n元经典逻辑度量空间中的平移变换

Transformation translation on n-ary classical logic metric space

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。

The transformation translation on n-ary classical logic metric space is formed by modular 2 addition and vector repre- sentation 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 Г（Г 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 for- mulas in classical logic metric space is defined normed.