VEL: A Formally Verified Reasoner for OWL2 EL Profile

TL;DR

This paper introduces VEL, a formally verified reasoner for OWL2 EL, ensuring correctness through machine-checked proofs and addressing previous proof errors to improve reliability in semantic reasoning.

Contribution

We developed VEL, the first formally verified OWL2 EL reasoner with machine-checkable correctness proofs, enhancing trustworthiness in semantic web reasoning systems.

Findings

VEL's formalization uncovered errors in original proofs.

VEL's correctness is guaranteed across all inputs.

The approach improves reliability of reasoning in critical domains.

Abstract

Over the past two decades, the Web Ontology Language (OWL) has been instrumental in advancing the development of ontologies and knowledge graphs, providing a structured framework that enhances the semantic integration of data. However, the reliability of deductive reasoning within these systems remains challenging, as evidenced by inconsistencies among popular reasoners in recent competitions. This evidence underscores the limitations of current testing-based methodologies, particularly in high-stakes domains such as healthcare. To mitigate these issues, in this paper, we have developed VEL, a formally verified EL++ reasoner equipped with machine-checkable correctness proofs that ensure the validity of outputs across all possible inputs. This formalization, based on the algorithm of Baader et al., has been transformed into executable OCaml code using the Coq proof assistant's extraction capabilities. Our formalization revealed several errors in the original completeness proofs, which led to changes to the algorithm to ensure its completeness. Our work demonstrates the necessity of mechanization of reasoning algorithms to ensure their correctness at theoretical and implementation levels.