Polynomial Datalog Rewritings for Expressive Description Logics with Closed Predicates

We consider instance queries mediated by an ontology expressed in the expressive DL ALCHIO with closed predicates. We observe that such queries are non-monotonic and cannot be expressed in monotonic variants of DATALOG, but a polynomial time translation into disjunctive DATALOG extended with negation as failure is feasible. If no closed predicates are present–in the case of classical instance checking in ALCHIO–our translation yields a positive disjunctive DATALOG program of polynomial size. To the best of our knowledge, this is the first polynomial time translation of an expressive (non-Horn) DL into disjunctive DATALOG.