Reasoning with the Description Logic DLRO using Bound Guarded Programs

Open answer set programming combines the strengths of logic programming (a rule-based presentation and a nonmonotonic semantics) and description logics (open domains). Reasoning under an open answer set semantics is undecidable in general, but decidability can be obtained for particular classes of logic programs, e.g., for bound guarded programs. In this paper, we show how bound guarded programs are expressive enough to simulate satisfiability checking in a DL with n-ary roles and nominals, yielding EXPTIME-completeness for both the DL reasoning and the reasoning with bound guarded programs under the open answer set semantics. We establish decidability of three query problems (query containment, consistency, and disjointness) for guarded queries by a reduction to bound guarded programs, resulting in an EXPTIME upper bound.