Logic, order and implicative systems

Authors

DOI:

https://doi.org/10.15448/1984-6746.2019.3.32214

Keywords:

Logical consequence. Order. Implication. Implicative algebra. Implicative logic

Abstract

In this paper, we discuss three basic topics for the understanding of a notion of
reason, they are, consequence relation, order relation and formal system. From a characterization of formal system, we define both mentioned relations. We detach an interrelationship between consequence and order. This way we present other formal systems that indicate specifically a concept of implication, given by implicative algebras and implicative logic. This implicative logic, which has as its models the implicative algebras, has only one operator, the implication operator, that once again leads us for the consequence and order notions. Finally, from the consequence notion presented in the text, we introduce an algebraic model for this implicative logic.

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Author Biographies

Cristiane Alexandra Lázaro, Universidade Estadual Paulista ‘Júlio de Mesquita Filho, Bauru, SP, Brasil.

Doutora em Matemática pela Universidade Estadual de Campinas (UNICAMP), Campinas (SP), Brasil. Professora Assistente na Universidade Estadual Paulista (UNESP), Bauru (SP), Brasil.

Hércules de Araujo Feitosa, Universidade Estadual Paulista ‘Júlio de Mesquita Filho, Bauru, SP, Brasil.

Doutor em Filosofia pela Universidade Estadual de Campinas, Brasil (UNICAMP), Campinas (SP), Brasil. Professor Assistente na Universidade Estadual Paulista (UNESP), Bauru (SP), Brasil.

Marcelo Reicher Soares, Universidade Estadual Paulista ‘Júlio de Mesquita Filho, Bauru, SP, Brasil.

Doutor em Matemática pela Universidade de São Paulo (USP), São Paulo, (SP), Brasil. Professor Assistente na Universidade Estadual Paulista (UNESP), Bauru (SP), Brasil.

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Published

2019-12-31

How to Cite

Lázaro, C. A., Feitosa, H. de A., & Soares, M. R. (2019). Logic, order and implicative systems. Veritas (Porto Alegre), 64(3), e32214. https://doi.org/10.15448/1984-6746.2019.3.32214

Issue

Vol. 64 No. 3 (2019): Epistemology & Philosophy of Language

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Articles

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