  SHACL is a W3C-proposed language for expressing structural constraints on RDF
graphs. The recommendation only specifies semantics for non-recursive SHACL;
recently, some efforts have been made to allow recursive SHACL schemas. In this
paper, we argue that for defining and studying semantics of recursive SHACL,
lessons can be learned from years of research in non-monotonic reasoning. We
show that from a SHACL schema, a three-valued semantic operator can directly be
obtained. Building on Approximation Fixpoint Theory (AFT), this operator
immediately induces a wide variety of semantics, including a supported, stable,
and well-founded semantics, related in the expected ways. By building on AFT, a
rich body of theoretical results becomes directly available for SHACL. As such,
the main contribution of this short paper is providing theoretical foundations
for the study of recursive SHACL, which can later enable an informed decision
for an extension of the W3C recommendation.
