Representation by tuples of Lukasiewicz–Moisil algebras of order n + 1 and applications
We intend to present a generalization of the techniques developed by Fidel, and independently by Vakarelov, widely known as twist–structure semantics, to the more general context of n–valued logics.
We focus here on the well–known Lukasiewicz–Moisil algebras of order n + 1. Departing from a twist–structure representation for De Morgan algebras, we construct an structure with more axes (2n + 2 axes actually) that shows to represent the Moisil operators more efficiently. With this representation, the theory of homomorphisms, filters and free algebras is simplified significantly. Finally, we complete this study with the presentation of a logic sound and complete with these new models.
MSC (2010): Primary 06D35, Secondary 03B60.
Key words: many valued logics, twist structures, Lukasiewicz–Moisil algebras.