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 fixpoint approach of Van Gelder, Ross and Schlipf , 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.
Keywordsdisjunctive logic programming query answering non-monotonic reasoning well-founded semantics handling inconsistency program transformations
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- 1.S. Brass, J. Dix: Characterizations of the Disjunctive Stable Semantics by Partial Evaluation, Proc. Third Intl. Conf. on Logic Programming an Non-Monotonic Reasoning (LPNMR'95), Springer LNAI 928, 1995, pp. 85–98, and: Journal of Logic Programming, vol. 32(3), 1997, pp. 207–228.MathSciNetGoogle Scholar
- 2.T. Eiter, N. Leone, D. Sacca: On the Partial Semantics for Disjunctive Deductive Databases, Annals of Mathematics and Artificial Intelligence, to appear.Google Scholar
- 3.B.A. Davey, H.A. Priestley: Introduction to Lattices and Order, Cambridge University Press, 1990.Google Scholar
- 5.M. Gelfond, V. Lifschitz: The Stable Model Semantics for Logic Programming, Proc. Fifth Intl. Conference and Symposium on Logic Programming (ICSLP'88), MIT Press, 1988, pp. 1070–1080.Google Scholar
- 7.J. W. Lloyd: Foundations of Logic Programming, second edition, Springer, 1987.Google Scholar
- 8.J. Lobo, J. Minker, A. Rajasekar: Foundations of Disjunctive Logic Programming, MIT Press, 1992.Google Scholar
- 9.T.C. Przymusinski: On the declarative semantics of Deductive Databases and Logic Programming, in: Foundations of Deductive Databases and Logic Programming, J. Minker ed., 1988, pp. 193–216.Google Scholar
- 10.T.C. Przymusinski: Extended Stable Semantics for Normal and Disjunctive Programs, Proc. Seventh Intl. Conference on Logic Programming, 1990, pp. 459–477.Google Scholar
- 12.D. Seipel:DisLog — A Disjunctive Deductive Database Prototype, Proc. Twelfth Workshop on Logic Programming (WLP'97), 1997, pp. 136–143. DisLog is available on the WWW at ”http://www-infol.informatik.uni-wuerzburg.de/databases/DisLog”.Google Scholar
- 14.D. Seipel, J. Minker, C. Ruiz: A Characterization of Partial Stable Models for Disjunctive Deductive Databases, Proc. Intl. Logic Programming Symposium (ILPS'97), MIT Press, 1997, pp. 245–259.Google Scholar
- 15.D. Seipel: Partial Evidential Stable Models For Disjunctive Databases, Proc. Workshop on Logic Programming and Knowledge Representation (LPKR'97) at the International Symposium on Logic Programming 1997 (ILPS'97), 1997.Google Scholar
- 16.A. Van Gelder, K.A. Ross, J.S. Schlipf:, Unfounded Sets and Well-Founded Semantics for General Logic Programs, Proc. Seventh ACM Symposium on Principles of Database Systems, 1988, pp. 221–230.Google Scholar
- 18.J.H. You, L. Y. Yuan: Three-Valued Formalisms of Logic Programming: Is It Needed?, Proc. Ninth ACM Symposium on Principles of Database Systems (PODS'90), 1990, pp. 172–182.Google Scholar