Adding datatypes to ontology-mediated queries (OMQs) often makes query answering hard. As a consequence, the use of datatypes in OWL 2 QL has been severely restricted. In this paper 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 over the datatypes. In a case study we apply this link to prove a P/coNP-dichotomy for OMQs over DL-Lite extended with the datatype (Q,<=). The proof employs a recent dichotomy result by Bodirsky and Kára for temporal constraint satisfaction problems.

In this paper, we provide more evidence for the contention that logical consequence should be understood in normative terms. Hartry Field and John MacFarlane covered the classical case. We extend their work, examining what it means for an agent to be obliged to infer a conclusion when faced with uncertain information or reasoning within a non-monotonic, defeasible, logical framework (which allows e. g. for inference to be drawn from premises considered true unless evidence to the contrary is presented).