Approximate assertional reasoning over expressive ontologies

In the Semantic Web, ontologies provide the required vocabulary for a meaningful and machine-understandable interpretation of data. Nowadays, expressive ontologies are usually written in the W3C standard language called the Web Ontology Language (OWL). In order to leverage the full power of OWL for emerging Semantic Web applications, ontology reasoning holds a key position by allowing access to implicit knowledge in ontologies. Analyzing the application domain of state-of-the-art OWL reasoning techniques, an important issue to be considered is the problem of scalable assertional reasoning over expressive ontologies with large terminological as well as assertional knowledge – a computationally intractable problem. In this thesis, we address this issue by means of logical approximation. Subsequently, we provide approximate reasoning methods for scalable assertional reasoning whose computational properties can be established in a well-understood way, namely in terms of soundness and completeness, and whose quality can be analyzed in terms of statistical measurements, namely recall and precision. The basic idea of these approximate reasoning methods is to speed up reasoning by trading off the quality of reasoning results against increased speed. The various aspects of this thesis span the fields of knowledge compilation, query answering, and resource-bounded reasoning. In the context of knowledge compilation, exploiting the fact that data complexity is polynomial for non-disjunctive datalog, a knowledge compilation technique with different useful approximations has been created, which allows tractable assertional reasoning. The logical properties, such as soundness and completeness, of these approximations have been investigated and a comprehensive evaluation using well-known benchmark ontologies has been conducted. Regarding query answering, a fast approximate reasoning system for instance retrieval has been developed. A central aspect of this approach is the approximate semantics for computing the approximate extensions of a complex concept expression. Based on this semantics, several algorithms have been developed that allow for scalable instance retrieval. In the context of resource-bounded reasoning, a combination of approximate reasoning algorithms has been examined by providing solid formal foundations for the assessment and comparison of approximate reasoning algorithms. Finally, an approximate ontology reasoning framework has been devised, which enables scalable assertional reasoning over expressive ontologies by loosely integrating the approximate reasoning solutions developed in this work.