Dichotomies in Ontology-Mediated Querying with the Guarded Fragment

TL;DR

This paper analyzes the complexity of ontology-mediated querying in the guarded fragment of first-order logic, identifying fragments with clear complexity dichotomies and exploring implications for Datalog-rewritability and the Feder-Vardi conjecture.

Contribution

It classifies the data complexity of GF-based ontologies, establishing dichotomies, linking to the Feder-Vardi conjecture, and analyzing the decidability of PTime query evaluation.

Findings

Identified GF fragments with PTime/coNP dichotomies.

Most BioPortal ontologies fit into these fragments.

Proved no dichotomy exists for certain GF fragments, linking to the Feder-Vardi conjecture.

Abstract

We study the complexity of ontology-mediated querying when ontologies are formulated in the guarded fragment of first-order logic (GF). Our general aim is to classify the data complexity on the level of ontologies where query evaluation w.r.t. an ontology O is considered to be in PTime if all (unions of conjunctive) queries can be evaluated in PTime w.r.t. O and coNP-hard if at least one query is coNP-hard w.r.t. O. We identify several large and relevant fragments of GF that enjoy a dichotomy between PTime and coNP, some of them additionally admitting a form of counting. In fact, almost all ontologies in the BioPortal repository fall into these fragments or can easily be rewritten to do so. We then establish a variation of Ladner's Theorem on the existence of NP-intermediate problems and use this result to show that for other fragments, there is provably no such dichotomy. Again for other fragments (such as full GF), establishing a dichotomy implies the Feder-Vardi conjecture on the complexity of constraint satisfaction problems. We also link these results to Datalog-rewritability and study the decidability of whether a given ontology enjoys PTime query evaluation, presenting both positive and negative results.