An alternative notion of quantifiers on three-valued Łukasiewicz algebras

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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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Autores principales:	Petrovich, A., Lattanzi, M.
Formato:	JOUR
Materias:	MV-algebras Quantifiers Three-valued Łukasiewicz algebras Algebra Bounded distributive lattice Existential quantifiers Representation theorem Three-valued Boolean algebra
Acceso en línea:	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

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spelling	todo:paper_15423980_v28_n4-5_p335_Petrovich2023-10-03T16:22:57Z An alternative notion of quantifiers on three-valued Łukasiewicz algebras Petrovich, A. Lattanzi, M. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, A. Lattanzi, M. 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.
format	JOUR
author	Petrovich, A. Lattanzi, M.
author_facet	Petrovich, A. Lattanzi, M.
author_sort	Petrovich, A.
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
url	http://hdl.handle.net/20.500.12110/paper_15423980_v28_n4-5_p335_Petrovich
work_keys_str_mv	AT petrovicha analternativenotionofquantifiersonthreevaluedłukasiewiczalgebras AT lattanzim analternativenotionofquantifiersonthreevaluedłukasiewiczalgebras AT petrovicha alternativenotionofquantifiersonthreevaluedłukasiewiczalgebras AT lattanzim alternativenotionofquantifiersonthreevaluedłukasiewiczalgebras
_version_	1807322002940231680

An alternative notion of quantifiers on three-valued Łukasiewicz algebras

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