On the categorizing of preserving quaternary regularly separable relations in partial four-valued logic

In many-valued logic theories, the decision and construction for Sheffer functions is an important problem. The decision for Sheffer functions is interrelated to the decision for completeness of functions set, and the solution can be reduced to determining the minimal coverings of precomplete. It's well known that each precomplete set is a function set, T(Gm) , preserving the relation Gm, therefore, the categorizing of this relation has provided the determination of precomplete set's minimal covering with more convenient ways. In this paper, preserving quaternary regularly separable relations in partial four-valued logic are categorized by similar relation.