The Decision And Construction Of Sheffer Functions In Partial Four-valued Logic

Multiple-valued logic is a kind of non-classical logics which have more than two logic values; its research contents involve three parts, which is the theory of multiple-valued logic, circuit and system, and its applications.Multiple-valued logic is the logic that has more than two values. It includes three parts that the research of the theory, circuit & system, and its applications.The structure theory of multiple-valued logic functions is one of the study contents of multiple-valued logic theory, which includes completeness theory, function denotation theory, and unidirectional trapdoor functions. One of the important and fundamental problems is the completeness decision on function classes; it is also the problem which must be solved in automata theory. The solution of this problem depends on determining all the precomplete classes (also called maximal closed sets) in multiple-valued logic function sets. The decision and construction on Sheffer functions in multiple-valued logic is another important problem of multiple-valued logic completeness theory, which depends on fining the minimal covering of the precomplete classes. For the complete multiple-valued logic functions, it has been solved. However, for the partial multiple-valued logic functions, it has not been solved thoroughly.Decision and construction problem on the Sheffer function in partial four-valued logic is studied deeply in this thesis. The algorithm of decision and contruction on Sheffer functions in partial four-valued logic is given by means of the minimal covering of precomplete classes in partial four-valued logic. This algorithm can determine whether a function is the Sheffer function or not, furthermore, it can contruct all Sheffer functions in partial four-valued logic. It provides useful experience for the solusion of the decision and construction on Sheffer functions in partial k-valued logic, where k is larger than 4.