The Decision For Sheffer Functions In Partial Multiple-valued Logic

Multiple -valued logic developed from two-valued logic .In classical two-valued logic, there are only two states, namely "true" and "false", any proposition must be either true or false, i.e., the law of the excluded middle is tenable. However, many things in objective world can not be described completely by two-valued logic. As a result, multiple-valued logic came into begin.The study of multiple-valued logic includes the theory, circuit & system, and applications. Now multiple-valued logic has been an important branch of the computer science and technology.In chapter 1, the achievements of completeness theory of functions in total and partial multiple-valued logic are summarized systematically; the decision for Sheffer functions is discussed. Lastly, some lately research on multiple-valued logic with relation to computer science and technology are introduced.hi chapter 2, the author studies the decision for Sheffer functions in partial multiple-valued logic, and gets the results as follows.1. Some full symmetric function sets must be die component part of the minimal covering of precomplete classes in P*k.2. Some simple separable function sets must be the component part of the minimal covering of precomplete classes in P*k.3. Some symmetric function sets must not to be the component part of the minimal covering of precomplete classes in P*k.4. Some regular separable function sets must not to be the component part of the minimal covering of precomplete classes in P*k.