The Decision On The Minimal Covering Of Function Sets Preserving Binary Simply Separable Relation In Partial Four-Valued Logic

Multiple-valued logic is the logic which has more than two values. It can easily solve the problem which can't be solved effectively by two-valued logic. Basing on its unique function and broad application foreground, it has been developed prosperously and became a significant branch of computer science. The research of multiple-valued logic includes many aspects, the most important parts are decision on completeness theory of function sets, decision and construction for Sheffer functions.The decision on completeness of function sets is one of the most crucial and fundamental problems in the construction theory of multiple-valued functions, and it also 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 the decision and construction for Sheffer function, which reduced to determining the minimal covering of precomplete classes. As to the complete multiple-valued logic function, it was solved. While concerning the partial multiple-valued logic function, it has not been fully solved yet.The work of this thesis is decision on minimal covering of precomplete classes in partial four-valued logic. It mainly discusses simply separable relation function sets. Firstly, the basic concepts of multiple-valued logic are summarized systematically, we also introduce the achievements of completeness theory in complete and partial multiple-valued logic. Then basing on the simple separable relation function sets were categorised by similar relation, first we pick out the function sets if they can be covered by T_E . To the rest which are not picked out, they are proved that they do belong to the minimal covering by constructing functions. As the results, we get seven classes ,totally 46 members of preserved binary simply separable relation function sets which are the members of the minimal covering in partial four-valued logic. Finally we present some properties of simple separable function sets in partial four-valued logic.