We present a novel approach to querying classically inconsistent description logic (DL) knowledge bases by adopting a paraconsistent semantics with the four 'Belnapian' values: exactly true (T), exactly false (F), both (B), and neither (N). In contrast to prior studies on paraconsistent DLs, we allow truth value operators in the query language over concept and role atoms, which can be used to differentiate between answers obtained from contradictory evidence and those based upon only positive evidence. We present a reduction to classical DL query answering that allows us to pinpoint the precise combined and data complexity of answering queries with values in paraconsistent ALCHI with two- and four-valued roles and their sublogics. Notably, we show that tractable data complexity is retained for Horn DLs. We also present a comparison with repair-based inconsistency-tolerant semantics, showing that the two approaches are incomparable: if we consider queries with the T (exactly true) operator, then we neither over-approximate the most cautious repair-based semantics, nor under-approximate the least cautious ones.
Li et al. (Wed,) studied this question.