An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras
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 inte...
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2017
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Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16618297_v11_n4_p439_Gonzalez http://hdl.handle.net/20.500.12110/paper_16618297_v11_n4_p439_Gonzalez |
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paper:paper_16618297_v11_n4_p439_Gonzalez2023-06-08T16:25:44Z An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras Four-valued Łukasiewicz algebras monadic logics quantifiers 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. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16618297_v11_n4_p439_Gonzalez http://hdl.handle.net/20.500.12110/paper_16618297_v11_n4_p439_Gonzalez |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-134 |
collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
topic |
Four-valued Łukasiewicz algebras monadic logics quantifiers |
spellingShingle |
Four-valued Łukasiewicz algebras monadic logics quantifiers An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras |
topic_facet |
Four-valued Łukasiewicz algebras monadic logics quantifiers |
description |
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. |
title |
An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras |
title_short |
An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras |
title_full |
An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras |
title_fullStr |
An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras |
title_full_unstemmed |
An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras |
title_sort |
alternative definition of quantifiers on four-valued łukasiewicz algebras |
publishDate |
2017 |
url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16618297_v11_n4_p439_Gonzalez http://hdl.handle.net/20.500.12110/paper_16618297_v11_n4_p439_Gonzalez |
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1768546369105035264 |