SHACL Satisfiability and Containment (Extended Paper)

TL;DR

This paper analyzes the satisfiability and containment problems in SHACL, a language for RDF validation, providing a formal translation to a first-order logic and mapping out their decidability and complexity.

Contribution

It introduces a formal translation of non-recursive SHACL into a new logic, SCL, and characterizes the decidability and complexity of key decision problems.

Findings

Satisfiability and containment are undecidable for the full language.

Decidable cases are identified for certain feature combinations.

Provides a detailed complexity map for SHACL sublanguages.

Abstract

The Shapes Constraint Language (SHACL) is a recent W3C recommendation language for validating RDF data. Specifically, SHACL documents are collections of constraints that enforce particular shapes on an RDF graph. Previous work on the topic has provided theoretical and practical results for the validation problem, but did not consider the standard decision problems of satisfiability and containment, which are crucial for verifying the feasibility of the constraints and important for design and optimization purposes. In this paper, we undertake a thorough study of different features of non-recursive SHACL by providing a translation to a new first-order language, called SCL, that precisely captures the semantics of SHACL w.r.t. satisfiability and containment. We study the interaction of SHACL features in this logic and provide the detailed map of decidability and complexity results of the aforementioned decision problems for different SHACL sublanguages. Notably, we prove that both problems are undecidable for the full language, but we present decidable combinations of interesting features.