JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (12): 9-16.doi: 10.6040/j.issn.1671-9352.0.2017.645

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Topological properties analysis of logical metric spaces on the residuated lattice

DUAN Jing-yao   

  1. Department of Mathematics and Information Sciences, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi, China
  • Online:2018-12-20 Published:2018-12-18

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Abstract: 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 new way to study the structure of residuated lattice, and lay a solid theoretical foundation for the robustness analysis of logical inference systems.

Key words: residuated lattice, Cauchy-sequence, complete, uniform topology

CLC Number: 

  • O153.1
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