缺省推理中的三个定理

THREE THEOREMS ABOUT DEFAULT REASONING

本文证明了缺省推理中的三个定理.定理1表明了缺省推理的非单调性这一特点.定理2的实际意义在于,在一个封闭规范缺省理论(D,W)中,只要W能推出D中某些缺省的结论,则可以把这样的缺省规则从理论中删除,所得到的较小的缺省理论其延伸仍与原来缺省理论一样.尤其是若W能推出D中所有的缺省规则结论,则(D,W)的延伸就是W,这就是本文推论的结论.

Three theorems about defaul reasoning have been proved. Theorem 1 indicates the feature of non-monotonicity for default reasoning. The virtual meaning of Theorem 2 is that if W can deduce some default rules' consequents in D in a closed normal default theory (D, W), then one can delete such default rules from the theory, and derive a smaller default theory with equal extension. Especially if W can deduce all consequents in D in a theory (D, W), then the extension of (D, W) is equal to W.