Normal forms for non-relational data

Abstract

The amount of data stored in today`s information systems is increasing rapidly. Most widely used for this task are relational database management systems. However, alternative data formats, like XML documents or graph databases, continue to become more and more popular. In all these data formats database design is an important task to avoid redundancies arising from badly designed schemata. Therefore, Normal Forms were developed. Most prominently, Boyce- Codd Normal Form (BCNF) is used for relational models. Arenas and Libkin introduced 2004 XML Normal Form for XML documents. So far, a normal form for graph databases has not been considered yet. Our goal is to define a normal form that captures the intuition of BCNF for graph databases. We will recall Boyce-Codd Normal Form and XML Normal Form and will then use ideas from these to define a normal form for graph databases. Description Logics (DLs) are ideally suited as a formal model for graph databases. Since BCNF is formulated over functional dependencies (FDs), we need to express FDs over DL knowledge bases (KBs). A first candidate are path-based identification constraints introduced by Calvanese in 2008. However, we show that path-based identification constraints are not powerful enough to model functional dependencies. Therefore, we propose tree-based identification constraints as an extension of path-based identification constraints. Based on tree-based identification constraints we look at redundancy in DLs. The main result of this thesis is a definition of Description Logic Normal Form, which is a faithful translation of BCNF to Description Logics. Additionally, we introduce a direct mapping from relational schemas to DL KBs and show that if a relational schema is in BCNF, then the DL KB, directly mapped from this schema, is in DLNF and vice versa.