  The Shapes Constraint Language (SHACL) was standardized by the World Wide Web
as a constraint language to describe and validate RDF data graphs. SHACL uses
the notion of shapes graph to describe a set of shape constraints paired with
targets, that specify which nodes of the RDF graph should satisfy which shapes.
An important question in practice is how to handle data graphs that do not
validate the shapes graph. A solution is to tolerate the non-validation and
find ways to obtain meaningful and correct answers to queries despite the
non-validation. This is known as consistent query answering (CQA) and there is
extensive literature on CQA in both the database and the KR setting. We study
CQA in the context of SHACL for a fundamental fragment of the Semantic Web
query language SPARQL. The goal of our work is a detailed complexity analysis
of CQA for various semantics and possible restrictions on the acceptable
repairs. It turns out that all considered variants of the problem are
intractable, with complexities ranging between the first and third level of the
polynomial hierarchy.
