  In this paper, we explore a quantitative approach to querying inconsistent
description logic knowledge bases. We consider weighted knowledge bases in
which both axioms and assertions have (possibly infinite) weights, which are
used to assign a cost to each interpretation based upon the axioms and
assertions it violates. Two notions of certain and possible answer are defined
by either considering interpretations whose cost does not exceed a given bound
or restricting attention to optimal-cost interpretations. Our main contribution
is a comprehensive analysis of the combined and data complexity of bounded cost
satisfiability and certain and possible answer recognition, for description
logics between ELbot and ALCO.
