¡÷ Bl_ ~ * Formal System And The Nm (?) The Form Of Systematic Study

With the deep study of artifical intelligence and information science,the study of fuzzy logic and many-valued logic have become one of the hot topics in the field. Recently,many scholars devoted themselves to the study of all kinds of logic system,and have achived a series of important research results. Professor Wu Hongbo introduced BL*Δsystem,and proved out that BL*Δis completeness. Professor Wang Sanmin established NML system and NML-algebra based on MTL system, and showed that NML is standard completeness.Based on the research of the above theories,the construction and the main contents of this paper are as follows:Chapter 1:Preliminaries. In this chapter,we gave the basic concepts and results of preordered set, lattice,residuate lattice and some kinds of logic system which will be used in this paper.Chapter 2:The syntactic theory of the generalized and collectively generalizedΔ-modus ponens problems in BLΔ*.Firstly,the concept ofΔ-root of theory in BLΔ* is proposed and basic properties of A-roots are investigated.Secondly, triple I solu-tions of the generalized and collectively generalized modus ponens problems in BLΔ* are discussed.Finally,the generalized and collectively generalizedΔ-modus ponens problems are prposed,the syntactic solutions of them are defined and the relations between their solutions and theΔ-roots of the corresponding formulas are studied.Chapter 3:On the finite strong completeness of NML. Firstly,the proper-ties of NML-chain are studied, and it is proved that each NML-chain is partially embeddable into [0,1] J.Secondly.the finite strong completeness theorem of NML is investigated by means of the partially embeddable property. Finally,it points out that NML does not enjoy the strong completeness about infinite theory.Chapter 4:The theory of truth degrees of formulas in NML3n+i system. Firstly,the definition of the truth degrees of formulas is proposed in 3n+1-valued NML system, and its main properties are discussed.Secondly,the truth modus po-nens and truth hypothetical syllogism are discussed.Finally,the concepts of similarity degree and pseudo-metric between formulas are introduced by means of the truth degree,and their main properties are studied.