Logic, order and implicative systems
DOI:
https://doi.org/10.15448/1984-6746.2019.3.32214Keywords:
Logical consequence. Order. Implication. Implicative algebra. Implicative logicAbstract
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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