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

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.