An algebraic treatment of propositional logic

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 eac...

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Detalles Bibliográficos
Autor: Merma Mora, Miguel Ángel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:Perú
Institución:Universidad Nacional Mayor de San Marcos
Repositorio:Revistas - Universidad Nacional Mayor de San Marcos
Idioma:español
OAI Identifier:oai:revistasinvestigacion.unmsm.edu.pe:article/18678
Acceso en línea:https://revistasinvestigacion.unmsm.edu.pe/index.php/tesis/article/view/18678
Access Level:acceso abierto
Palabra clave:Lógica proposicional
Interpretación algebraica
Álgebra de Boole
Reducción algebraica
Propositional logic
Algebraic interpretation
Boolean algebra
Algebraic reduction
Descripción
Sumario: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.