Expressiveness of shacl features and extensions for full equality and disjointness tests

. SHACL is a W3C-proposed schema language for expressing structural constraints on RDF graphs. Recent work on formalizing this language has revealed a striking relationship to description logics. SHACL expressions can use three fundamental features that are not so common in description logics. These features are equality tests; disjointness tests; and closure constraints. Moreover, SHACL is peculiar in allowing only a restricted form of expressions (so-called targets) on the left-hand side of inclusion constraints. The goal of this paper is to obtain a clear picture of the impact and expressiveness of these features and restrictions. We show that each of the three features is primitive: using the feature, one can express boolean queries that are not expressible without using the feature. We also show that the restriction that SHACL imposes on allowed targets is inessential, as long as closure constraints are not used. In addition, we show that enriching SHACL with "full" versions of equality tests, or disjointness tests, results in a strictly more powerful language.