An algebraic treatment of propositional logic

• Autor: Merma Mora, Miguel Ángel
• Formato: artículo
• Fecha de Publicación: 2019
• Institución: Universidad Nacional Mayor de San Marcos
• Repositorio: Revistas - Universidad Nacional Mayor de San Marcos
• Lenguaje: español
• OAI Identifier: oai:ojs.csi.unmsm:article/18678
• Enlace del recurso: https://revistasinvestigacion.unmsm.edu.pe/index.php/tesis/article/view/18678
• Nivel de acceso: acceso abierto
• Materia: Lógica proposicional; Interpretación algebraica; Álgebra de Boole; Reducción algebraica; Propositional logic; Algebraic interpretation; Boolean algebra; Algebraic reduction

Propositional logical language is translated into algebraic language. For this it establishes two fundamental correspondences, that exists between the truth (V) and the zero (0) and that which relates the falsehood (F) with the one (1). These correspondences establish the algebraic equivalent of each one of the operators of the propositional logic and, in turn, allow to reduce by algebraic means any formula of propositional logic. If the formula in question is tautological, its algebraic version is reductible to 0; If the formula is contradictory, its algebraic version is reductible to 1 and if the formula is contingent, its algebraic version is not reduced to 0 or to 1, but to an expression of smaller extension that admits between the values of its algebraic matrix at least a 0 and at least A 1.