Mathematical Foundation for Semistructured Data

The rapid growth of the World Wide Web and its technologies has resulted in enormous amounts of data being used over the Internet by Web Services and Web-based applications. The increase in semistructured data usage is not limited to Web applications but expands into various other applications such as digital libraries, biological databases and multimedia data management systems. This expansion of semistructured data usage creates the need for effective and efficient utilization of semistructured data [15]. With such a rapid increase in its usage semistructured data needs to be stored, manipulated, and queried to be utilized properly by various applications and tools. For these purposes, many researchers have proposed to design and develop adequate database systems for semistructured data. As a result, several database systems have already been developed for eXtensible Markup Language (XML) [6], which is a common representation for semistructured data, while traditional database companies, such as Oracle, have provided XML support for their existing database systems. As with widely used database systems, various operations that transform the schema have been adopted by the database systems developed for semistructured data to provide effective and efficient data storage and utilization. These schema transforming operations are often performed using algorithms developed specifically for semistructured data storage. The schema transforming operation guided by the algorithms must perform correctly to ensure the consistency of the data and ensure no information is lost. Although the algorithms claim to maintain the lossless and dependency preserving properties, the database systems developed for semistructured data lack verification support to prove the correctness of the transformations. In widely adopted database systems, one of the features that is used to prove the correctness of the operations and algorithms is the mathematical foundation. For example, in relational database systems, a mathematical foundation has been extraordinarily useful in the definition of normalization, to prove that lossless and dependency proving algorithms can be defined. Also a mathematical foundation has been defined to capture object oriented concepts, and used to reason about the correctness of query results in object oriented database systems. Such verification support for operations and the algorithms of database systems ensures the correctness of data manipulations, making the mathematical foundation essential. However, current developments of database systems that store semistructured data lack a mathematical foundation. When there is no general formal way of distinguishing between correct and incorrect transformations, incorrect data transformation can be introduced resulting in unreliable or even corrupt data. Without establishing a well defined mathematical foundation, many limitations will be imposed on the functionality of the database systems for semistructured data making it not as effective and reliable as it should be. Therefore this research proposes to establish a well defined mathematical foundation for semistructured data in order to address this problem. The derived mathematical foundation will verify whether operations and algorithms that transform the schema of semistructured data maintain the lossless and dependency preserving properties.