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

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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Detalles Bibliográficos
Publicado: 2011
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:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0955792X_v21_n5_p739_Bou
http://hdl.handle.net/20.500.12110/paper_0955792X_v21_n5_p739_Bou
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_0955792X_v21_n5_p739_Bou
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spelling paper:paper_0955792X_v21_n5_p739_Bou2023-06-08T15:55:56Z On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice 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. 2011 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0955792X_v21_n5_p739_Bou 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
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.
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
publishDate 2011
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0955792X_v21_n5_p739_Bou
http://hdl.handle.net/20.500.12110/paper_0955792X_v21_n5_p739_Bou
_version_ 1768545701544853504

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