Shapes from Examples: Foundations of Shape Learning in Recursive SHACL

• URL: http://arxiv.org/abs/2607.27934v2
• Date: Thu, 06 Aug 2026 12:02:36 GMT
• Title: Shapes from Examples: Foundations of Shape Learning in Recursive SHACL
• Abstract summary: SHACL shapes enable data graph validation, making automatic shape learning essential for knowledge graph applications.<n>We investigate the well-known fitting approach to this task: given sets P and N of positive and negative example nodes from an input graph, compute a shape expression C, possibly using shape names defined in a shape catalogue, that validates at every node in P and none in N.
• Score: 2.099922236065961
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: SHACL shapes enable data graph validation, making automatic shape learning essential for knowledge graph applications. We investigate the well-known fitting approach to this task: given sets P and N of positive and negative example nodes from an input graph, compute a shape expression C, possibly using shape names defined in a recursive shape catalogue, that validates at every node in P and none in N. We focus on the case where C is written in a core fragment of SHACL corresponding to the Description Logic ELI. For the catalogue, we consider the well-founded, stable, and supported semantics. We address fitting existence and most specific fitting computation, establish tight exponential-time upper bounds for both problems, and obtain polynomial bounds for relevant special cases.

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