邻域语义学与推演系统的完全性

Neighbourhood Semantics and Completeness of Deductive Systems

Completeness is regarded as an important criterion in deciding whether or not a deductive system is a logical system. However, completeness is related to semantic interpretations, therefore, it may fail to serve as such a criterion when arbitrary semantic interpretations are admitted. In this article we introduce a formal language that is suitable for all propositional logics, and construct the semantics - neighbourhood semantics - for this language. Furthermore, we discuss 6 different types of completeness for deductive systems and obtain some formal results from the discussion. Also, we analyze the meaning of the 6 types of completeness in the background of the general semantics and thus explain some important principles in the correspondence of the 6 types of completeness to the general semantics. Finally, we give a simple argument for the view that the combinatorial principle and the principle that validity is determined by values are the fundamental principles of logical analysis, and, on the basis of this we discuss how a deductive system can be a logical system.