Adding DL-Lite TBoxes to Proper Knowledge Bases

Levesque's proper knowledge bases proper KBs correspond to infinite sets of ground positive and negative facts, with the notable property that for FOL formulas in a certain normal form, which includes conjunctive queries and positive queries possibly extended with a controlled form of negation, entailment reduces to formula evaluation. However proper KBs represent extensional knowledge only. In description logic terms, they correspond to ABoxes. In this paper, we augment them with DL-Lite TBoxes, expressing intensional knowledge i.e., the ontology of the domain. DL-Lite has the notable property that conjunctive query answering over TBoxes and standard description logic ABoxes is reducible to formula evaluation over the ABox only. Here, we investigate whether such a property extends to ABoxes consisting of proper KBs. Specifically, we consider two DL-Lite variants: $$\\textit{DL-Lite}_{ rdfs }$$, roughly corresponding to RDFS, and $$\\textit{DL-Lite}_{ core }$$, roughly corresponding to OWL 2 QL. We show that when a $$\\textit{DL-Lite}_{ rdfs }$$ TBox is coupled with a proper KB, the TBox can be compiled away, reducing query answering to evaluation on the proper KB alone. But this reduction is no longer possible when we associate proper KBs with $$\\textit{DL-Lite}_{ core }$$ TBoxes. Indeed, we show that in the latter case, query answering even for conjunctive queries becomes coNP-hard in data complexity.