Stable Model Semantics for Recursive SHACL

Abstract

SHACL (SHape Constraint Language) is a W3C recommendation for validating graph-based data against a set of constraints (called shapes). Importantly, SHACL allows to define recursive shapes, i.e. a shape may refer to itself, directly of indirectly. The recommendation left open the semantics of recursive shapes, but proposals have emerged recently to extend the official semantics to support recursion. These proposals are based on the principle of possibility (or non-contradiction): a graph is considered valid against a schema if one can assign shapes to nodes in such a way that all constraints are satisfied. This semantics is not constructive, as it does not provide guidelines about how to obtain such an assignment, and it may lead to unfounded assignments, where the only reason to assign a shape to a node is that it allows validating the graph. In contrast, we propose in this paper a stricter, more constructive semantics for SHACL, based on stable models, which are well-known in Answer Set Programming (ASP). This semantics additionally requires a shape assignment to be properly justified by the input constraints. We further exploit the connection to logic programming, and show that SHACL constraints can be naturally represented as logic programs, and that the validation problem for a graph and a SHACL schema can be encoded as an ASP reasoning task. The proposed semantics also enjoys computationally tractable validation in the presence of constraints with stratified negation (as opposed to the previous semantics). We also extend our semantics to 3-valued stable models, which yields a more relaxed notion of validation, tolerant to certain faults in the schema or data. By exploiting a connection between 3-valued stable model semantics and the well-founded semantics for logic programs, we can use our translation into ASP to show another tractability result. Finally, we provide a preliminary evaluation of the approach, which leverages an ASP solver to perform graph validation.