n元经典逻辑度量空间中的平移变换

计算机工程与应用 ›› 2013, Vol. 49 ›› Issue (6): 59-61.

n元经典逻辑度量空间中的平移变换

马巧云

西安文理学院数学与计算机工程学院，西安 710065

出版日期:2013-03-15 发布日期:2013-03-14

Transformation translation on n-ary classical logic metric space

MA Qiaoyun

College of Mathematics and Computer Engineering, Xi’an Science and Article University, Xi’an 710065, China

Online:2013-03-15 Published:2013-03-14

摘要/Abstract

摘要： 利用模2的加法运算和逻辑公式的向量表示构造了n元经典逻辑度量空间中的平移变换。得到了平移变换的一些简单性质，证明了平移变换保持非运算，但不保持交、并、蕴涵运算；得到了逻辑理论的发散度、有限理论的相容度在平移变换之下不变的结论。证明了平移变换之集构成一个群；在经典逻辑度量空间中以公式类中公式的真度为范数，进一步证明了[(Fn(S),ρ)]关于该范数可以构成次范整线性空间。

关键词: n元经典逻辑度量空间, 平移变换, 次范整线性空间

Abstract: The transformation translation on n-ary classical logic metric space is formed by modular 2 addition and vector representation of formula. Some simple properties of transformation translation are obtained. It is proved that not operation is kept and intersection operation, and operation, if then operation are not kept through transform translation. The divergence degrees and consistency degrees of [Γ(Γ?Fn(S))]are not changed through transform translation. It is also proved that these transformation translation constitute a group, and the space [(Fn(S),ρ)]thereby makes a sub-normed Z-linear space when the truth degree of formulas in classical logic metric space is defined normed.

Key words: n-ary classical logic metric space, transformation translation, sub-normed Z-linear space

马巧云. n元经典逻辑度量空间中的平移变换[J]. 计算机工程与应用, 2013, 49(6): 59-61.

MA Qiaoyun. Transformation translation on n-ary classical logic metric space[J]. Computer Engineering and Applications, 2013, 49(6): 59-61.

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