Formal Modelling and Application of Graph Transformations in the Resource Description Framework

Abstract

In this thesis, a connection between two areas of research is developed. On the one hand, the Resource Desription Framework (RDF) is the basis of the Semantic Web. On the other hand, algebraic graph transformation has a long history of providing formally well-founded modification concepts for various graph and graph-like structures. By designing an algebraic transformation approach for RDF, the rich theoretical results of algebraic graph transformation are made available to the RDF world. To achieve this goal, the formal abstract syntax and semantics of RDF is first reformulated in the language of category theory which is used heavily in graph transformation. Then, an abstract, categorical transformation framework is developed which is suitable for being afterwards instantiated by RDF structures. This is necessary since the existing frameworks are not applicable in an unmodified form. The main theoretical results are a sequential composition operation for transformation rules and theorems showing the possibility to analyse and synthesise transformations for these sequentially composed rules. Moreover, these results are also available for transformation rules with negative application conditions. The applicability of the resulting concept of RDF graph transformations is shown by two application scenarios. One is a classical Semantic Web application managing bibliographical metadata, while the other uses RDF as an abstract syntax for domainspecific modelling languages.