Partial evidential stable models for disjunctive deductive databases
In this paper we consider the basic semantics of stable and partial stable models for disjunctive deductive databases (with default negation), cf. [9,16]. It is well-known that there are disjunctive deductive databases where no stable or partial stable models exist, and these databases are called inconsistent w.r.t. the basic semantics.
We define a consistent variant of each class of models, which we call evidential stable and partial evidential stable models. It is shown that if a database is already consistent w.r.t. the basic semantics, then the class of evidential models coincides with the basic class of models. Otherwise, the set of evidential models is a subset of the set of minimal models of the database. This subset is non-empty, if the database is logically consistent. It is determined according to a suitable preference relation, whose underlying idea is to minimize the amount of reasoning by contradiction.
The technical ingredients for the construction of the new classes of models are two transformations of disjunctive deductive databases. First, the evidential transformation is used to realize the preference relation, and to define evidential stable models. Secondly, based on the tu-transformation the result is lifted to the three-valued case, that is, partial evidential stable models are defined.
Keywordsdisjunctive logic programming non-monotonic reasoning stable and partial stable models handling inconsistency program transformations
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- 2.S. Brass, J. Dix: A Disjunctive Semantics Based upon Partial and Bottom-Up Evaluation, Proc. Intl. Conference on Logic Programming (ICLP'95), MIT Press, 1995, pp. 199–213.Google Scholar
- 3.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
- 4.C. V. Damásio, L.M. Pereira: Abduction over 3-valued Extended Logic Programs, Proc. Third Intl. Conf. on Logic Programming an Non-Monotonic Reasoning (LPNMR'95), Springer LNAI 928, 1995, pp. 29–42.Google Scholar
- 6.T. Eiter, N. Leone, D. Sacca: On the Partial Semantics for Disjunctive Deductive Databases, Annals of Mathematics and Artificial Intelligence, to appear.Google Scholar
- 9.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
- 13.J. W. Lloyd: Foundations of Logic Programming, second edition, Springer, 1987.Google Scholar
- 14.J. Lobo, J. Minker, A. Rajasekar: Foundations of Disjunctive Logic Programming, MIT Press, 1992.Google Scholar
- 15.I. NiemelÄ, P. Simons: Efficient Implementation of the Well-founded and Stable Model Semantics, Proc. Joint Intl. Conference and Symposium on Logic Programming (JICSLP'96), MIT Press, 1996, pp. 289–303.Google Scholar
- 19.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
- 20.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-info1.informatik.uni-wuerzburg.de/databases/DisLog”.Google Scholar
- 21.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 (PODS'88), 1988, pp. 221–230.Google Scholar
- 23.C. Witteveen, W. van der Hoek: A General Framework for Revising Nonmonotonic Theories, Proc. Fourth Intl. Conf. on Logic Programming an Non-Monotonic Reasoning (LPNMR'97), Springer LNAI 1265, 1997, pp. 258–272.Google Scholar
- 24.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