| 剩余格上逻辑度量空间的拓扑性质 |
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| 引用本文： | 段景瑶. 剩余格上逻辑度量空间的拓扑性质[J]. 山东大学学报(理学版), 2018, 53(12): 9-16. DOI: 10.6040/j.issn.1671-9352.0.2017.645 |
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| 作者姓名： | 段景瑶 |
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| 作者单位： | 宝鸡文理学院数学与信息科学学院, 陕西 宝鸡 721013 |
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| 基金项目： | 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) |
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| 摘 要： | 首先研究了逻辑度量空间(［0,1］, ρR)与度量空间(F(X),HR)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。
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| 关 键 词： | 剩余格 Cauchy-序列 完备 一致拓扑 |
Topological properties analysis of logical metric spaces on the residuated lattice |
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| DUAN Jing-yao. Topological properties analysis of logical metric spaces on the residuated lattice[J]. Journal of Shandong University, 2018, 53(12): 9-16. DOI: 10.6040/j.issn.1671-9352.0.2017.645 |
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| Authors: | DUAN Jing-yao |
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| Affiliation: | Department of Mathematics and Information Sciences, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi, China |
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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. |
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| Keywords: | residuated lattice Cauchy-sequence complete uniform topology |
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