摘要
探讨了逻辑度量空间的结构,证明了在经典逻辑度量空间上存在一种反射变换φ,且φ保持逻辑等价关系不变,并且是同态映射;φ自然导出Lindenbaum代数上的一个反射变换φ*,φ*是Lindenbaum代数上的自同构变换,并且是等距变换.研究了φ*的不动点性态,得到了不动点的一般形式,即[A]∨φ*([A])或[A]∧φ*([A])(A∈F(S)).最后指出当n>2时,对于n值G del逻辑系统,相应的逻辑度量空间不具有上述性质.
The construction of a logic metric space is studied in detail.It is proved that there exists a reflexive transformation φ on a classical logic metric space.The transformation φ is a homomorphic mapping and keeps the logic equivalence relation unchanged.And φ naturally induces a reflexive transformation φ* 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 poin...
出处
《陕西师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2009年第6期1-4,共4页
Journal of Shaanxi Normal University：Natural Science Edition
基金
国家自然科学基金资助项目(10771129)
陕西师范大学研究生培养创新基金资助项目(2009CXB006)
