剩余格上逻辑度量空间的拓扑性质  

Topological properties analysis of logical metric spaces on the residuated lattice

作　　者：段景瑶 DUAN Jing-yao(Department of Mathematics and Information Sciences,Baoji University of Arts and Sciences,Baoji 721013,Shaanxi,China)

机构地区：[1]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《山东大学学报（理学版）》2018年第12期9-16,共8页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11626035);宝鸡市科技计划资助项目(2017JH2-22);宝鸡文理学院重点资助项目(ZK2017023)

摘　　要：首先研究了逻辑度量空间([0,1],ρ_R)与度量空间(F(X),H_R)的关系,其次讨论了[0,1]剩余格上逻辑度量空间中Cauchy-列的收敛性问题,最后在一般剩余格上建立了一致拓扑结构,为我们研究一般剩余格的结构提供了一种新的方法,并为逻辑推理系统的鲁棒性分析奠定了理论基础。Firstly,the relation between logical metric space( [0,1],ρR) and metric space( F( X),HR) is analysized. Secondly,convergence of the Cauchy-sequences are investigate. Finally,the uniform topology is constructed on the general residuated lattice.The work provides a newway to study the structure of residuated lattice,and lay a solid theoretical foundation for the robustness analysis of logical inference systems.

关 键 词：剩余格 Cauchy-序列 完备 一致拓扑 

分 类 号：O153.1[理学—数学] O189.1[理学—基础数学]