Reasoning about Explanations for Non-validation in SHACL

Abstract

The Shapes Constraint Language (SHACL) is a recently standardized language for describing and validating constraints over RDF graphs. The SHACL specification describes the so-called validation reports, which are meant to explain to the users the outcome of validating an RDF graph against a collection of constraints. Specifically, explaining the reasons why the input graph does not satisfy the constraints is challenging. In fact, the current SHACL standard leaves it open on how such explanations can be provided to the users. In this paper, inspired by works on logic-based abduction and database repairs, we study the problem of explaining non-validation of SHACL constraints. In particular, in our framework non-validation is explained using the notion of a repair, i.e., a collection of additions and deletions whose application on an input graph results in a repaired graph that does satisfy the given SHACL constraints. We define a collection of decision problems for reasoning about explanations, possibly restricting to explanations that are minimal with respect to cardinality or set inclusion. We provide a detailed characterization of the computational complexity of those reasoning tasks, including the combined and the data complexity.

Rewriting Approaches for Ontology-Mediated Query Answering

“…SHACL is particularly close to expressive Description Logics (DLs), the logics under-lying OWL, as already observed in several works (Bogaerts, Jakubowski, and den Bussche 2022; Leinberger et al 2020;Ortiz 2023;Ahmetaj et al 2021). Specifically, since SHACL adopts the closed world assumption, it is closely related to an extension of the DL ALCOIQ with regular role expressions and equalities, where all roles and some concept names are viewed as closed predicates (see e.g.…”

“…In this section, we introduce RDF graphs, SHACL, validation against RDF graphs, and (well-designed) SPARQL queries. We follow the abstract syntax and semantics for the fragment of SHACL core studied in (Ahmetaj et al 2021); for more details on the W3C specification of SHACL core we refer to (Knublauch and Kontokostas 2017).…”

“…A possible solution is to fix the data graph before reasoning. In the style of database repairs, (Ahmetaj et al 2021;Ahmetaj et al 2022) propose to fix the data graph through (minimal) additions or removals of facts such that the resulting data graph validates the shapes graph.…”

“…Our main goal is a detailed complexity analysis of the CQA problem. We thus build on (Ahmetaj et al 2021), which analyzes the complexity of the main reasoning problems for repairs w.r.t. SHACL constraints, such as checking the existence of a repair and deciding if a particular fact is added or deleted in at least one or in all repairs.…”

“…Indeed, it seems plausible to assume that a SHACL shapes graph is carefully designed so that no conflicting constraints are introduced. If this is not guaranteed, the existence of a repair can be tested with NP-power as shown in (Ahmetaj et al 2021). In case of a negative outcome of this test, it may still be possible to provide a repair that validates a subset of the targets.…”