On η-valued functionally complete truth functions

Introduction. It is well known that the familiar Sheffer stroke function of the 2-valued propositional calculus is functionally complete (i.e., for any m, all 22' truth functions of m variables can be defined' in terms of the stroke function). Indeed, it is not difficult to show that of the 16 2-valued functions of two variables, exactly two of them are functionally complete. In this note we describe a rather large class of n-valued (n 2 2) functionally complete functions of two variables (cf. [1]-[12]). The proofs given are short, elementary and self-contained.