Duality in finite many-valued logics (Q2534158)

The notion of duality is a familiar one in the two-valued propositional calculus. As there is only one negation connective in the two-valued propositional calculus, the dual of a truth-function can be uniquely determined. In many-valued logics there are many negation connectives. Intuitively as one would expect, it is possible to define a dual corresponding to a truth-function relative to each of the different negations. In this paper, an attempt is made to generalize the notion of duality to many-valued logics by requiring that the definition of duality must meet some natural conditions. It is suggested that among the different negations, the negation function \[\begin{pmatrix} 1 & 2 & 3 &\dots & n \\ n & n -1 & n - 2 & \dots & 1\end{pmatrix}, \] which is a permutation of order 2 of the set of truth-values, is a natural choice.