L_n System And L_n * Degree Of Theory In The System

In2006, professor Wang Guojun put forward a new theory-Quantitative Logic. This theory receives widespread attention not only because it grades the logic con-cepts from semantics, but also because it introduces numerical calculation into math-ematical logic. This work is a bridge between symbolic language and numerical com-putation, which makes the mathematical logic more flexibility and greatly expands its practical applications. Recently, professor Wu Hongbo proposed the concept of generalized truth degree and studied its main properties.Based on the research of the above theories, the construction and the main contents of this paper are as follows:Chapter1:Preliminaries. In this chapter,we give the basic concepts and results of the truth degree, similarity, pseudometric which will be used in this paper.Chapter2:The common properties of the truth degree theories in system Ln and system L*n. Firstly, some common properties of the truth degree in system Ln and system L*n are given:Secondly, some common properties of the similarity between formulas are discussed in system Ln and system L*n. Finally, some common properties of the pseudometric between formulas are studied in system Ln and system Ln*.Chapter3:Some special properties of the truth degree and the similarity between formulas in system Ln. Firstly, some special properties of the truth degree are given in system Ln. Secondly, some special properties of the similarity between formulas are given in system Ln.Chapter4:Conclusions of the approximate reasoning in system Ln*. In this chapter, we give a brief discussion of the theory of the approximate reasoning in system Ln*Chapter5:Counter-examples of the similarity propositions and their correction forms in system Ln, system Ln*and system L*. Firstly, the erroneous similarity proposition is pointed out and the counter-example is given in system Ln. Secondly, the erroneous similarity proposition is pointed out and the counter-example is given in system Ln*. Thirdly, the erroneous similarity proposition is pointed out and the counter-example is given in system L*. Finally, the correction forms of the erroneous propositions are given in system Ln, system Ln*and system L*.