A characterization of adjunction in a many-valued modal system

Galois connections are pairs of functions, defined over ordered sets, that preserve some particular aspects. They are studied in the context of algebraic structures. As a logic topic, we take the four-valued logic PM4N that contemplates, at least, two modal operators for the notions of necessary an...

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Main Authors: Hércules de Araújo Feitosa, Romulo Albano de Freitas
Format: Article
Language:Portuguese
Published: UNESP 2025-07-01
Series:CQD Revista Eletrônica Paulista de Matemática
Subjects:
Online Access:https://sistemas.fc.unesp.br/ojs/index.php/revistacqd/article/view/489
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author Hércules de Araújo Feitosa
Romulo Albano de Freitas
author_facet Hércules de Araújo Feitosa
Romulo Albano de Freitas
author_sort Hércules de Araújo Feitosa
collection DOAJ
description Galois connections are pairs of functions, defined over ordered sets, that preserve some particular aspects. They are studied in the context of algebraic structures. As a logic topic, we take the four-valued logic PM4N that contemplates, at least, two modal operators for the notions of necessary and possible. In this paper, we develop a particular four-valued implication for PM4N, which constitutes a Galois pair with the two modal operators. Then, we show some properties of the logic just considering the correlates algebraic developments.
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issn 2316-9664
language Portuguese
publishDate 2025-07-01
publisher UNESP
record_format Article
series CQD Revista Eletrônica Paulista de Matemática
spelling doaj-art-b5cc8ffda27f4bf0816381be1c2133a22025-08-20T02:40:14ZporUNESPCQD Revista Eletrônica Paulista de Matemática2316-96642025-07-012510.21167/cqdv25e25005A characterization of adjunction in a many-valued modal systemHércules de Araújo Feitosa0Romulo Albano de Freitas1Unesp/Department of MathematicsUnesp - Universidade Estadual Paulista "Júlio de Mesquita Filho"Galois connections are pairs of functions, defined over ordered sets, that preserve some particular aspects. They are studied in the context of algebraic structures. As a logic topic, we take the four-valued logic PM4N that contemplates, at least, two modal operators for the notions of necessary and possible. In this paper, we develop a particular four-valued implication for PM4N, which constitutes a Galois pair with the two modal operators. Then, we show some properties of the logic just considering the correlates algebraic developments.https://sistemas.fc.unesp.br/ojs/index.php/revistacqd/article/view/489Galois connectionMany-valued logicModal logicAlgebraic logic
spellingShingle Hércules de Araújo Feitosa
Romulo Albano de Freitas
A characterization of adjunction in a many-valued modal system
CQD Revista Eletrônica Paulista de Matemática
Galois connection
Many-valued logic
Modal logic
Algebraic logic
title A characterization of adjunction in a many-valued modal system
title_full A characterization of adjunction in a many-valued modal system
title_fullStr A characterization of adjunction in a many-valued modal system
title_full_unstemmed A characterization of adjunction in a many-valued modal system
title_short A characterization of adjunction in a many-valued modal system
title_sort characterization of adjunction in a many valued modal system
topic Galois connection
Many-valued logic
Modal logic
Algebraic logic
url https://sistemas.fc.unesp.br/ojs/index.php/revistacqd/article/view/489
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