We establish a principled schema design framework for data with missing values. The framework is based on the new notion of an embedded functional dependency, which is independent of the interpretation of missing values, able to express completeness and integrity requirements on application data, and capable of capturing redundant data value occurrences that may cause problems with processing data that meets the requirements. We establish axiomatic, algorithmic, and logical foundations for reasoning about embedded functional dependencies. These foundations enable us to introduce generalizations of Boyce-Codd and Third normal forms that avoid processing difficulties of any application data, or minimize these difficulties across dependency-preserving decompositions, respectively. We show how to transform any given schema into application schemata that meet given completeness and integrity requirements, and the conditions of the generalized normal forms. Data over those application schemata are therefore fit for purpose by design. Extensive experiments with benchmark schemata and data illustrate the effectiveness of our framework for the acquisition of the constraints, the schema design process, and the performance of the schema designs in terms of updates and join queries.

中文翻译：

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嵌入式功能依赖和数据完整性 量身定制的数据库设计

我们为缺失值的数据建立了一个原则性的模式设计框架。该框架基于嵌入式函数依赖的新概念，独立于缺失值的解释，能够表达对应用程序数据的完整性和完整性要求，并能够捕获可能导致处理数据问题的冗余数据值出现符合要求的。我们为推理嵌入式函数依赖关系建立了公理、算法和逻辑基础。这些基础使我们能够引入 Boyce-Codd 和第三范式的推广，从而避免任何应用程序数据的处理困难，或分别在依赖保留分解中最小化这些困难。我们展示了如何将任何给定模式转换为满足给定完整性和完整性要求以及广义范式条件的应用模式。因此，这些应用程序模式上的数据符合设计目的。对基准模式和数据的广泛实验说明了我们的框架在获取约束、模式设计过程以及模式设计在更新和连接查询方面的性能方面的有效性。