An Alternating Well-Founded Semantics for Query Answering in Disjunctive Databases

The well{founded semantics has been introduced for normal databases (i.e. databases that may have default negation in their rule bodies, but do not have disjunctions). In this paper we propose an extension of the well{founded semantics to the disjunctive case. For this purpose we investigate the alternating xpoint approach of Van Gelder, Ross and Schlipf 16], and develop a suitable generalization to the case of disjunctive rule heads. Given a disjunctive database P , the new alternating well{founded semantics derives a set ADWFSP of partial Herbrand interpretations of P. This set coincides with the set of minimal models if there are no default negations in the database. For general disjunctive databases it is always not empty (if all rule heads are non{empty), i.e. ADWFSP is consistent. The alternating well{founded semantics is very useful for query answering in disjunctive databases. During a xpoint computation the nal set ADWFSP is approximated by a sequence (In)n2I N 0 of sets In of partial Herbrand interpretations. At any step of the xpoint computation it holds: If the query already holds in In, then the query will also hold in ADWFSP, and the computation can be terminated. For other semantics like the semantics of stable and partial stable models, so far no computations are known that have this property.