Querying Description Logic Knowledge Bases

Abstract

Knowledge representation systems provide a mechanism for storing facts about some part of the real world in a knowledge base, inferring new knowledge based on the given facts, and querying knowledge bases. The ability to infer new knowl- edge is one of the distinguishing features compared to databases. Such inference services require the definition of knowledge in a language for which such inference algorithms exist, e.g., a Description Logic (DL). A DL language allows for the specification of concepts, individuals that are instances of these concepts, and roles, which are interpreted as binary relations over the individuals. Description Logics have proved useful in a wide range of applications and form the foundations of the Web Ontology Language (OWL), which is used in the Semantic Web as a means for specifying machine processable information. Despite their popularity, the retrieval facilities provided by DL systems are still limited. Current algorithms are incomplete or impose restrictions on the types of allowed queries. This thesis identifies sources of incompleteness in existing algorithms and presents extended retrieval procedures eliminating the deficien- cies described above. More precisely, we present query answering algorithms for unrestricted conjunctive queries for the DLs SHIQ and SHOQ—the former of which was a long standing open problem. Furthermore, the correctness of the presented algorithms is proved formally and an analysis of the theoretical com- plexity is given. The planned future work is targeted on optimisation techniques to improve the algorithm’s practicality. The work presented in this thesis should be of value mainly to implementors of Description Logic systems, as the presented algorithms build the theoretical foundation for implementable query answering interfaces. Additionally, the al- gorithms can also be used in order to extend a DL system with datalog style rules.