An alternating well-founded semantics for query answering in disjunctive databases

  • Dietmar Seipel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1495)


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 fixpoint 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 Adwfs p 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. Adwfs p is consistent. The alternating well-founded semantics is very useful for query answering in disjunctive databases. During a fixpoint computation the final set Adwfs p is approximated by a sequence (I n )n∈∕0 of sets I n of partial Herbrand interpretations. At any step of the fixpoint computation it holds: If the query already holds in I n then the query will also hold in Adwfs p, 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.


disjunctive logic programming query answering non-monotonic reasoning well-founded semantics handling inconsistency program transformations 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Dietmar Seipel
    • 1
  1. 1.University of WürzburgWürzburgGermany

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