The Semantic Explanation Of System S6

System S6 possesses two peculiarities: (1) it has no necessity principle N, so abnormal worlds must be introduced into its semantics; (2) it includes MMp as its axiom. Though the semantic explanation of MMp can use abnormal worlds but on the other hand can also use general worlds. The difference between the two kinds of explanations reflects the diversity of our judge principles of possible worlds. We can regard abnormal worlds as dead points but on the other hand we can use a constructive way to prove that they're not dead points. This contradiction reflects the complex situation faced by the semantics of S6. But this paper tries to make clear such complex situation and to describe the suitable possible worlds background of S6's semantic explanation.The paper is mainly divided into six parts:1. ntroduction of S6 and explanation (demonstration) of some special theories and syntax characters.2. emantic explanation of S6. Also explains the introducing of abnormal worlds, abnormal frames, set X and the changes of evaluation V. Points out that letting SB rule be ineffective in abnormal worlds is the way to avoid logic contradiction to happen in them.3. Points out that S6 uses the dead point character of abnormal worlds to avoid asharper question__can possible worlds permit contradictions to exist inside? Fromre-pondering the definition of accessible relation to reveal that it's unnecessary for abnormal worlds to be dead points.4. Demonstrates that abnormal worlds can be not dead points by a constructiveway on the basis of the third part. But the demonstration relies on two hypotheses: (1) can possible worlds be permitted to include logic contradiction? (2) Can possible worlds be composed only by propositions?5. Search for answers to question (1) (2) through re-pondering the definition of possible worlds. First, criticizes the viewpoint that possible worlds cannot be defined. Second, reviews the six representative definitions of possible worlds and find out each one's answers to question (1) and (2). The author supports definition I, II and III to give confirmative answers to question (1) and (2); for the same reason, gives doubts to definition IV, V and VI while considering their persisting in consistent set is unnecessary.6. With question (1) and (2) in mind, the author re-ponders the philosophical noumenon status of possible worlds and criticizes the real existent theory as well as the possible state theory but agrees with the viewpoint that negates the question of possible worlds' substantiality.