Partial semantics for disjunctive deductive databases
We consider in this paper interesting subclasses of partial stable models which reduce the degree of undefinedness, namely M-stable (Maximal-stable) models, which coincide with regular models, preferred extension, and maximal stable classes, and L-stable (Least undefinedstable) models, and we extend them from normal to disjunctive deductive databases.
L-stable models are shown to be the natural relaxation of the notion of total stable model; on the other hand the less strict M-stable models, endowed with a modularity property, may be appealing from the programming and computational point of view. M-stable and L-stable models are also compared with regular models on disjunctive deductive databases. It appears that, unlike on normal deductive databases, M-stable models do not coincide with regular models. Moreover, both M-stable and L-stable models satisfy the CWA principle, while regular models do not.
KeywordsLogic Program Stable Model Deductive Database Modularity Property Normal Program
Unable to display preview. Download preview PDF.
- 1.K. Apt and H. Blair. Arithmetic Classification of Perfect Models of Stratified Programs. In Proc. of the Fifth Joint Int'l Conference and Symposium on Logic Programming (JICSLP-88), pp. 766–779. 1988.Google Scholar
- 2.C. Baral and V. Subrahmanian. Stable and Extension Class Theory for Logic Programs and Default Logic. Journal of Automated Reasoning, 8:345–366, 1992.Google Scholar
- 3.J. Dix. Classifying Semantics of Disjunctive Logic Programs. In K. Apt, editor, Proc. JICSLP-92, pp. 798–812. 1992.Google Scholar
- 4.P. Dung. Negation as Hypotheses: An Abductive Foundation for Logic Programming. In Proc. ICLP-91, pp. 3–17. 1991.Google Scholar
- 5.T. Eiter, G. Gottlob, and H. Mannila. Adding Disjunction to Datalog. In Proc. PODS '94, pp. 267–278, May 1994.Google Scholar
- 6.T. Eiter, N. Leone, and D. Saccà. On the Partial Semantics for Disjunctive Deductive Databases. Technical Report CD-TR 95/82, Christian Doppler Lab for Expert Systems, TU Vienna, 1995.Google Scholar
- 8.M. Gelfond and V. Lifschitz. The Stable Model Semantics for Logic Programming. In Proc. Fifth Intl Conference and Symposium, pp. 1070–1080. 1988.Google Scholar
- 10.V. Lifschitz and H. Turner. Splitting a Logic Program. In Proc. ICLP-94, pp. 23–38, MIT-Press, 1994.Google Scholar
- 11.J. Minker. On Indefinite Data Bases and the Closed World Assumption. In Proc. CADE '82, pp. 292–308, LNCS 138. Springer, 1982.Google Scholar
- 12.T. Przymusinski. Stable Semantics for Disjunctive Programs. New Generation Computing, 9:401–424, 1991.Google Scholar
- 13.R. Reiter. On Closed-World Databases. In H. Gallaire and J. Minker, editors, Logic and Data Bases, pp. 55–76. Plenum Press, New York, 1978.Google Scholar
- 15.D. Saccá. The Expressive Powers of Stable Models for Bound and Unbound DAT-ALOG Queries. Journal of Computer and System Sciences, 1996. To appear.Google Scholar
- 17.J. D. Ullman. Principles of Database and Knowledge Base Systems. Computer Science Press, 1988.Google Scholar
- 18.A. van Gelder, K. Ross, and J. Schlipf. The Well-Founded Semantics for General Logic Programs. Journal of the ACM, 38(3):620–650, 1991.Google Scholar