The Minimal Covering of Maximal Partial Clones in 4-valued Logic

Abstract

A partial function f on a k-element set Ek is a partial Sheffer function if every partial function on Ek is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone on Ek, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on Ek. It is shown that there is only one minimal covering for k = 4 and it is determined. Additionally all 1 102 coherent relations for k = 4 are given in a full list.