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
Autores principales:	González, L.J., Lattanzi, M.B., Petrovich, A.G.
Formato:	JOUR
Materias:	Four-valued Łukasiewicz algebras monadic logics quantifiers
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_16618297_v11_n4_p439_Gonzalez
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

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spelling	todo:paper_16618297_v11_n4_p439_Gonzalez2023-10-03T16:28:43Z An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras González, L.J. Lattanzi, M.B. Petrovich, A.G. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 González, L.J. Lattanzi, M.B. Petrovich, A.G. 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.
format	JOUR
author	González, L.J. Lattanzi, M.B. Petrovich, A.G.
author_facet	González, L.J. Lattanzi, M.B. Petrovich, A.G.
author_sort	González, L.J.
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
url	http://hdl.handle.net/20.500.12110/paper_16618297_v11_n4_p439_Gonzalez
work_keys_str_mv	AT gonzalezlj analternativedefinitionofquantifiersonfourvaluedłukasiewiczalgebras AT lattanzimb analternativedefinitionofquantifiersonfourvaluedłukasiewiczalgebras AT petrovichag analternativedefinitionofquantifiersonfourvaluedłukasiewiczalgebras AT gonzalezlj alternativedefinitionofquantifiersonfourvaluedłukasiewiczalgebras AT lattanzimb alternativedefinitionofquantifiersonfourvaluedłukasiewiczalgebras AT petrovichag alternativedefinitionofquantifiersonfourvaluedłukasiewiczalgebras
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An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras

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