A standardized and widely used way to organize structured knowledge on the internet are knowledge graphs (KGs). KGs can be viewed as graphs with labels on edges and/or nodes. Ontologies are a way to formally describe KGs that contain, next to the concrete information in the graph, implicit reasoning rules like each student has a student number. In practice, ontologies are used to make data more suitable for applications.
In the years after the standardization of KGs in the form of RDF data, and ontologies in the form of OWL, a big need for a language to describe and validate the correctness of KGs came up. This lead to the introduction of SHACL. Although lots of issues around SHACL remain open and aspects are lacking, SHACL is widely adopted as it is so important in practice. To have reliable SHACL technologies, it is very important to understand SHACL better and provide solid foundations.
In my dissertation, I am focusing on what it means to combine SHACL with ontologies. This problem is envisioned in the SHACL standard, but there is no technical guidance provided. The goal is of my PhD is to provide solid foundation for this combination. There is a great interest in this work in among others the semantic web community. However, there do not exist any satisfying proposals outside of this project yet.