Arthur Ryman
This article provides a formalization of the W3C Draft Core SHACL Semantics specification using Z notation. This formalization exercise has identified a number of quality issues in the draft. It has also established that the recursive definitions in the draft are well-founded. Further formal validation of the draft will require the use of an executable specification technology.
Arthur Ryman
An RDF data shape is a description of the expected contents of an RDF document (aka graph) or dataset. A major part of this description is the set of constraints that the document or dataset is required to satisfy. W3C recently (2014) chartered the RDF Data Shapes Working Group to define SHACL, a standard RDF data shape language. We refer to the ability to name and reference shape language elements as recursion. This article provides a precise definition of the meaning of recursion as used in Resource Shape 2.0. The definition of recursion presented in this article is largely independent of language-specific details. We speculate that it also applies to ShEx and to all three of the current proposals for SHACL. In particular, recursion is not permitted in the SHACL-SPARQL proposal, but we conjecture that recursion could be added by using the definition proposed here as a top-level control structure.