Logic, order and implicative systems

In this paper, we discuss three basic topics for the understanding of a notion ofreason, 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...

Descripción completa

Detalles Bibliográficos
Autores: Lázaro, Cristiane Alexandra, Feitosa, Hércules de Araujo, Soares, Marcelo Reicher
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:Brasil
Institución:Pontifícia Universidade Católica do Rio Grande do Sul (PUCRS)
Repositorio:Veritas (Porto Alegre. Online)
Idioma:portugués
OAI Identifier:oai:ojs.revistaseletronicas.pucrs.br:article/32214
Acceso en línea:https://revistaseletronicas.pucrs.br/veritas/article/view/32214
Access Level:acceso abierto
Palabra clave:Logical consequence. Order. Implication. Implicative algebra. Implicative logic
Consecuencia lógica
Orden. Implicación. Álgebra implicativa. Lógica implicativa.
Consequência lógica. Ordem. Implicação. Álgebra implicativa. Lógica implicativa.
Descripción
Sumario:In this paper, we discuss three basic topics for the understanding of a notion ofreason, 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.