模式逻辑和辅助关系

Diego Figueira, L. Libkin
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引用次数: 5

摘要

在有限结构的逻辑研究中,一个常见的主题是添加辅助谓词来增强表现力和传达额外的信息。示例包括为捕获复杂类添加顺序或算术,或者使用现实生活中的声明性语言。最近的一个趋势是向单词、树和图添加数据值比较关系,以捕获现代数据模型,如XML和图数据库。这样的添加通常会导致底层逻辑的良好属性的丧失。我们的目标是表明,如果我们使用基于模式的逻辑、标准的XML和图形数据查询,就可以避免这种损失。这种逻辑的本质是辅助关系相对于结构中的其他关系在局部进行测试。这些逻辑证明了Hanf和Gaifman局部性定理的强版本,它们被用来证明一个同态保持定理,以及一个可满足性问题的可决性结果。我们将讨论将这些结果应用于数据森林上的模式逻辑,从而应用于查询XML数据。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Pattern logics and auxiliary relations
A common theme in the study of logics over finite structures is adding auxiliary predicates to enhance expressiveness and convey additional information. Examples include adding an order or arithmetic for capturing complexity classes, or the power of real-life declarative languages. A recent trend is to add a data-value comparison relation to words, trees, and graphs, for capturing modern data models such as XML and graph databases. Such additions often result in the loss of good properties of the underlying logic. Our goal is to show that such a loss can be avoided if we use pattern-based logics, standard in XML and graph data querying. The essence of such logics is that auxiliary relations are tested locally with respect to other relations in the structure. These logics are shown to admit strong versions of Hanf and Gaifman locality theorems, which are used to prove a homomorphism preservation theorem, and a decidability result for the satisfiability problem. We discuss applications of these results to pattern logics over data forests, and consequently to querying XML data.
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