A characterization of adjunction in a many-valued modal system

Authors

DOI:

https://doi.org/10.21167/cqdv25e25005

Keywords:

Galois connection, Many-valued logic, Modal logic, Algebraic logic

Abstract

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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Author Biographies

  • Hércules de Araujo Feitosa, Unesp/Department of Mathematics, Unesp/Departamento de Matemática
    Undergraduated in Mathematics from Fundação Educacional de Bauru (1984), Master in
    Fundamentals of Mathematics from Universidade Estadual Paulista - UNESP - IGCE (1992)
    and PhD in Logic and Philosophy of Science from Universidade Estadual de Campinas -
    UNICAMP - IFCH (1998). Since 1988 he has been a professor at UNESP, Faculty of Sciences,
    Department of Mathematics, Bauru Campus. He is currently an associate professor (livre
    docente) and is accredited in the Postgraduate Program in Philosophy at UNESP - FFC -
    Marília. His academic experience has an emphasis on teaching Logic and Fundamentals of
    Mathematics and his scientific investigations are focused on logic, translations between logics,
    algebraic models, quantifiers and non-classical logics.
  • Romulo Albano de Freitas, Unesp/FC, Unesp - Universidade Estadual Paulista "Júlio de Mesquita Filho"

    Graduado em Licenciatura em Matemática pela Universidade Estadual Paulista "Júlio de Mesquita Filho" - Unesp, campus de Bauru. É membro do grupo de pesquisa, certificado pelo CNPQ, "Sistemas Adaptativos, Lógica e Computação Inteligente" (SALCI). Tem experiência em ensino e pesquisa em Lógica. Atualmente, mestrando pelo Programa de Pós-Graduação em Filosofia da FFC - Unesp Marília, com ênfase em Lógica. Têm interesse em desenvolvimentos algébricos para lógica/lógicas algébricas, lógicas não-clássicas e teoria da prova.

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Published

2025-07-08

Issue

v. 25, 2025 - Edição Ermac

Section

Edição Especial ERMAC 2024

License

Copyright (c) 2025 C.Q.D. - Revista Eletrônica Paulista de Matemática

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

FEITOSA, Hércules de Araujo; FREITAS, Romulo Albano de. A characterization of adjunction in a many-valued modal system. C.Q.D. - Revista Eletrônica Paulista de Matemática, Bauru, v. 25, p. e25005, 2025. DOI: 10.21167/cqdv25e25005. Disponível em: https://revistas.bauru.unesp.br/index.php/revistacqd/article/view/489. Acesso em: 2 jun. 2026.

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