The Decision On The Minimal Covering Of Precomplete Classes In Partial Multiple-valued Logic

Multiple-valued logic is the logic that has more than two values. Multiple-valued logic can solve many problems easily while two-valued logic has too many difficulties to solve them, so multiple-valued logic has a bright future. The research of multiple-valued logic includes many aspects. Two of its most important parts are completeness theory of function sets, decision and construction for Sheffer functions.In multiple-valued logic theory, completeness theory of function sets is an important and fundamental problem, it is also the problem which must be solved in automata theory and multiple-valued logic network. The solution of this problem depends on determining all the precomplete classes in multiple-valued logic function sets.Another important problem in multiple-valued logic completeness theory is decision for Sheffer functions, which reduced to determining the minimal covering of precomplete classes in multiple-valued logic.The main work of this thesis is decision on minimal covering of precomplete classes in partial multiple-valued logic. In this paper, we focus on the simple seperable function sets (m=2) .In chapter 1, the basic concepts and important achievements of multiple-valued logic are summarized systematically. Some recently research on multiple-valued logic are also introduced. In chapter 2,we study the simple separable function sets (m=2) whose relation graph are connective or disconnective respectively, and achieve some useful results. In chapter 3,we attempt to study the function sets when m=3, and obtain the conclusion that one kind of full symmetric function sets must be the component part of the minimal covering of precomplete classes.