增加两类算子的Goguen n值命题逻辑系统的t真度及性质  

t Truth Degree and Properties of Goguen n-valued Propositional Logic System by Adding New Operators

作　　者：南宁 惠小静[1] 金明慧 NAN Ning;HUI Xiao-jing;JIN Ming-hui(College of Mathematics and Computer Science,Yan'an University,Yan'an 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《模糊系统与数学》2021年第2期50-58,共9页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11471007,61763045);国家级大学生创新创业训练计划项目(201910719023);研究生教育创新计划项目(YCX2020096)。

摘　　要：在n值Goguen命题逻辑系统中增加了两类算子对合否定~和Δ算子,将该系统记为Goguen_(~,Δ).在此系统中建立t真度的概念,基于此真度给出了命题之间的t相似度与t伪距离(t任取~,Δ)。证明了t真度的MP规则、HS规则及运算性质。接着,在证明t伪距离的基础上建立了度量空间,并论证了算子?,∨在逻辑度量空间(F(S),d_n)中关于伪距离d_n是连续的。In the n-valued Goguen propositional logic system, two kinds of operators, involution negation ~ and Δ are added, and the system is denoted as Goguen~,Δ. The concept of t-truth degree is established in this system. Based on this truth degree, the t-similarity degree and t-pseudo-metric between propositions are given(t take ~,Δ). The MP rule, HS rule and operational properties of t-truth degree are proved. Then, on the basis of proving t-pseudo-metric, metric space is established. It is proved that the operators ? and ∨ are continuous with respect to pseudo distance dn in logical metric space(F(S),dn).

关 键 词：Goguen命题逻辑系统 t真度 t相似度 t伪距离 连续性 

分 类 号：O142[理学—数学]