Lukasiewicz Implication Prealgebras

• Autores: Figallo, Aldo Victorio; Pelaitay, Gustavo Andrés
• Año de publicación: 2017
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: LUKASIEWICZ IMPLICATION PREALGEBRAS; I-PREALGEBRAS; LUKASIEWICZ RESIDUATION BCK-ALGEBRAS
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

In this paper we revise the Lukasiewicz implication prealgebras which we will call Lukasiewicz I−prealgebras to sum up. They were used by Antonio Jes´us Rodr´ıguez Salas on his doctoral thesis under the name of Sales prealgebras. These structures are a natural generalization of the notion of I−prealgebras, introduced by A. Monteiro in 1968 aiming to study using algebraic techniques the {→}-fragment of the three-valued Lukasiewicz propositional calculus. The importance of Lukasiewicz I−prealgebras focuses on the fact that from these structures we can directly prove that Lindembaun-Tarski algebra in the {→}- fragment of the infinite-valued Lukasiewicz implication propositional calculus is a Lukasiewicz residuation BCK-algebra in the sense of Berman and Blok [1]. This last result is indicated without a proof on Komori’s paper ([8]) and it is suggested on his general lines on the Rodriguez Salas thesis.
Fil: Figallo, Aldo Victorio. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentina
Fil: Pelaitay, Gustavo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentina