In this article, we address the problem of how to extend the definition of functional dependencies (FDs) in incomplete relations to XML documents (called XFDs) using the well-known strong satisfaction approach.We propose a syntactic definition of strong XFD satisfaction in an XML document and then justify it by showing that, similar to the case in relational databases, for the case of simple paths, keys in XML are a special case of XFDs. We also propose a normal form for XML documents based on our definition of XFDs and provide a formal justification for it by proving that it is a necessary and sufficient condition for the elimination of redundancy in an XML document.
AbstractÐFunctional dependencies (FDs) and inclusion dependencies (INDs) are the most fundamental integrity constraints that arise in practice in relational databases. In this paper, we address the issue of normalization in the presence of FDs and INDs and, in particular, the semantic justification for Inclusion Dependency Normal Form (IDNF), a normal form which combines Boyce-Codd normal form with the restriction on the INDs that they be noncircular and key-based. We motivate and formalize three goals of database design in the presence of FDs and INDs: noninteraction between FDs and INDs, elimination of redundancy and update anomalies, and preservation of entity integrity. We show that, as for FDs, in the presence of INDs being free of redundancy is equivalent to being free of update anomalies. Then, for each of these properties, we derive equivalent syntactic conditions on the database design. Individually, each of these syntactic conditions is weaker than IDNF and the restriction that an FD not be embedded in the righthand side of an IND is common to three of the conditions. However, we also show that, for these three goals of database design to be satisfied simultaneously, IDNF is both a necessary and sufficient condition.Index TermsÐRelational database design, normal forms, functional dependency, inclusion dependency.
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