SHACL validation over DL-Lite, ELHI and Horn-SHIQ ontologies (or calculating the core chase layer-by-layer)
SHACL is a widely used W3C standard to manage RDF data: it is used to express integrity constraints on "complete" data. These constraints may contain recursion and negation and many other kinds of exotic features, like counting over paths expressed by regular expressions. As SHACL is intended for validation over complete data, we add ontologies to the RDF data (and create a knowledge base) and ask what it means to combine both: we define validation of SHACL combined with ontologies as SHACL validation over the core chase of this knowledge base.
However, creating the core chase is not feasible in practice. To tackle this, we propose a way to build the core chase in a layer-by-layer manner, based on pre-calculated building blocks and without having to look for non-embedding endomorphisms, as the usual core construction does. We use these building blocks to rewrite SHACL validation in case of ontologies to plain SHACL validation.