Towards an algebrization of a linear temporal logic

Authors

DOI:

https://doi.org/10.21167/cqdv25e25007

Keywords:

Logic, Algebraic Logic, Temporal Logic, Neighbourhood Logic

Abstract

The subject of this paper is the Propositional Neighbourhood Logic (PNL), a case of linear temporal logic and an extension of Classical Propositional Logic that results from the inclusion of modal operators that deal with certain temporal aspects. In this context, the validity of a proposition is strictly related to some temporal interval. We highlight some formal aspects of this logic and its formalization in some deductive systems (or proof systems), which naturally reflect the formal aspects of time. We aim to investigate algebraic models for Propositional Neighbourhood Logic. However, in this work, we focus exclusively on presenting the Soundness result, one of the necessary steps towards obtaining an adequate (sound and complete) model, between the axiomatic system of PNL and the planned algebraic model.

Author Biographies

  • Romulo Albano de Freitas, Unesp/PPGFil - Marília, Unesp/PPGFil - Marília

    Graduated in Mathematics from Universidade Estadual Paulista "Júlio de Mesquita Filho" -
    Unesp, Bauru campus. He is a member of the research group, certified by CNPQ, "Sistemas
    Adaptativos, Lógica e Computação Inteligente" (SALCI). He has experience in teaching and
    research in Logic. Currently studying for a master's degree in the Postgraduate Program in
    Philosophy at FFC - Unesp Marília, with an emphasis on Logic. Has interest in algebraic
    developments for logics/algebraic logic, non-classical logics and proof theory.

  • Hércules de Araujo Feitosa, Unesp/Departamento de Matemática, Unesp/Department of Mathematics

    Graduated 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.

  • Luiz Henrique da Cruz Silvestrini, Unesp/Departamento de Matemática, Unesp/Department of Mathematics

    Undergraduated in Mathematics (Full Licentiate), UNESP, FC, Bauru, 2002. Masters Degree in Philosophy (Philosophy of Mind, Epistemology and Logic), UNESP, FFC, Marília, 2005. Ph.D in Philosophy (Logic), UNICAMP, IFCH, Campinas, 2011. Assistant Professor at the São Paulo State University (UNESP), School of Sciences, Department of Mathematics. Experienced in Logic and Epistemology. Proficient on the following subjects: non-classical logics, theories of truth, quantifiers, and tableaux method.

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Published

2025-07-25

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

Towards an algebrization of a linear temporal logic. C.Q.D. - Revista Eletrônica Paulista de Matemática, Bauru, v. 25, p. e25007, 2025. DOI: 10.21167/cqdv25e25007. Disponível em: https://sistemas.fc.unesp.br/ojs/index.php/revistacqd/article/view/461. Acesso em: 12 oct. 2025.

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