Two deductions systems for the Logic PM4N

Authors

DOI:

https://doi.org/10.22481/intermaths.v3i2.11378

Keywords:

Deduction systems, Many-valued logics, Tableaux, Sequent calculus

Abstract

The logic PM4N was introduced by Jean-Yves Beziau as a modal and 4-valued system. In this introductory paper, the author presented the system from a matrix logic with four values disposed in a Boolean algebra with a modal operator for the notion of necessity. From that matrix semantics, the paper shows some valid results and stresses some motivations of the matrix semantics and of the system PM4N. In this paper we develop some additional aspects of that logic and present two deductive systems for it, a simple system of tableaux and a sequent calculus.

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Author Biographies

Hércules de Araújo Feitosa, São Paulo State University - UNESP: Bauru, São Paulo/SP, Brazil

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 worked at UNESP, College of Science, Department of Mathematics, Bauru Campus. He is currently an accredited Professor at the Graduate Program in Philosophy at UNESP - FFC - Marília. He has an academic experience in teaching Logic and Fundamentals of Mathematical Logic and his scientific investigations are directed to logic, translations between logics, algebraic models, quantifiers and non-classical logics. E-mail: hercules.feitosa@unesp.br

Romulo Albano de Freitas, São Paulo State University - UNESP: Bauru, São Paulo/SP, Brazil

Graduating in Mathematics Degree from Universidade Estadual Paulista Julio de Mesquita Filho - UNESP, Bauru campus. He is a member of the research group, certified by CNPQ, "Adaptive Systems, Logic and Intelligent Computing" (SALCI). He has already had experience in teaching and research in Logic, working as a monitor of the discipline "Computational Logic" at the Universidade Estadual Paulista Julio de Mesquita Filho - UNESP - and also participating as a colleger in the extension project "Logical Reasoning and the Principles of Argumentation" - RacioLog (project with grant and resources from PROEX). He is currently developing research in Logic and Proof Theory. E-mail: r.freitas@unesp.br

Marcelo Reicher Soares, São Paulo State University - UNESP: Bauru, São Paulo/SP, Brazil

Post-Doctorate at the Center for Logic, Epistemology and History of Science CLE-UNICAMP (2015), he holds a PhD in Mathematics from the University of São Paulo - USP (2000), a Master's degree in Mathematics from the University of São Paulo - USP (1989) and has Full Degree in Mathematics from Universidade São Francisco (1983). He is currently Assistant Professor Doctor II at the Universidade Estadual Paulista Júlio de Mesquita Filho - UNESP and works as a professor and advisor in the Graduate Program in Mathematics at the National PROFMAT 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. He participates in the Research Groups, certified by the CNPQ, “Adaptive Systems, Logic and Intelligent Computing” and “Logic and Epistemology”. E-mail: reicher.soares@unesp.br

References

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Published

2022-12-31

How to Cite

Feitosa, H. de A., de Freitas, R. A., & Soares, M. R. (2022). Two deductions systems for the Logic PM4N. INTERMATHS, 3(2), 38-55. https://doi.org/10.22481/intermaths.v3i2.11378

Issue

Vol. 3 No. 2 (2022)

Section

Artigos

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