Mathematical Foundations of Databases

在这个项目中，数据库的理论基础是 正在通过离散数学的使用进行研究。 研究工作是为了实现两个主要的次级目标，即： (1)找到概念上简单的集合论和/或代数 数据库问题和实践的模型，特别是 与关系数据库模型相关联。的例子 模型是那些对象的历史，电子表格，连续的， 数据查询语言和嵌套关系。这些模型在 与熟悉的逻辑和编程语言形成对比 模型 (2)使用这些模型来解决以下重要问题 数据库研究和可能在计算机科学的其他领域 兴趣这些问题是由以下机构提出的： 底层数据库物理状况和设计方法 或（B）分析考虑和基础数学 形式主义 本研究的结果有望制定一个更好的 了解当前的数据库问题，并提供 用于检查和解决数据库管理问题的工具。为 例如，活动的一条线是解决基本的 数据重构的问题，即，这是什么意思，怎么能 它是可以实现的，以及与之相关的基本法律是什么？ 了

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.