Explaining Ontology-Mediated Query Answers using Proofs over Universal Models (Technical Report)

TL;DR

This paper introduces a proof-based approach to explain query answers in ontology-mediated systems, analyzing the complexity of proof existence under various conditions and ontologies.

Contribution

It adapts an existing proof framework for conjunctive query answering to improve explainability in ontology-mediated query answering, with a complexity analysis.

Findings

Complexity varies with query shape and ontology type.

Proof existence can be determined within specific complexity bounds.

The approach enhances explainability in ontology-based data access.

Abstract

In ontology-mediated query answering, access to incomplete data sources is mediated by a conceptual layer constituted by an ontology, which can be formulated in a description logic (DL) or using existential rules. In the literature, there exists a multitude of complex techniques for incorporating ontological knowledge into queries. However, few of these approaches were designed for explainability of the query answers. We tackle this challenge by adapting an existing proof framework toward conjunctive query answering, based on the notion of universal models. We investigate the data and combined complexity of determining the existence of a proof below a given quality threshold, which can be measured in different ways. By distinguishing various parameters such as the shape of the query, we obtain an overview of the complexity of this problem for several Horn DLs.