A Duality for -0-Valued -Lukasiewicz–Moisil Algebras and Applications
A.V. Figallo, I. Pascual and A. Ziliani
Philosophical problems arising from the idea that there are statements which are neither true nor false, led to the formulation of many–valued logics by Łukasiewicz. Since then, plenty of research has been developed in this area. In 1968, Gr.C. Moisil found an example which gave him the motivation he had been looking for in order to legitimate the introduction and study of infinitely–valued Łukasiewicz algebras, so he defined θ-valued Łukasiewicz algebras, where θ is the order type of a chain. In this article, we determine a topological duality for θ-valued Łukasiewicz–Moisil algebras (or LMθ -algebras) equivalent to the one given by A. Filipoiu in 1980. Not only does the duality enable us to obtain a description of the LMθ -congruences on an LMθ -algebra, but also to characterize the subdirectly irreducible LMθ -algebras. Furthermore, we extend the above study to the case of LMθ -algebras with negation arriving through a different method at the results indicated by V. Boicescu et al (Łukasiewicz–Moisil Algebras, Annals of Discrete Mathematics 49, North–Holland, 1991).
Keywords: Theta-valued Lukasiewicz-Moisil algebras, topological dualities, congruences, subdirectly irreducible algebras.