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Nowadays, the amount of data generated by users on the Web has increased dramatically, and managing it efficiently is getting more challenging, especially for small or medium-sized organizations. Often, the data to be managed is encoded in a low-level format, requiring domain experts to manually produce a high-level conceptual view from the raw data. A virtual Knowledge Graph (VKG) is a semantic framework that stands as a data integration paradigm aiming to provide convenient, user-friendly access to the data. VKGs, formerly known as ontology-based data access (OBDA), have emerged as an information management system that solves the complex problem of data integration by exposing the end users to an ontology that is typically expressed in some fragment of the Web Ontology Language (OWL2), standardized by the World Wide Web Consortium (W3C). The framework is a virtual approach that typically consists of three main components: an ontology, which is a high-level and conceptual representation of the domain of interest, a set of data sources, and the mapping between the two.

However, with the vision of the Semantic Web, which has consisted of enabling the "Read/Write" Web for structured data, the main focus of research in VKGs has been centered around query-answering which consists of using the ontology layer to extract information specified through a query from the underlying data sources. Yet the problem of updates in VKGs has, however, received little attention and represents an important feature that will enable VKGs to be fully-fledged and, thus, let user fully manage their data from the ontology they are exposed to. This dissertation aims to study and introduce the notions of ontology-based update in the context of VKGs and to study the foundational issues of this extension. In other words, the aim is to study how updates posed over the ontology layer are rewritten into equivalent updates over the underlying data sources.

However, due to the complex nature of VKG mappings, the translation of ontology-based updates is not always deterministic and might lead to extra unintended updates in the knowledge graph, which we refer to as side effects. Considering ontologies specified in DL-LiteR, the formal counterpart of OWL 2 QL, we study how to efficiently translate ontology-based updates by relying on the reverse of VKG mappings. Secondly, based on a given comparison metric for ontology-based update translations, we compute a set of translations with minimum side effects. We also introduce the notion of preference (provided by the user in a declarative format) that can be used to provide a deterministic translation. Finally, we demonstrate the practical feasibility of our approach by implementing the proposed techniques within the Ontop VKG system, translating SPARQL Update operations into SQL statements via R2RML mappings.