🤖 AI Summary
This work addresses the lack of explainable provenance in Description Logic (DL) ontology reasoning. We systematically extend the semiring-based provenance framework to lightweight DLs, notably ELHI⊥, for the first time. We introduce a generic semiring provenance semantics that unifies why-provenance, positive Boolean provenance, and lineage provenance, while revealing intrinsic connections to DL model interpretations and fuzzy reasoning. Leveraging commutative semiring algebra and DL semantics, we establish precise computational complexity characterizations—P, NP, or ExpTime—for various provenance problems. Moreover, we derive sufficient conditions under which satisfiability reasoning for ELHI⊥ ontologies remains decidable under provenance tracking. Our results demonstrate that provenance semantics exhibit favorable scalability under restricted semirings, thereby establishing a formally rigorous and explainable foundation for provenance analysis in DL ontologies.
📝 Abstract
We investigate semiring provenance--a successful framework originally defined in the relational database setting--for description logics. In this context, the ontology axioms are annotated with elements of a commutative semiring and these annotations are propagated to the ontology consequences in a way that reflects how they are derived. We define a provenance semantics for a language that encompasses several lightweight description logics and show its relationships with semantics that have been defined for ontologies annotated with a specific kind of annotation (such as fuzzy degrees). We show that under some restrictions on the semiring, the semantics satisfies desirable properties (such as extending the semiring provenance defined for databases). We then focus on the well-known why-provenance, for which we study the complexity of problems related to the provenance of an assertion or a conjunctive query answer. Finally, we consider two more restricted cases which correspond to the so-called positive Boolean provenance and lineage in the database setting. For these cases, we exhibit relationships with well-known notions related to explanations in description logics and complete our complexity analysis. As a side contribution, we provide conditions on an $mathcal{ELHI}_ot$ ontology that guarantee tractable reasoning.
