An Algebraic Construction of Moisil Operators in (n+1)-valued Lukasiewicz Propositional Calculus

Lukasiewcz residuation algebras of order (n + 1) (or Cn+1-algebras) with Moisil possibility operators were introduced by A. V. Figallo in [5]. These algebras constitute a variety and are algebraic models of a fragment of the (n + 1)-valued Lukasiewicz propositional calculus. In this calculus Lukasiewicz implication -> along with unary conectives (sigma(i))(i is an element of J), better known as Moisil possibility operators, are taken as primitives. Let Ln+1 = {0, 1/n, 2/n, ... , n-1/n, 1} and J = {1, 2, ... , n}. Then, this variety is generated by the algebra < Ln+1, ->, (sigma(i))(i is an element of J), 1 >, where -> is defined by x -> y = min{1, 1 - x + y} and sigma(i) : Ln+1 -> Ln+1 is defined by sigma(i)(j/n) = {(1 if j + 1 >= n + 1) (0) (if j + 1 < n + 1) , for every j is an element of {0} boolean OR J, i is an element of J. In the present work, we describe a method, inspired by the one developed by W. Suchon in [14], for constructing unary operators sigma(i), 2 <= i <= n, from -> and sigma(1).