Fixpoint Semantics for Recursive SHACL

Bart Bogaerts
Maxime Jakubowski

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.

In Andrea Formisano, Yanhong Annie Liu, Bart Bogaerts, Alex Brik, Veronica Dahl, Carmine Dodaro, Paul Fodor, Gian Luca Pozzato, Joost Vennekens and Neng-Fa Zhou: Proceedings 37th International Conference on Logic Programming (Technical Communications) (ICLP 2021), Porto (virtual event), 20-27th September 2021, Electronic Proceedings in Theoretical Computer Science 345, pp. 41–47.
Published: 17th September 2021.

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