一元子结构谓词逻辑中相似的代数语义  

Algebraic Semantics of Similarity in Monadic Substructural Predicate Logics

作　　者：王军涛 王梅[2] 折延宏[1] WANG Jun-tao;WANG Mei;SHE Yan-hong(School of Science,Xi’an Shiyou University,Xi’an,Shaanxi 710065,China;School of Electrical and Control Engineering,University of Science and Technology,Xi’an,Shaanxi 710021,China)

机构地区：[1]西安石油大学理学院,陕西西安710065 [2]陕西科技大学电气与控制工程学院,陕西西安710021

出　　处：《电子学报》2023年第4期956-964,共9页Acta Electronica Sinica

基　　金：国家自然科学基金(No.12001423,No.61976244,No.12171294);陕西省自然科学基础研究计划(No.2020JQ-762,No.2021JQ-580);陕西省教育厅自然科学研究专项计划(No.20JK0626)。

摘　　要：借助一元模糊谓词逻辑与S5型模糊模态逻辑的等价性,建立了一元子结构谓词逻辑中相似联结词的代数语义,引入了相似一元剩余格,并研究了其基本的代数性质.其次,研究了相似一元剩余格上的相似滤子,刻画了可表示的相似一元剩余格.最后,引入了相似一元剩余格对应的逻辑系统,证明了其完备性定理,并解决了其最小半线性扩张问题.Using the equivalence between monadic fuzzy predicate logics and S5 type fuzzy modal logic,the algebra-ic semantics of similarity in monadic substructural predicate logics are introduced,the resulting class of algebras called simi-larity monadic residuated lattices,and their basic algebraic properties are studied.Secondly,the similarity filters of similari-ty monadic residuated lattices are introduced,and representable similarity monadic residuated lattices are characterized by using them.Finally,the logic system corresponding to similarity monadic residuated lattices is established,and its mini-mum semilinear extension and completeness are studied.

关 键 词：一元子结构谓词逻辑 相似一元剩余格 相似滤子 完备性 半线性扩张 

分 类 号：O155[理学—数学]