陕西师范大学学报（自然科学版）2009，Vol.37Issue(6)：1-4,4.
经典逻辑度量空间上的反射变换
Reflexive transforms on a classical logic metric space
摘要
Abstract
The construction of a logic metric space is studied in detail. It is proved that there exists a reflexive transformation ψ on a classical logic metric space. The transformation ψ is a homomorphic mapping and keeps the logic equivalence relation unchanged. And ψ naturally induces a reflexive transformation ψ~* on the Lindenbaum algebra, which is an automorphic and isometric transformation of the Lindenbaum algebra. Moreover, the general forms of fixed points have been obtained by studying the features of fixed points (such as [A]∨ψ~*([A]) or [A]∧ ψ~*([A]),A∈F(S)). Lastly, the above mentioned interesting properties do not hold for the n-valued Godel type logic metric space whenever n>2.关键词
经典逻辑/Lindenbaum代数/逻辑度量空间/反射变换/自同构/不动点/Godel/n值逻辑度量空间Key words
classical logic/ Lindenbaum'algebra/ logic metric space/ reflexive transformation/automorphism/ fixed point/ n-valued Godel type logic metric space分类
数理科学引用本文复制引用
胡明娣,王国俊..经典逻辑度量空间上的反射变换[J].陕西师范大学学报（自然科学版）,2009,37(6):1-4,4.基金项目
国家自然科学基金资助项目(10771129) （10771129）
陕西师范大学研究生培养创新基金资助项目(2009CXB006) （2009CXB006）
