| 相似剩余格及其对应逻辑系统的完备性 |
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| 引用本文： | 王军涛.相似剩余格及其对应逻辑系统的完备性[J].高校应用数学学报(A辑),2021(1):111-126. |
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| 作者姓名： | 王军涛 |
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| 作者单位： | 西安石油大学理学院 |
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| 基金项目： | 国家自然科学基金(12001423,61976244,11961016);陕西省自然科学基础研究计划(2020JQ-762);陕西省教育厅自然科学研究专项计划(20JK0626)。 |
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| 摘 要： | 引入了相似剩余格的概念,讨论了剩余格上相似算子和等价算子的关系,并得到了真值剩余格和相似剩余格相互转化的方法.其次,研究了相似剩余格上的相似滤子,利用相似滤子刻画了可表示的相似剩余格.最后,引入了相似剩余格对应的逻辑系统,证明了其完备性定理,并得到了其成为半线性逻辑的条件.
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| 关 键 词： | 模糊逻辑 相似剩余格 相似滤子 完备性 |
Similarity residuated lattices and the completeness of their corresponding logics |
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| WANG Jun-tao.Similarity residuated lattices and the completeness of their corresponding logics[J].Applied Mathematics A Journal of Chinese Universities,2021(1):111-126. |
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| Authors: | WANG Jun-tao |
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| Institution: | (School of Science,Xi'an Shiyou University,Xi'an 710065,China) |
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| Abstract: | In this paper,the notion of similarity residuated lattices is introduced,the relationship between similarity and equivalence on residuated lattices is discussed,and the transformation method between very true and similarity residuated lattice is given.Then the similarity filters on similarity residuated lattices are studied,and some characterizations of representable similarity residuated lattices based on similarity filters are given.Finally,the corresponding logic of similarity residuated lattices is introduced and its corresponding completeness theorem is proved,and the condition for this logic to be semilinear is obtained. |
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| Keywords: | fuzzy logic similarity residuated lattice similarity filter completeness |
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