论泛集合、泛逻辑和泛代数的关系  

On the Relationship among Universal Set,Universal Logic and Universal Algebra

作　　者：何华灿[1] 罗敏霞[1] 

机构地区：[1]西北工业大学计算机学院,西安710072

出　　处：《重庆工学院学报》2006年第2期1-6,共6页Journal of Chongqing Institute of Technology

基　　金：国家自然科学基金资助项目(60273087);北京市自然科学基金资助项目(4032009)

摘　　要：根据描述清晰事物的经典集合、经典逻辑和L indenbaum代数是三位一体的同构关系的事实,猜想在描述复杂事物的泛集合、泛逻辑和泛代数之间也存在这种三位一体关系,以此作为研究的基础,建立了部分代数系统之间的层次关系,并给出了与之同构的逻辑系统,并利用泛逻辑学中关于线序柔性命题逻辑学的研究成果,部分证实了上述猜想.According to the fact that there is trinitarian isomorphic relationship among classical set, classical logic and Lindenbaum algebra, which describe the clear things, this paper firstly supposes that there is also this kind of trinitarian isomorphic relationship among Universal set, Universal logic and U- niversal algebra and thus establishes the hierarchy among some algebra systems. Secondly, it gives the isomorphic logic systems correspondingly. Finally, it partly proves the correctness of this supposition by using the study results of the flexible proposition logic on linear order of Universal logic.

关 键 词：泛集合 泛逻辑 泛代数 同构关系 柔性逻辑学 

分 类 号：O14[理学—数学]