Fixpoint Semantics for Recursive SHACL

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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.

Original languageEnglish
Title of host publicationProceedings 37th International Conference on Logic Programming (Technical Communications)
PublisherOpen Publishing Association
Number of pages7
Publication statusPublished - 17 Sep 2021
Event37th International Conference on Logic Programming - Porto, Porto, Portugal
Duration: 20 Sep 202127 Sep 2021
Conference number: 37

Publication series

NameElectronic Proceedings in Computer Science
PublisherOpen Publishing Association
ISSN (Print)2075-2180
ISSN (Electronic)2075-2180


Conference37th International Conference on Logic Programming
Abbreviated titleICLP

Bibliographical note

Funding Information:
Our results have been presented without taking a stance on the choice of semantics. It is important to realize though, that if one wants to view Def as an (inductive) definition of the shapes, it has been argued repeatedly that the well-founded semantics correctly formalizes this [17]. Under the well-founded semantics, SHACL integrates first-order constraints (of a restricted form) with inductive definitions and aggregates, and hence can be seen as a fragment of the language FO(ID, Agg), the formal foundation of the IDP language [13]. It is a topic for future work to investigate whether this can be exploited for either extending SHACL, or for developing alternative validation mechanisms, building on IDP. Acknowledgements This research was supported by the Flemish Government in the “Onderzoekspro-gramma Artificiële Intelligentie (AI) Vlaanderen” programme and by FWO Flanders project G0B2221N.

Funding Information:
This research was supported by the Flemish Government in the ?Onderzoeksprogramma Artifici?le Intelligentie (AI) Vlaanderen? programme and by FWO Flanders project G0B2221N.

Publisher Copyright:
© B. Bogaerts & M. Jakubowski This work is licensed under the Creative Commons Attribution License.

Copyright 2021 Elsevier B.V., All rights reserved.


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