Mutually Exclusive Nuances of Truth in Moisil Logic

Moisil logic, having as algebraic counterpart Lukasiewicz-Moisil algebras, provides an alternative way to reason about vague information based on the following principle: a many-valued event is characterized by a family of Boolean events. However, using the original definition of Lukasiewicz-Moisil algebra, the principle does not apply for subalgebras. In this paper we identify an alternative and equivalent definition for the n-valued Lukasiewicz-Moisil algebras, in which the determination principle is also saved for arbitrary subalgebras, which are characterized by a Boolean algebra and a family of Boolean ideals. As a consequence, we prove a duality result for the n-valued Lukasiewicz-Moisil algebras, starting from the dual space of their Boolean center. This leads us to a duality for MVn-algebras, since are equivalent to a subclass of n-valued Lukasiewicz-Moisil algebras.