R <sub> 0 </ Sub> Algebra Simplified And Relatively True Nature Of The Study

In order to establish a strict logical basis for fuzzy reasoning, Professor Wang Guojun proposed a new fuzzy propositional calculus system L* and R0-algebra which match with the system L* in the semantic. The establishment of these new theories has aroused concerns of domestic and foreign experts and scholars. Professor Wu Hongbo proposed the lattice implication representation of R0-algebra. This result not only simplified the algebra R0 but also make it semantically correspond with L* system more harmonious. In ChapterⅡof this article, combining with properties of lattices, we further simplify conditions in R0-algebra and give out the V-semi-lattice implication representation of R0-algebra. Afterwards, in order to integrate the flexibility of computational mathematics into mathematical logic and expand its range of applications, by grading the basic concepts in propositional logics, Professor Wang Guojun introduced the concept that truth degrees of formulas. On this basis, the two-valued propositional logic system L, continuous valued propositional logic system Lukasiewicz,L* and n-valued logic system Ln,Ln* were graded, thus the theory of quantitative logic was established. Professor Wu Hongbo introduced the relative truth degree of formulas and relative pseudo-distance beteen two formulas in two-valued propositional logic system L and n-valued propositional logic system Ln,Ln*, thus let the usual truth degree of formulas as exceptional cases of the relative truth degree,thus expand the application scope of the theory of truth degree. Based on these results,in the chapterⅢand chapterⅣof this article, we do further research of the relative truth degree in various systems.Full-text is divided into four chapters, the actual structure and content arrange-ment are as follows:ChapterⅠ:Preliminaries.In this chapter,we recall the basic knowledge of par-tially ordered set,lattice,semilattice,MV-algebra,R0-algebra,propositional logic system Lukasiewicz and L* which are used in this paper.ChapterⅡ:The V-semi-lattice implication representation of R0-algebra and its simplified form. In the first part of this chapter, combining with properties of lattice, we further study the inherent link between conditions in R0-algebra and then get the V-semi-lattice implication representation of R0-algebra. In the second part, with the correspondence of axioms in the fuzzy system L* and conditions in R0-algebra, this representation form is further simplifed.ChapterⅢ:The relative truth degree of formulas in continuous-valued prepo-sitional logic system Lukasiewicz and some of its propoties. Total can be divided into three sections. In sectionⅠ, we recalled the relevant knowledge of truth degree, such as the expansion of the function induced by formulas and integral truth degree of formulas. In sectionⅡ, the relative truth degree of formulas in propositional logic system Lukasiewicz is defined, and its various fundamental properties are dis-cussed. On the basis of sectionⅡ, the relative pseudo-distance beteen two formulas is proposed in sectionⅢand aslo its various fundamental properties are discussed.ChapterⅣ:The relative divergence and relative consistency degree of theories in propositional logic system Ln*. Total can be divided into three sections. In the first section, some properties of relative truth degree of formulas in propositional logic system Ln* are further studied. In sectionⅡ,the relative divergence degree of theories and its related properties are described. In sectionⅢ, theηΓ0 consistency degree of any theory relate to a particular theoryΓ0 is introduced and the equivalent characterization of consistent theory, inconsistent theory, fully consistent theory relate to a particular theoryΓ0 are given. For finite theories, we aslo define theδΓ0 consistency degree relate to a particular theoryΓ0, and give out the intrinsic link between these two kinds of consistency degree.