Mathematical Foundations of Databases

在这个项目中，数据库的理论基础正在通过使用离散数学进行调查。研究主要有两个子目标，即：(1)找到概念上简单的数据库问题和实践的集合论和/或代数模型，特别是与关系数据库模型相关的模型。这些模型的例子包括对象历史、电子表格、顺序数据查询语言和嵌套关系。这样的模型与我们熟悉的逻辑和编程语言模型形成对比。(2)使用这些模型来解决数据库研究和其他计算机科学领域的重要问题。这些问题是由(a)基础数据库物理情况和设计方法或(b)分析考虑和基础数学形式提出的。预期这项研究的结果将有助于更好地理解当前的数据库问题，并为检查和解决数据库管理问题提供工具。例如，一项活动是处理数据重组的基本问题，即，它是什么意思，如何完成，以及与之相关的基本规律是什么。

In this project the theoretical foundations of databases are being investigated through the use of discrete mathematics. Research is conducted toward two major subgoals, i.e. to: (1) Find conceptually simple set-theoretic and/or algebraic models of database issues and practices, especially those associated with the relational database model. Examples of such models are those for object histories, spreadsheets, sequential- data query languages, and nested relations. Such models are in contrast with the familiar logical and programming language models. (2) Use these models to address significant questions of database studies and possibly in other areas of computer science interest. Such questions are being suggested by either (a) the underlying database physical situation and design methodologies or (b) analytic considerations and the underlying mathematical formalism. Results of this research are expected to formulate a better understanding of current database concerns, as well as provide tools for examining and solving database management problems. For example, one line of activity is addressing the fundamental problem of data restructuring, i.e., what does it mean, how can it be accomplished, and what are the fundamental laws related to it.