On relational algebra with marked nulls preliminary version
On relational algebra with marked nulls preliminary version
复制标题
关于带有标记空值的关系代数初步版本
DOI：
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发表时间：
1984
期刊：
影响因子：
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通讯作者：
W. Lipski
中科院分区：
文献类型：
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作者：
W. Lipski
我们制定了一些自然的条件，应该满足的关系代数的扩展，从通常的关系表与空值，我们解释这些条件背后的动机。粗略地说，我们的条件说，扩展代数使得在将关系表达式（查询）应用于具有空值（数据库状态）的表的结果中正确计算“真元组”成为可能，并且计算可以递归地执行，遵循表达式的结构。我们证明了这些条件与作者和T.伊米列斯基我们给出了一个简单的证明的正确性的“天真”的关系代数的扩展表标记为空值，其中的空值被视为，如果他们是正规值，并支持投影，积极选择，工会，加入和重命名的属性的操作。我们还表明，这样一个表达式（查询）的天真的评价的结果是等于响应的查询定义---在一个证明理论框架---由赖特。
We formulate some natural conditions which should be satisfied in an extension of the relational algebra from the usual relations to tables with null values, and we explain the motivation behind these conditions. Roughly speaking, our conditions say that the extended algebra makes it possible to correctly compute the "true tuples" in the result of applying a relational expression (query) to tables with nulls (database state), and that the computation can be carried out recursively, following the structure of the expression. We prove that these conditions are exactly equivalent to other conditions proposed earlier by the author and T. Imieliński. We give a simple proof of the correctness of the "naive" extension of the relational algebra to tables with marked nulls, where the nulls are treated as if they were regular values, and which supports the operations of projection, positive selection, union, join and renaming of attributes. We also show that the result of the naive evaluation of such an expression (query) is equal to the response to the query as defined --- in a proof-theoretic framework --- by Reiter.