Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte la política de Acceso Abierto del editor

Abstract:

The notion of an existential m-quantifier on a three-valued Łukasiewicz algebra is introduced and studied. The class of three-valued Łukasiewicz algebras endowed with an existential m-quantifier is equational and hence determines a variety denoted by Vm. We prove that the existential m-quantifiers are interdefinable with the existential quantifiers introduced by Luiz Monteiro. Hence every algebra in Vm is term equivalent to a monadic three-valued Łok;ukasiewicz algebra. We characterize the simple algebras in the variety Vm which turns out to be semisimple. We also find some connections between existential mquantifiers and those existential quantifiers defined on bounded distributive lattices considered by Cignoli in [3], including Boolean algebras. Finally, we prove a Kripke-style representation theorem. ©2017 Old City Publishing, Inc.

Registro:

Documento: Artículo
Título:An alternative notion of quantifiers on three-valued Łukasiewicz algebras
Autor:Petrovich, A.; Lattanzi, M.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Buenos Aires, Pabellón i - Ciudad Universitaria, Buenos Aires, Argentina
Facultad de Ciencias Exactas y Naturales, Universidad Nacional de la Pampa, Av. Uruguay 151, Santa Rosa, La Pampa, Argentina
Palabras clave:MV-algebras; Quantifiers; Three-valued Łukasiewicz algebras; Algebra; Bounded distributive lattice; Existential quantifiers; MV-algebras; Quantifiers; Representation theorem; Three-valued; Boolean algebra
Año:2017
Volumen:28
Número:4-5
Página de inicio:335
Página de fin:360
Título revista:Journal of Multiple-Valued Logic and Soft Computing
Título revista abreviado:J. Mult.-Valued Logic Soft Comput.
ISSN:15423980
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15423980_v28_n4-5_p335_Petrovich

Referencias:

  • Boicescu, V., Filipoiu, A., Georgescu, G., Rudeanu, S., (1991) Łukasiewicz-Moisil Algebras, , North-Holland
  • Chang, C.C., Algebraic Analysis of Many-Valued Logics (1958) Trans. Amer. Math. Soc, 88, pp. 467-490
  • Cignoli, R., Quantifiers on distributive lattices (1991) Discrete Mathematics, 96, pp. 183-197
  • Cignoli, R., D'Ottaviano, I., Mundici, D., (2000) Algebraic Foundations of Many-valued Reasoning, , Kluwer Academic Publishers
  • Cimadamore, C., Díaz Varela, P., Monadic MV-algebras are Equivalent to Monadic l-groups with Strong Unit (2011) Studia Logica, 98, pp. 175-201
  • Di Nola, A., Grigolia, R., On monadic MV-Algebras (2004) Annals of Pure and Applied Logic, 128 (1-3), pp. 125-139
  • Georgescu, G., Iorgulescu, A., Leustean, I., Monadic and Closure MV-Algebras (1998) Multiple Valued Logic, 3, pp. 235-257
  • Grigolia, R.S., Algebraic analysis of Łukasiewicz-Tarski's n-valued logical systems (1977) Selected Papers on Łukasiewicz Sentential Calculi, pp. 81-92. , R. Wójcicki, G. Malinowski (Eds.)
  • Hájek, P., (1998) Methamathematics of Fuzzy Logic, , Kluwer Academic Publishers
  • Halmos, P., Algebraic logic i (1955) Compositio Mathematica, 12, pp. 217-249
  • Iorgulescu, A., (1984) Algebre Łukasiewicz-Moisil (1 + θ)-valente Cu Negaţie, , Universitatea Bucureşti, PhD Thesis (in Romanian), iunie
  • Iorgulescu, A., On the construction of three-valued Łukasiewicz-Moisil algebras (1984) Discrete Mathematics, 48, pp. 213-227
  • Iorgulescu, A., Functors between categories of three-valued Łukasiewicz-Moisil algebras- i (1984) Discrete Mathematics, 49, pp. 121-131
  • Iorgulescu, A., Monadic involutive pseudo-BCK algebras (2008) Acta Universitatis Apulensis, (15), pp. 159-178
  • Iorgulescu, A., Connections between MVn algebras and n-valued Łukasiewicz-Moisil algebras Part II (1999) Discrete Mathematics, 202 (1-3), pp. 113-134
  • Lattanzi, M., Petrovich, A., (2007) A Duality for Monadic (n+1)-valued MV-algebras, pp. 107-117. , Actas del IX Congreso Dr. Antonio A. R. Monteiro
  • Monteiro, L., Sur les Algebres de Łukasiewicz Inyectives (1974) Notas de Lógica Matemática, 23-25, pp. 578-581. , 24
  • Monteiro, L., (1974) Algebras de Łukasiewicz Trivalentes Monádicas, Notas de Lógica Matemática 32, , Instituto de Matemática, Universidad Nacional del Sur
  • Mundici, D., Interpretation of FAC∗-algebras in Łukasiewicz Sentential Calculus (1986) J. Funct. Anal, 65 (1), pp. 15-63
  • Petrovich, A., Existential Demi-quantifiers on L-groups, Submitted to Publication
  • Rutledge, J.D., (1959) A Preliminary Investigation of the Infinitely Many-valued Predicate Calculus, , Ph. D. Thesis, Cornell University
  • Schwartz, D., Theorie der polyadischen MV-algebren endlicher Ordnung (1977) Math. Nachr, 78, pp. 131-138
  • Schwartz, D., Polyadic MV-algebras Zeitschrift für Math (1980) Logik und Grundlagen der Mathematik, 26, pp. 561-564

Citas:

---------- APA ----------
Petrovich, A. & Lattanzi, M. (2017) . An alternative notion of quantifiers on three-valued Łukasiewicz algebras. Journal of Multiple-Valued Logic and Soft Computing, 28(4-5), 335-360.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15423980_v28_n4-5_p335_Petrovich [ ]
---------- CHICAGO ----------
Petrovich, A., Lattanzi, M. "An alternative notion of quantifiers on three-valued Łukasiewicz algebras" . Journal of Multiple-Valued Logic and Soft Computing 28, no. 4-5 (2017) : 335-360.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15423980_v28_n4-5_p335_Petrovich [ ]
---------- MLA ----------
Petrovich, A., Lattanzi, M. "An alternative notion of quantifiers on three-valued Łukasiewicz algebras" . Journal of Multiple-Valued Logic and Soft Computing, vol. 28, no. 4-5, 2017, pp. 335-360.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15423980_v28_n4-5_p335_Petrovich [ ]
---------- VANCOUVER ----------
Petrovich, A., Lattanzi, M. An alternative notion of quantifiers on three-valued Łukasiewicz algebras. J. Mult.-Valued Logic Soft Comput. 2017;28(4-5):335-360.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15423980_v28_n4-5_p335_Petrovich [ ]