Towards Universal Languages for Tractable Ontology Mediated Query Answering
This addresses foundational theoretical limitations in ontology languages for query answering, with incremental contributions to understanding expressiveness in tractable OMQA.
The paper tackled the problem of finding universal languages for tractable ontology mediated query answering (OMQA) families, proving that no universal language exists for three families like first-order rewritable ones, but introduced locality as an approximation to show a universal language exists for OMQA-languages with locality.
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.