Complete Approximations of Incomplete Queries

Julien Corman, Werner Nutt, Ognjen Savković
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Abstract

This paper studies the completeness of conjunctive queries over a partially complete database and the approximation of incomplete queries. Given a query and a set of completeness rules (a special kind of tuple generating dependencies) that specify which parts of the database are complete, we investigate whether the query can be fully answered, as if all data were available. If not, we explore reformulating the query into either Maximal Complete Specializations (MCSs) or the (unique up to equivalence) Minimal Complete Generalization (MCG) that can be fully answered, that is, the best complete approximations of the query from below or above in the sense of query containment. We show that the MSG can be characterized as the least fixed-point of a monotonic operator in a preorder. Then, we show that an MCS can be computed by recursive backward application of completeness rules. We study the complexity of both problems and discuss implementation techniques that rely on an ASP and Prolog engines, respectively.
不完整查询的完整近似值
本文研究部分完整数据库上连接查询的完备性以及不完备查询的近似。给定一个查询和一组指定数据库哪些部分是完整的完备性规则(一种特殊的元组生成依赖关系),我们会研究查询是否能得到完整的回答,就像所有数据都可用一样。如果不能,我们就会探索将查询重新表述为最大完整特化(MCS)或可完全回答的(唯一等价)最小完整泛化(MCG),也就是说,在查询包含的意义上,查询从下往上的最佳完整近似。我们证明,MSG 可以表征为前序中单调算子的最小定点。然后,我们证明可以通过递归反向应用完备性规则来计算 MCS。我们研究了这两个问题的复杂性,并讨论了分别依赖 ASP 和 Prolog 引擎的实现技术。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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