2014/12/09 by Denisa Diaconescu, Diaconescu, Denisa, Ioana Leustean +1
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO
paper · pdf · doi:10.48550/arxiv.1412.3008
arxiv created 2014/12/09 · arxiv updated 2014/12/10
Moisil logic, having as algebraic counterpart Łukasiewicz-Moisil algebras, provide 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 Łukasiewicz-Moisil algebra, the principle does not apply for subalgebras. In this paper we identify an alternative and equivalent definition for the n-valued Łukasiewicz-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 Łukasiewicz-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 Łukasiewicz-Moisil algebras.