文章从双语句对的译文等价树中抽取翻译等价对。

In this paper, translation equivalences are extracted from translation corresponding trees of bilingual sentence pairs.

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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.

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针对差别矩阵求约简过程中合取范式向析取范式等价转换的难题，提出一种基于差别矩阵构造约简树的有效方法。

Aiming at the problem of equivalent conversion from conjunctive normal form to disjunctive normal form, an effective algorithm was proposed to construct reduction tree based on discernibility matrix.

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