OWL and SHACL are two prominent W3C standards for managing RDF graphs, the data model of the Web. They are used for different purposes and make different assumptions about the completeness of data: SHACL is used for expressing integrity constraints on complete data, while OWL allows inferring implicit facts from incomplete data; SHACL reasoners perform validation, while OWL reasoners do logical inference. Integrating these two tasks into one uniform approach is a relevant but challenging problem. The SHACL standard envisions graph validation in combination with OWL entailment, but it does not provide technical guidance on how to realize this. To address this problem, we propose a new intuitive semantics for validating SHACL constraints with OWL 2 QL ontologies based on a suitable notion of the chase. We propose an algorithm that rewrites a set of recursive SHACL constraints (with stratified negation) and an OWL 2 QL ontology into a stand-alone set of SHACL constraints that preserves validation for every input graph, which can in turn be evaluated using an off-the-shelf SHACL validator. We show that validation in this setting is EXPTIME-complete in combined complexity, but only PTIME-complete in data complexity, i.e., if the constraints and the ontology are fixed.
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