The Semantic Web aims to make web data machine-readable by embedding semantics into the data. As key technologies in the Semantic Web, ontologies and knowledge graphs (KGs) are used to formalize and represent knowledge in a structured way. They are core components in application scenarios involving searching, integrating, managing, and extracting value from heterogeneous data sources at scale, and are widely used by major data and database providers and consumers, such as Google, Amazon, and Netflix. As a result, their quality is critical for developing high-quality semantically enabled applications. However, in practice, many ontologies and KGs, especially large-scale ones, contain defects. Using such defective resources can lead to incorrect conclusions or missed valid conclusions. Ensuring their quality, particularly in terms of correctness and completeness, is a major challenge. 

In this thesis, we focus on repairing ontologies and KGs represented by description logic knowledge bases. We first discuss the kind of defects concerning correctness and completeness that can occur in ℰℒℋ⟂ ontologies and KGs. We then propose an interactive repairing approach that combines five basic quality-improving operations: debugging, removing, weakening, strengthening, and adding, to address the problem of repairing ℰℒℋ⟂ ontologies and KGs with defects. Traditional debugging approaches repair ontologies and KGs by simply removing incorrect information, which may result in the loss of correct information that was previously derivable from the removed information. In contrast, our approach aims to preserve as much correct knowledge as possible while removing incorrect information by, in addition to removing the incorrect information, also adding correct knowledge, thereby mitigating the negative effects and improving the quality of repaired ontologies and KGs. 

Furthermore, we show that there are also choices to be made when using and combining these operations such as how to combine them and when to apply them, as well as the different autonomy levels of different components in a KG. We define combination operators that reflect these different choices, and discuss how these choices influence the quality of the repaired ontologies and KGs in terms of correctness and completeness. Comparing these different combinations provides insights into how to make choices based on the desired level of correctness and completeness of repaired ontologies and KGs. Finally, we conduct experiments and present several use cases to validate our approach and demonstrate the framework. Overall, this framework serves as a template for developing repair systems with specific properties regarding correctness and completeness of the repaired ontologies and KGs.