On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice

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This article deals with many-valued modal logics, based only on the necessity operator, over a residuated lattice. We focus on three basic classes, according to the accessibility relation, of Kripke frames: the full class of frames evaluated in the residuated lattice (and so defining the minimum mod...

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Autores principales:	Bou, F., Esteva, F., Godo, L., Rodríguez, R.O.
Formato:	JOUR
Materias:	fuzzy logic many-valued logic Many-valued modal logic modal logic substructural logic Computer circuits Fuzzy logic Lattice constants Axiomatization Idempotent Kripke frames Modal logic Residuated lattices Substructural logic Many valued logics
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_0955792X_v21_n5_p739_Bou
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

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spelling	todo:paper_0955792X_v21_n5_p739_Bou2023-10-03T15:51:50Z On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice Bou, F. Esteva, F. Godo, L. Rodríguez, R.O. fuzzy logic many-valued logic Many-valued modal logic modal logic substructural logic Computer circuits Fuzzy logic Lattice constants Axiomatization Idempotent Kripke frames Modal logic Residuated lattices Substructural logic Many valued logics This article deals with many-valued modal logics, based only on the necessity operator, over a residuated lattice. We focus on three basic classes, according to the accessibility relation, of Kripke frames: the full class of frames evaluated in the residuated lattice (and so defining the minimum modal logic), the ones evaluated in the idempotent elements and the ones only evaluated in 0 and 1. We show how to expand an axiomatization, with canonical truth-constants in the language, of a finite residuated lattice into one of the modal logic, for each one of the three basic classes of Kripke frames. We also provide axiomatizations for the case of a finite MV chain but this time without canonical truth-constants in the language. © 2009 The Author. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0955792X_v21_n5_p739_Bou
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	fuzzy logic many-valued logic Many-valued modal logic modal logic substructural logic Computer circuits Fuzzy logic Lattice constants Axiomatization Idempotent Kripke frames Modal logic Residuated lattices Substructural logic Many valued logics
spellingShingle	fuzzy logic many-valued logic Many-valued modal logic modal logic substructural logic Computer circuits Fuzzy logic Lattice constants Axiomatization Idempotent Kripke frames Modal logic Residuated lattices Substructural logic Many valued logics Bou, F. Esteva, F. Godo, L. Rodríguez, R.O. On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice
topic_facet	fuzzy logic many-valued logic Many-valued modal logic modal logic substructural logic Computer circuits Fuzzy logic Lattice constants Axiomatization Idempotent Kripke frames Modal logic Residuated lattices Substructural logic Many valued logics
description	This article deals with many-valued modal logics, based only on the necessity operator, over a residuated lattice. We focus on three basic classes, according to the accessibility relation, of Kripke frames: the full class of frames evaluated in the residuated lattice (and so defining the minimum modal logic), the ones evaluated in the idempotent elements and the ones only evaluated in 0 and 1. We show how to expand an axiomatization, with canonical truth-constants in the language, of a finite residuated lattice into one of the modal logic, for each one of the three basic classes of Kripke frames. We also provide axiomatizations for the case of a finite MV chain but this time without canonical truth-constants in the language. © 2009 The Author.
format	JOUR
author	Bou, F. Esteva, F. Godo, L. Rodríguez, R.O.
author_facet	Bou, F. Esteva, F. Godo, L. Rodríguez, R.O.
author_sort	Bou, F.
title	On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice
title_short	On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice
title_full	On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice
title_fullStr	On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice
title_full_unstemmed	On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice
title_sort	on the minimum many-valued modal logic over a finite residuated lattice
url	http://hdl.handle.net/20.500.12110/paper_0955792X_v21_n5_p739_Bou
work_keys_str_mv	AT bouf ontheminimummanyvaluedmodallogicoverafiniteresiduatedlattice AT estevaf ontheminimummanyvaluedmodallogicoverafiniteresiduatedlattice AT godol ontheminimummanyvaluedmodallogicoverafiniteresiduatedlattice AT rodriguezro ontheminimummanyvaluedmodallogicoverafiniteresiduatedlattice
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On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice

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