Approximation Properties of Positive Boolean Functions

The universal approximation property is an important characteristic of models employed in the solution of machine learning problems. The possibility of approximating within a desired precision any Borel measurable function guarantees the generality of the considered approach. The properties of the class of positive Boolean functions, realizable by digital circuits containing only and and or ports, is examined by considering a proper coding for ordered and nominal variables, which is able to preserve ordering and distance. In particular, it is shown that positive Boolean functions are universal approximators and can therefore be used in the solution of classification and regression problems.