Stratified Negation in RDF Rules: A Correct Approach (Extended Version)

2026-07-30

AI Summary

This work addresses the challenge of defining well-founded semantics for RDF rule languages—such as N3 and SHACL Rules—when default negation is introduced, a problem exacerbated by sparse triple data and blank nodes that obscure dependency structures and hinder reliable stratification. To resolve this, the paper proposes a novel chaining-based stratification method that integrates multi-step dependency analysis, integrity constraint filtering, and negation-as-failure semantics. It establishes, for the first time, a stratification criterion tailored to existential rules, effectively overcoming the difficulties posed by blank nodes and sparse graph structures. The approach guarantees a unique, minimal, and justifiable semantics for RDF rules with negation, and its feasibility and practicality are demonstrated through a prototype implementation.

Abstract

Combining RDF rule languages, such as N3 or SHACL Rules, with default negation is challenging. Existing methods to stratify negation often fail for RDF rules, since individual triples do not carry enough information to meaningfully restrict potential dependencies. Blank nodes in rule heads further complicate the matter, since the order of rule applications may determine whether new values are created, which in turn can change the applicability of rules with negation. To solve these open problems, we propose chain stratification as a robust new condition that guarantees a well-behaved semantics for RDF rules with negation, and existential rules in general. Our condition combines an elaborate analysis of potential multistep derivations with a mechanism for using integrity constraints to discard impossible cases. Applying rules in any order that respects chain stratification is guaranteed to derive an RDF graph that is unique, lean, and justified under the usual negation-as-failure semantics. To show the practicality, we also provide a prototype implementation.

Problem

• stratified negation
• RDF rules
• default negation
• blank nodes
• rule dependencies

Innovation

• chain stratification
• RDF rules
• default negation
• existential rules
• negation-as-failure