本文对示例或学习的理论进行了初步的研究。首先,扩充了解的规则空间,由范式解扩充到任意公式解。然后,得到了如下结果:(1)讨论了随着例子集合的变化,相应规则解集合的变化情况;(2)正例集与反例集相交时,规则解不存在;(3)若正例集与反例集之并等于全部例子构成的空间,则规则解唯一;(4)在有解情况下,必然存在两个基础解,在半序关系“”下,这两个解分别为最小元,最大元。(5)规则集合关于运算∧,∨作成一个有界分配格。两个基础解是此格的上,下界。(6)对应于GS算法的GS定理。

In this paper, an initial study of learning from examples is made. After the rule-space of solutions is enlarged from normal formula solutions to all general formula solutions, the following conclusions are got:1. Discussing the change of corresponding rules set, with the change of examples set. 2. There are no solutions when positive-examples set intersets negative-examples set. 3. If the union of positive-examples set and negative-examples set equals to the space which consists of all examples, the rule-solution is unique is unique.4.If the soultions exist,there must be two basic solutions,and these two solutions are maximum and minimun,under the relation of partialorder“=>”.5.the rule set for the opearate ∧,∨ forms a bounded distributive lattice,and the two basic solutions are the upper bound and the lower bound of this lattice respectively.6.GS theorem corresponding to GS algorithm is given.