Abstract:
An alternative notion of an existential quantifier on four-valued Łukasiewicz algebras is introduced. The class of four-valued Łukasiewicz algebras endowed with this existential quantifier determines a variety which is denoted by M23L4. It is shown that the alternative existential quantifier is interdefinable with the standard existential quantifier on a four-valued Łukasiewicz algebra. Some connections between the new existential quantifier and the existential quantifiers defined on bounded distributive lattices and Boolean algebras are given. Finally, a completeness theorem for the monadic four-valued Łukasiewicz predicate calculus corresponding to the dual of the alternative existential quantifier is proven. © 2017, Springer International Publishing AG, part of Springer Nature.
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Documento: |
Artículo
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Título: | An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras |
Autor: | González, L.J.; Lattanzi, M.B.; Petrovich, A.G. |
Filiación: | Facultad de Ciencias Exactas y Naturales, Universidad Nacional de La Pampa, Avda. Uruguay 151, Santa Rosa, La Pampa 6300, Argentina Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Buenos Aires, Pabellón I - Ciudad Universitaria, Buenos Aires, Argentina
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Palabras clave: | Four-valued Łukasiewicz algebras; monadic logics; quantifiers |
Año: | 2017
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Volumen: | 11
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Número: | 4
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Página de inicio: | 439
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Página de fin: | 463
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DOI: |
http://dx.doi.org/10.1007/s11787-017-0181-4 |
Título revista: | Logica Universalis
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Título revista abreviado: | Log. Universalis
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ISSN: | 16618297
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16618297_v11_n4_p439_Gonzalez |
Referencias:
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Citas:
---------- APA ----------
González, L.J., Lattanzi, M.B. & Petrovich, A.G.
(2017)
. An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras. Logica Universalis, 11(4), 439-463.
http://dx.doi.org/10.1007/s11787-017-0181-4---------- CHICAGO ----------
González, L.J., Lattanzi, M.B., Petrovich, A.G.
"An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras"
. Logica Universalis 11, no. 4
(2017) : 439-463.
http://dx.doi.org/10.1007/s11787-017-0181-4---------- MLA ----------
González, L.J., Lattanzi, M.B., Petrovich, A.G.
"An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras"
. Logica Universalis, vol. 11, no. 4, 2017, pp. 439-463.
http://dx.doi.org/10.1007/s11787-017-0181-4---------- VANCOUVER ----------
González, L.J., Lattanzi, M.B., Petrovich, A.G. An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras. Log. Universalis. 2017;11(4):439-463.
http://dx.doi.org/10.1007/s11787-017-0181-4