Some results on the simply separable function sets in partial k-valued logic

In multiple-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 of the later problem depends on determining all precomplete classes. For partial multiple-valued logic, the decision problem for completeness had been thoroughly solved by determining all the precomplete classes (seven species altogether), but the decision and construction for Sheffer functions haven´t been solved completely. In this paper, we focus on the third species of precomplete sets - the simply separable function set, research and discuss the number and construction problem of it.