命题逻辑系统理论(广义)根性质及应用  

Properties and applications of the roots of theories in propositional logic systems

作　　者：张建成[1] 苏连塔[1] 

机构地区：[1]泉州师范学院数学与计算机学院,福建泉州362000

出　　处：《山东大学学报（工学版）》2013年第4期87-92,共6页Journal of Shandong University（Engineering Science）

基　　金：福建省教育厅A类科技资助项目(2010JA10235)

摘　　要：应用演绎定理、广义演绎定理和公式真度理论,基于经典命题逻辑系统、Lukasiewicz命题逻辑系统,Gdel命题逻辑系统和R0-命题逻辑系统上讨论理论Γ的根和广义根性质,给出了一个有(广义)根的理论Γ的结论集D(Γ)的结构。应用(广义)根的性质与构造,获得了理论Γ的相容度、发散度和公式A是Γ-结论的隶属度等新的计算公式。By means of theory of truth degrees of formulas, the properties of the generalized roots of theories in classi- cal two-valued logic system, Lukasiewicz propositional logic, Godel propositional logic, and the R0-propositional logic were first studied according to deduction theorems. Then, it was proved that all consequences of a theory Г, named D（Г）, were completely determined by its generalized root whenever Г had a generalized root. Finally, a new algo- rithm of divergence degree, consistency degree, and Membership degree of Г-conclusion was obtained.

关 键 词：命题逻辑 理论根 广义根 发散度 相容度 隶属度 

分 类 号：O141.1[理学—数学] O153[理学—基础数学]