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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UNESP
2025-07-01
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| Series: | CQD Revista Eletrônica Paulista de Matemática |
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| 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. |
| format | Article |
| id | doaj-art-b5cc8ffda27f4bf0816381be1c2133a2 |
| institution | DOAJ |
| 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 |
| work_keys_str_mv | AT herculesdearaujofeitosa acharacterizationofadjunctioninamanyvaluedmodalsystem AT romuloalbanodefreitas acharacterizationofadjunctioninamanyvaluedmodalsystem AT herculesdearaujofeitosa characterizationofadjunctioninamanyvaluedmodalsystem AT romuloalbanodefreitas characterizationofadjunctioninamanyvaluedmodalsystem |