Contents I. Introduction
Traditionally, multiple-valued logic deals with truth functions of the form , where is a finite set of truth values. We slightly generalize this setup by allowing the domain and the codomain of the function to be different sets, and we do not assume that they are finite sets. We investigate the partially ordered set of functions that can be obtained from an arbitrary n-variable function via identifications of variables. Such functions are called minors of , and they are naturally partially ordered, since some minors of can be also minors of each other; we shall use the symbol to denote this poset of minors of the function . In fact, the minor relation is a partial order on the set of all functions of several variables from to , if we regard functions differing only in inessential variables and/or in the order of their variables as equivalent. Our goal is to characterize the principal ideals of this poset up to isomorphism (see Figure 2). We give the precise definitions in Section II; here we present only an illustrative example.
