Tractable ontology-mediated query answering with datatypes

Abstract

Adding datatypes to ontology-mediated queries (OMQs) often makes query answering hard, even for lightweight languages. As a consequence, the use of datatypes in ontologies, e.g. in OWL 2 QL, has been severely restricted. We propose a new, non-uniform, way of analyzing the data-complexity of OMQ answering with datatypes. Instead of restricting the ontology language we aim at a classification of the patterns of datatype atoms in OMQs into those that can occur in non-tractable OMQs and those that only occur in tractable OMQs. To this end we establish a close link between OMQ answering with datatypes and constraint satisfaction problems (CSPs) over the datatypes. Given that query answering in this setting is undecidable in general already for very simple datatypes, we introduce, borrowing from the database literature, a property of OMQs called the Bounded Match Depth Property (BMDP). We apply the link to CSPs– using results and techniques in universal algebra and model theory–to prove PTIME/co-NP dichotomies for OMQs with the BDMP over Horn-ALCHI extended with (1) all finite datatypes, (2) rational numbers with linear order and (3) certain families of datatypes over the integers with the successor relation.