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.
SHACL (Shapes Constraint Language) expresses constraints on RDF data by means of so-called shapes. Its central service is validation: verifying whether a data graph complies with a SHACL document. But so far, there are no static analysis services to compare documents. In this paper, we study the following problem: decide whether all graphs that validate one SHACL document also validate another. Unlike previous works that have considered the implication of shape expressions only, we consider documents comprising (recursive) shape definitions and targets. We show that implication (a.k.a. containment) is undecidable under the supported and the stable model semantics, even for the fragment that uses the description logic ALCIO for shape expressions. Under the well-founded semantics, in surprising contrast, it is decidable in single exponential time. Our key technical contribution is a translation of SHACL under the well-founded semantics into the full hybrid mu-calculus, revealing a novel link between well-founded models and a fixed point modal logic, and a worst-case optimal automata-based decision procedure.
SHACL is a core technology for validating the conformance of RDF knowledge graphs (KGs). Yet, authoring SHACL shapes requires technical expertise that most domain experts lack. Translating natural language requirements into SHACL (NL2SHACL) would lower this barrier. However, there is no dedicated benchmark for NL2SHACL, and evaluating generated shapes requires methods beyond string comparison, as semantically equivalent shapes can differ in serialisation and structure. To tackle these challenges, we present NL2SHACL-Bench, a benchmark suite for natural language to SHACL translation. Using NL2SHACL-Bench, we evaluate four state-of-the-art large language models (LLMs) for this task. Our results show that current LLMs are highly capable of generating syntactically valid SHACL, but still struggle to produce semantically equivalent constraints for complex logical and structural patterns. This indicates that NL2SHACL-Bench provides a meaningful basis for measuring advances in the NL2SHACL state of the art.
Bounded fitting is an attractive paradigm for learning logical formulas from labeled data examples that offers PAC-style generalization guarantees and can often be implemented leveraging SAT solvers. It has been successfully applied to learning concepts of the description logic ALC. We study bounded fitting for learning concepts in expressive description logics that extend ALC with inverse roles, qualified number restrictions, and feature comparisons. We investigate under which conditions bounded fitting keeps its favorable theoretical properties in this setting, and implement it using a SAT solver. We compare our tool with state-of-the-art concept learners with encouraging results, demonstrating that it is a practical approach to expressive concept learning.