Functional dependencies and its axiom system in XML

Abstract

According to the analysis of existing complicated functional dependencies constraint, we conclude the conditions of defining functional dependency in XML, and then we introduce the concept of the node value equality. A new path language and a new definition of functional dependencies in XML (XFD) are proposed. XFD includes the relative XFD and the absolute XFD, in which absolute key and relative key are the particular cases. We focus on the logical implication and the closure problems, and propose a group of inference rules. Finally, some proofs of the correctness and completeness are given. XFD is powerful on expressing functional dependencies in XML causing data redundancy, and has a complete axiom system. Functional dependencies play an important role in database, which is widely used in integrity constraints and the design of database. Also this kind of data constraint mechanism plays an important role in XML data management. Considering that the XML data constraints come from the application semantic, we hope to express these semantic constraints in XML schema, so that the database can avoid operations that will cause inconsistency.To present functional dependencies, relational database utilizes relational schema, while XML has its own schema, such as XML Data [1] , XML Schema [2] , and XML DTD [3] . The semantic described by these specifications is insufficient to express functional dependencies. Many researches try to apply functional dependencies on XML but there are still unsolved problems. We read a large number of XML documents and take the widely used XML DTD in practice as the schema for our example, as shown in the following.Some researchers are attempting to extend the concept of functional dependencies on XML. Based on the concept of tree tuple, Arenas et al [4] propose a definition of functional dependencies in XML (XFD), which treats DTD as a relational schema, paths on the DTD are the attributes of the schema. Vincent et al [5] proposes a XFD based on the concept of closest node, similar to the way that key is defined in Ref.[6], closest node is the node mapped from the left side and the right side of the XFD in the XML tree, whose path instance has the maximum common prefix. Vincent et al [7] point out that the definitions in Ref.[4] and [5] are equal when there is no null

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