SHACL Validation in the Presence of Ontologies: Semantics and Rewriting Techniques
This addresses a major challenge in semantic web technologies for data managers and researchers, but it is incremental as it builds on existing standards and focuses on specific logics.
The paper tackles the semantic and computational challenges of combining SHACL validation with OWL ontologies by proposing a semantics based on core universal models and a rewriting technique to reduce validation to standard SHACL. It shows that SHACL validation with ontologies is EXPTIME-complete in general and PTIME-complete in data complexity.
SHACL and OWL are two prominent W3C standards for managing RDF data. These languages share many features, but they have one fundamental difference: OWL, designed for inferring facts from incomplete data, makes the open-world assumption, whereas SHACL is a constraint language that treats the data as complete and must be validated under the closed-world assumption. The combination of both formalisms is very appealing and has been called for, but their semantic gap is a major challenge, semantically and computationally. In this paper, we advocate a semantics for SHACL validation in the presence of ontologies based on core universal models. We provide a technique for constructing these models for ontologies in the rich data-tractable description logic Horn-ALCHIQ. Furthermore, we use a finite representation of this model to develop a rewriting technique that reduces SHACL validation in the presence of ontologies to standard validation. Finally, we study the complexity of SHACL validation in the presence of ontologies, and show that even very simple ontologies make the problem EXPTIME-complete, and PTIME-complete in data complexity.