitatii Ovidius Constanta, Vol. 21, No. 1 (2013), pp. 285–304.en
dc.references[29] Gr. C. Moisil, Essais sur les logiques non Chrysippiennes, Ed. Academiei, Bucarest, 1972.en
dc.references[30] H. Priestley, Representation of distributive lattices by means of ordered Stone spaces, Bulletin of the London Mathematical Society, Vol. 2 (1970), pp. 186–190.en
dc.references[31] H. Priestley, Ordered topological spaces and the representation of distributive lattices, Proceedings of the London Mathematical Society, Vol. 3 (1972), pp. 507–530.en
dc.references[32] H. Priestley, Ordered sets duality for distributive lattices, Annals of Discrete Mathematics, Vol. 23 (1984), pp. 39–60.en
dc.references[33] C. Sanza, Notes on n × m-valued Łukasiewicz algebras with negation, Logic Journal of the IGPL, Vol. 6, No. 12 (2004), pp. 499–507.en
dc.references[34] C. Sanza, n × m-valued Łukasiewicz algebras with negation, Reports on Mathematical Logic, Vol. 40 (2006), pp. 83–106.en
dc.references[35] C. Sanza, On n × m-valued Łukasiewicz-Moisil algebras, Central European Journal of Mathematics, Vol. 6, No. 3 (2008), pp. 372–383.en
dc.references[36] W. Suchoń, Matrix Łukasiewicz Algebras, Reports on Mathematical Logic, Vol. 4 (1975), pp. 91–104.en
dc.contributor.authorEmailFigallo, Aldo V. - avfigallo@gmail.com
dc.contributor.authorEmailPascual, Inés - ipascual756@hotmail.com
dc.contributor.authorEmailPelaitay, Gustavo - gpelaitay@gmail.com
dc.identifier.doi10.18778/0138-0680.2020.02
dc.relation.volume49


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