Satisfiability and Containment of Recursive SHACL

by   Paolo Pareti, et al.

The Shapes Constraint Language (SHACL) is the recent W3C recommendation language for validating RDF data, by verifying certain shapes on graphs. Previous work has largely focused on the validation problem and the standard decision problems of satisfiability and containment, crucial for design and optimisation purposes, have only been investigated for simplified versions of SHACL. Moreover, the SHACL specification does not define the semantics of recursively-defined constraints, which led to several alternative recursive semantics being proposed in the literature. The interaction between these different semantics and important decision problems has not been investigated yet. In this article we provide a comprehensive study of the different features of SHACL, by providing a translation to a new first-order language, called SCL, that precisely captures the semantics of SHACL. We also present MSCL, a second-order extension of SCL, which allows us to define, in a single formal logic framework, the main recursive semantics of SHACL. Within this language we also provide an effective treatment of filter constraints which are often neglected in the related literature. Using this logic we provide a detailed map of (un)decidability and complexity results for the satisfiability and containment decision problems for different SHACL fragments. Notably, we prove that both problems are undecidable for the full language, but we present decidable combinations of interesting features, even in the face of recursion.


page 1

page 2

page 3

page 4


SHACL Satisfiability and Containment (Extended Paper)

The Shapes Constraint Language (SHACL) is a recent W3C recommendation la...

Fixpoint Semantics for Recursive SHACL

SHACL is a W3C-proposed language for expressing structural constraints o...

A Review of SHACL: From Data Validation to Schema Reasoning for RDF Graphs

We present an introduction and a review of the Shapes Constraint Languag...

ExpTime Tableaux for Type PDL

The system of Type PDL (τPDL) is an extension of Propositional Dynamic L...

On the Complexity of Linear Temporal Logic with Team Semantics

A specification given as a formula in linear temporal logic (LTL) define...

Recurrence extraction and denotational semantics with recursive definitions

With one exception, our previous work on recurrence extraction and denot...

Integrating deduction and model finding in a language independent setting

Software artifacts are ubiquitous in our lives being an essential part o...

Please sign up or login with your details

Forgot password? Click here to reset