During the past 15 years, schema mappings have been extensively used in formalizing and studying such critical data interoperability tasks as data exchange and data integration. Much of the work has focused on GLAV mappings, i.e., schema mappings specified by source-to-target tuple-generating dependencies (s-t tgds), and on schema mappings specified by second-order tgds (SO tgds), which constitute the closure of GLAV mappings under composition. In addition, nested GLAV mappings have also been considered, i.e., schema mappings specified by nested tgds, which have expressive power intermediate between s-t tgds and SO tgds. Even though nested GLAV mappings have been used in data exchange systems, such as IBM’s Clio, no systematic investigation of this class of schema mappings has been carried out so far. In this article, we embark on such an investigation by focusing on the basic reasoning tasks, algorithmic problems, and structural properties of nested GLAV mappings. One of our main results is the decidability of the implication problem for nested tgds. We also analyze the structure of the core of universal solutions with respect to nested GLAV mappings and develop useful tools for telling apart SO tgds from nested tgds. By discovering deeper structural properties of nested GLAV mappings, we show that also the following problem is decidable: Given a nested GLAV mapping, is it logically equivalent to a GLAV mapping?

中文翻译：

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关于嵌套元组生成依赖的语言

在过去的 15 年中，模式映射已广泛用于形式化和研究数据交换和数据集成等关键数据互操作性任务。大部分工作都集中在 GLAV 映射上，即由源到目标的元组生成依赖关系 (st tgds) 指定的模式映射，以及由二阶 tgds (SO tgds) 指定的模式映射，它们构成了组成下的 GLAV 映射。此外，还考虑了嵌套 GLAV 映射，即由嵌套 tgds 指定的模式映射，其表达能力介于 st tgds 和 SO tgds 之间。尽管嵌套的 GLAV 映射已用于数据交换系统，例如 IBM 的 Clio，但迄今为止尚未对此类模式映射进行过系统研究。在本文中，我们通过关注嵌套 GLAV 映射的基本推理任务、算法问题和结构特性来进行这样的调查。我们的主要结果之一是嵌套 tgds 的蕴涵问题的可判定性。我们还分析了关于嵌套 GLAV 映射的通用解决方案的核心结构，并开发了有用的工具来区分 SO tgds 和嵌套 tgds。通过发现嵌套 GLAV 映射的更深层次的结构特性，我们表明以下问题也是可判定的：给定嵌套 GLAV 映射，它在逻辑上是否等同于 GLAV 映射？我们还分析了关于嵌套 GLAV 映射的通用解决方案的核心结构，并开发了有用的工具来区分 SO tgds 和嵌套 tgds。通过发现嵌套 GLAV 映射的更深层次的结构特性，我们表明以下问题也是可判定的：给定嵌套 GLAV 映射，它在逻辑上是否等同于 GLAV 映射？我们还分析了关于嵌套 GLAV 映射的通用解决方案的核心结构，并开发了有用的工具来区分 SO tgds 和嵌套 tgds。通过发现嵌套 GLAV 映射的更深层次的结构特性，我们表明以下问题也是可判定的：给定嵌套 GLAV 映射，它在逻辑上是否等同于 GLAV 映射？