根据这些算法和关系代数等价定理，给出了对关系代数查询树进行逻辑优化的规则，并证明了逻辑优化的正确性。
With these algorithms and the equivalence theory, the several rules to logically optimize the accessing trees were presented and the correctness for the logical optimization was proved.
最后证明了属性约简在布尔矩阵和代数两种不同表示下是等价的。
Finally, the equivalence properties between Boolean matrix representation and algebra representation of attribute reduction are proved.
并举例说明，对于不一致决策表，其属性约简的代数表示不能用条件信息量来等价表示。
Through examples, it shows that attribute reduction of an inconsistent decision table cannot entirely be represented by conditional information quantity.
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