An alternative notion of quantifiers on three-valued Łukasiewicz algebras

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 a...

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Autor principal:	Petrovich, Alejandro Gustavo
Publicado:	2017
Materias:	MV-algebras Quantifiers Three-valued Łukasiewicz algebras Algebra Bounded distributive lattice Existential quantifiers Representation theorem Three-valued Boolean algebra
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15423980_v28_n4-5_p335_Petrovich http://hdl.handle.net/20.500.12110/paper_15423980_v28_n4-5_p335_Petrovich
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_15423980_v28_n4-5_p335_Petrovich
record_format	dspace
spelling	paper:paper_15423980_v28_n4-5_p335_Petrovich2025-07-30T18:56:47Z An alternative notion of quantifiers on three-valued Łukasiewicz algebras Petrovich, Alejandro Gustavo MV-algebras Quantifiers Three-valued Łukasiewicz algebras Algebra Bounded distributive lattice Existential quantifiers MV-algebras Quantifiers Representation theorem Three-valued Boolean algebra 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. Fil:Petrovich, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15423980_v28_n4-5_p335_Petrovich http://hdl.handle.net/20.500.12110/paper_15423980_v28_n4-5_p335_Petrovich
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	MV-algebras Quantifiers Three-valued Łukasiewicz algebras Algebra Bounded distributive lattice Existential quantifiers MV-algebras Quantifiers Representation theorem Three-valued Boolean algebra
spellingShingle	MV-algebras Quantifiers Three-valued Łukasiewicz algebras Algebra Bounded distributive lattice Existential quantifiers MV-algebras Quantifiers Representation theorem Three-valued Boolean algebra Petrovich, Alejandro Gustavo An alternative notion of quantifiers on three-valued Łukasiewicz algebras
topic_facet	MV-algebras Quantifiers Three-valued Łukasiewicz algebras Algebra Bounded distributive lattice Existential quantifiers MV-algebras Quantifiers Representation theorem Three-valued Boolean algebra
description	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.
author	Petrovich, Alejandro Gustavo
author_facet	Petrovich, Alejandro Gustavo
author_sort	Petrovich, Alejandro Gustavo
title	An alternative notion of quantifiers on three-valued Łukasiewicz algebras
title_short	An alternative notion of quantifiers on three-valued Łukasiewicz algebras
title_full	An alternative notion of quantifiers on three-valued Łukasiewicz algebras
title_fullStr	An alternative notion of quantifiers on three-valued Łukasiewicz algebras
title_full_unstemmed	An alternative notion of quantifiers on three-valued Łukasiewicz algebras
title_sort	alternative notion of quantifiers on three-valued łukasiewicz algebras
publishDate	2017
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15423980_v28_n4-5_p335_Petrovich http://hdl.handle.net/20.500.12110/paper_15423980_v28_n4-5_p335_Petrovich
work_keys_str_mv	AT petrovichalejandrogustavo analternativenotionofquantifiersonthreevaluedłukasiewiczalgebras AT petrovichalejandrogustavo alternativenotionofquantifiersonthreevaluedłukasiewiczalgebras
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An alternative notion of quantifiers on three-valued Łukasiewicz algebras

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