Modal laws in many-valued systems

Authors

DOI:

https://doi.org/10.14393/BEJOM-v5-2024-70314

Keywords:

Modal laws, Four valued logics, Modal logics, Paraconsistent logics

Abstract

Since Dugundji, it has been known that there is no finite matrix semantics for modal logics between S1 and S5. However, it remains interesting to know what can be valid among the modal laws relative to many-valued matrices. The logic PM4N was introduced by Jean-Yves Beziau as a modal and 4-valued system, planned to accept several modal laws. From that matrix semantics, the paper shows some valid results. In this paper, we compare the system PM4N with two well-known logics: the usual modal system S5 and the paraconsistent logic J3. We show that the set of S5 theorems is properly included in the set of PM4N theorems; and every theorem of PM4N is a theorem of J3.

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Author Biographies

Hércules de Araujo Feitosa, Universidade Estadual Paulista - FC - Bauru

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.

Romulo Albano de Freitas, Universidade Estadual Paulista - FFC - 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.

Marcelo Reicher Soares, Universidade Estadual Paulista - FC - Bauru

Post-Doctorate at the Centro de Lógica, Epistemologia e História da Ciência CLE-UNICAMP (2015), PhD in Mathematics from the Universidade de São Paulo - USP (2000), Master in Mathematics from the Universidade de São Paulo - USP (1989) and holds a degree Degree in Mathematics from Universidade São Francisco (1983). He is currently an Assistant Professor at the Universidade Estadual Paulista Júlio de Mesquita Filho - UNESP and works as a professor and advisor in the Postgraduate Program in Mathematics in the PROFMAT National Network. He has experience in teaching and research in the area of Mathematical Analysis, with an emphasis on Generalized Colombeau Functions. He currently works in Fundamentals and Mathematical Logic with an emphasis on Non-Standard Analysis and Algebraic Logic. Participates in the Research Groups, certified by CNPQ, "Sistemas Adaptativos, Lógica e Computação Inteligente" and " Lógica e Epistemologia ".

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Published

2024-05-09

How to Cite

FEITOSA, H. de A.; DE FREITAS, R. A.; SOARES, M. R. Modal laws in many-valued systems: . BRAZILIAN ELECTRONIC JOURNAL OF MATHEMATICS, Uberlândia, v. 5, p. 1–22, 2024. DOI: 10.14393/BEJOM-v5-2024-70314. Disponível em: https://seer.ufu.br/index.php/BEJOM/article/view/70314. Acesso em: 22 dec. 2024.

Issue

Vol. 5 (2024): Brazilian Electronic Journal of Mathematics

Section

Articles - Pure Mathematics

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Copyright (c) 2024 Hércules de Araujo Feitosa, Romulo Albano de Freitas, Marcelo Reicher Soares

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