Algebraic properties of a learning multiple-valued logic network

A simple arithmetic piecewise linear operator that can be used as a basic element to construct a large multiple-valued network is defined. The algebra is proved to be a functionally complete set and capable of constructing any multiple-valued logic functions. The layered piecewise linear node networks provide a natural and general architecture for backpropagation, thus making a learning multiple-valued logic network possible.<<ETX>>