Towards Universal Languages for Tractable Ontology Mediated Query Answering

TL;DR

This paper investigates the existence of universal ontology languages for tractable ontology mediated query answering, proving limitations and proposing a new property called locality to achieve universality in certain cases.

Contribution

It introduces the concept of locality to approximate first-order rewritability and identifies a universal language for OMQA-languages with locality.

Findings

No universal language exists for each family of tractable OMQA-languages.

Locality can be used to approximate first-order rewritability.

A language of disjunctive embedded dependencies is universal for OMQA with locality.

Abstract

An ontology language for ontology mediated query answering (OMQA-language) is universal for a family of OMQA-languages if it is the most expressive one among this family. In this paper, we focus on three families of tractable OMQA-languages, including first-order rewritable languages and languages whose data complexity of the query answering is in AC0 or PTIME. On the negative side, we prove that there is, in general, no universal language for each of these families of languages. On the positive side, we propose a novel property, the locality, to approximate the first-order rewritability, and show that there exists a language of disjunctive embedded dependencies that is universal for the family of OMQA-languages with locality. All of these results apply to OMQA with query languages such as conjunctive queries, unions of conjunctive queries and acyclic conjunctive queries.