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.
例如，这种理论模型允许用更有效的等价操作来代替关系代数操作同时不影响结果。
This theoretical model allows, for example, that relational algebra operations to be replaced by more efficient equivalent operations whereas not interfere with the result.
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.
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