正规统计缺省扩充的证明

Proof of normal statistical default extensions

讨论了带有误差参数的统计缺省理论.引入了闭正规统计缺省概念,指出存在正规统计缺省理论没有在ε内的统计扩充,但在添加封闭性后每个正规闭统计缺省理论都有扩充.证明了半单调性和正交性等基本性质,对闭正规统计缺省理论的证明作了研究,论证了在一定条件下序列的存在性蕴涵统计扩充的存在性,给出了相容正规缺省理论扩充存在的充要条件.

The theory of statistical default logic with error parameters is discussed. The concept of closed normal statistical default has been introduced, and it is pointed out that there exists a closed normal statistical default without any extension within ε, but under the condition of closeness it is proved that every closed normal statistical default has an extension. The semi-monotone theorem and the orthogonal theorem are obtained. Moreover, it is proved that the existence of a proof series implies the existence of an extension for closed normal statistical default. Finally, a necessary and sufficient condition for the existence of extensions of closed normal statistical default is given.