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...
| Autores: | , , |
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| 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. |
| 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. |
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