Finding Good Proofs for Answers to Conjunctive Queries Mediated by Lightweight Ontologies (Technical Report)

TL;DR

This paper explores the complexity of generating comprehensible proofs for query answers in ontology-mediated systems, focusing on lightweight ontologies like DL-Lite_R and EL, and aims to improve answer transparency.

Contribution

It adapts a proof framework for axiom entailment to conjunctive query answering, analyzing complexity and proof quality thresholds for lightweight ontologies.

Findings

Complexity analysis of proof existence under various parameters.

Identification of tractable cases for DL-Lite_R and EL.

Insights into temporal query answering complexity.

Abstract

In ontology-mediated query answering, access to incomplete data sources is mediated by a conceptual layer constituted by an ontology. To correctly compute answers to queries, it is necessary to perform complex reasoning over the constraints expressed by the ontology. In the literature, there exists a multitude of techniques incorporating the ontological knowledge into queries. However, few of these approaches were designed for comprehensibility of the query answers. In this article, we try to bridge these two qualities by adapting a proof framework originally applied to axiom entailment for conjunctive query answering. 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 a query, we obtain an overview of the complexity of this problem for the lightweight ontology languages DL-Lite_R and EL, and also have a brief look at temporal query answering.