The Decision On The Minimal Covering Of Function Sets Preserving Ternary And Quaternary Simply Separable Relations In Partial Four-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 mainly includes three aspects: theory, circuit & system, and its applications. The completeness of multiple-valued logic function is an important subject of multiple-valued logic theory.In the theory of multiple-valued logic completeness, one of primary and important problems is the completeness of function sets,which can be solved depending on the decision for all the precomplete sets of partial K-valued function sets. And another is the decision and make of sheffer functions, which can be solved by finding out all of the minimal covering of the precomplete sets.The main work of this thesis is decision on minimal covering of precomplete classes in partial four-valued logic. We focus on function sets preserving simply separable relations .The thesis is divided into five chapters. The first chapter is exordium, mainly introduced the background of this task and some recently research on multiple-valued logic. At the same time, the main work of my task is also summarized.In the second chapter, we introduced the basic concepts and theorem of completeness theory. In which the function sets preserving simply separable relations and the theorem of completeness are emphasized. In the third chapter, we educed a conclusion which adapt to all general occasion and proved 26 classes sum to 58 of 90 function sets that preserving ternary and quaternary simply separable relations are not belong to the minimal covering of precomplete function sets in partial four-valued logic by means of the property of similar relationship. In the fourth chapter, we proved the rest 16 classes sum to 32 of precomplete sets deducted from chapter 3 must among the minimal covering of precomplete sets in partial four-valued logic. Finally we educed some sheffer functions on partitial four-valued logic in chapter 5.