The World Wide Web contains large amounts of data, and in most cases this data has no explicit structure. The lack of structure makes it difficult for automated agents to understand and use such data. A step towards a more structured World Wide Web is the Semantic Web, which aims at introducing semantics to data on the World Wide Web. One of the key technologies in this endeavour are ontologies, which provide a means for modeling a domain of interest and are used for search and integration of data. In recent years many ontologies have been developed. To be able to use multiple ontologies it is necessary to align them, i.e., find inter-ontology relationships. However, developing and aligning ontologies is not an easy task and it is often the case that ontologies and their alignments are incorrect and incomplete. This can be a problem for semantically-enabled applications. Incorrect and incomplete ontologies and alignments directly influence the quality of the results of such applications, as wrong results can be returned and correct results can be missed. This thesis focuses on the problem of completing ontologies and ontology networks. The contributions of the thesis are threefold. First, we address the issue of completing the is-a structure and alignment in ontologies and ontology networks. We have formalized the problem of completing the is-a structure in ontologies as an abductive reasoning problem and developed algorithms as well as systems for dealing with the problem. With respect to the completion of alignments, we have studied system performance in the Ontology Alignment Evaluation Initiative, a yearly evaluation campaign for ontology alignment systems. We have also addressed the scalability of ontology matching, which is one of the current challenges, by developing an approach for reducing the search space when generating the alignment.Second, high quality completion requires user involvement. As users' time and effort are a limited resource we address the issue of limiting and facilitating user interaction in the completion process. We have conducted a broad study of state-of-the-art ontology alignment systems and identified different issues related to the process. We have also conducted experiments to assess the impact of user errors in the completion process. While the completion of ontologies and ontology networks can be done at any point in the life-cycle of ontologies and ontology networks, some of the issues can be addressed already in the development phase. The third contribution of the thesis addresses this by introducing ontology completion and ontology alignment into an existing ontology development methodology.

This work presents mainly two contributions to Description Logics (DLs) research by means of Formal Concept Analysis (FCA) methods: supporting bottom-up construction of DL knowledge bases, and completing DL knowledge bases. Its contribution to FCA research is on the computational complexity of computing generators of closed sets.