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.

中文翻译：

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递归 SHACL 的固定点语义

SHACL 是 W3C 提议的语言，用于在 RDF 图上表达结构约束。该建议仅规定了非递归 SHACL 的语义；最近，已经做出一些努力来允许递归 SHACL 模式。在本文中，我们认为，为了定义和研究递归 SHACL 的语义，可以从多年的非单调推理研究中吸取教训。我们表明，从 SHACL 模式，可以直接获得三值语义运算符。建立在近似固定点理论 (AFT) 的基础上，该运算符立即引入了各种语义，包括以预期方式相关的受支持、稳定和有根据的语义。通过建立在 AFT 的基础上，大量的理论结果可直接用于 SHACL。像这样，