Distance functional dependencies in the presence of complex values

Abstract

Distance functional dependencies (dFDs) have been introduced in the context of the relational data model as a generalisation of error-robust functional dependencies (erFDs). An erFD is a dependency that still holds, if errors are introduced into a relation, which cause the violation of an original functional dependency. A dFD with a distance d=2e+1 corresponds to an erFD with at most e errors in each tuple. Recently, an axiomatisation of dFDs has been obtained. Database theory, however, does no longer deal only with flat relations. Modern data models such as the higher-order Entity-Relationship model (HERM), object oriented datamodels (OODM), or the eXtensible Meakup Language (XML) provide constructors for complex values such as finite sets, multisets and lists. In this article, dFDs with complex values are investigated. Based on a generalisation of the HAmming distance for tuples to complex values, which exploits a lattice structure on subattributes, the major achievement is a finite axiomatisation of the new class of dependencies.