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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Detalles Bibliográficos
Publicado: 2017
Materias:
Four-valued Łukasiewicz algebras
monadic logics
quantifiers
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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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_16618297_v11_n4_p439_Gonzalez
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spelling paper:paper_16618297_v11_n4_p439_Gonzalez2025-07-30T19:01:23Z 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
_version_ 1840321991756742656

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