A Proof Procedure for Stable Theories

Jose Alberto Fernandez, Jorge Lobo.

Computer Science Department,
University of Maryland
College Park

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Abstract

Bibliography

• [Apt90] K.R. Apt. Logic programming. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 493-574. Elsevier, 1990.
• [BF88] N. Bidoit and C. Froidevaux. General logical databases and programs: Default logic semantics and stratification. Journal of Information and Computation, 1988.
• [BLM89] C. Baral, J. Lobo, and J. Minker. Generalized disjunctive well-founded semantics for logic programs. Technical report, Dept of Computer Science, University of Maryland, College Park Md 20742, 1989. To appear in the Journal of Annals of Mathematics and Artifitial Intelligence.
• [BNNS93] C. Bell, A. Nerode, R. Ng, and V.S. Subrahmanian. Mixed integer programming methods for computing non-monotonic deductive databases. Journal of the ACM, 1993. To Appear. A preliminary version available as a University of Maryland TR Nr. CS-TR-2801, Dec 1991.
• [FLMS93] Jose Alberto Fernandez, Jorge Lobo, Jack Minker, and V.S. Subrahmanian. Disjunctive LP + integrity constraints = stable model seman- tics. Annals of Mathematics and Artificial Intelligence, 8(3-4):449-474, 1993.
• [FM93] Jose Alberto Fernandez and Jack Minker. Bottom-up computation of perfect models for disjunctive theories. The Journal of Logic Programming, 1993. Submitted. Preliminary version presented at the ILPS'91 Workshop on Disjunctive Logic Programs, San Diego, California.
• [GL88] M. Gelfond and V. Lifschitz. The Stable Model Semantics for Logic Programming. In R.A. Kowalski and K.A. Bowen, editors, Proc. 5th International Conference and Symposium on Logic Programming, pages 1070-1080, Seattle, Washington, August 15-19 1988.
• [GL90] M. Gelfond and V. Lifschitz. Classical negation in logic programs and disjunctive databases. 1990. (submitted for publication).
• [GLPT91] M. Gelfond, V. Lifschitz, H. Przymusinska, and M. Truszczynski. Disjunctive defaults. In J. Allen, R. Fikes, and E. Sandewall, editors, Principles of Knowledge Representation and Reasoning: Proceedings of the Second International Conference, pages 230-237, Sa Mateo, California, April 22-25 1991. Morgan Kaufman.
• [GPP89] M. Gelfond, H. Przymusinska, and T.C. Przymusinski. On the Relationship between Circumscription and Negation as Failure. Artificial Intelligence, 38:75-94, 1989.
• [IKH92] Katsumi Inoue, Miyuki Koshimura, and Ryuzo Hasegawa. Embedding negation as failure into a model generation theorem prover. In Proceedings of the Eleventh International Conference on Automated Deduction, Saratoga Springs, NY, 1992.
• [Kow78] R.A. Kowalski. Logic for data description. In H. Gallaire J. Minker, editor, Logic and Data Bases, pages 77-102. Plenum Press, New York, 1978.
• [KS90] Robert A. Kowalski and Fariba Sadri. Logic programs with exceptions. In Warren and Szeredi, editors, Proceedings of the 7th International Logic Programming Conference, pages 598-613, Jerusalem, 1990. MIT Press.
• [Lif85] V. Lifschitz. Computing circumscription. In IJCAI 85, pages 121-127, 1985.
• [LMR92] J. Lobo, J. Minker, and A. Rajasekar. Fundations of Disjunctive Logic Programming. MIT Press, 1992.
• [Mar89] W. Marek. Stable theories in autoepistemic logic. Fundamenta Informaticae, 12:243-254, 1989.
• [McC80] J. McCarthy. Circumscription - a form of non-monotonic reasoning. Artificial Intelligence, 13(1 and 2):27-39, 1980.
• [McC86] J. McCarthy. Applications of circumscription to formalizing commonsense knowledge. Artificial Intelligence 28, pages 89-116, 1986.
• [Min82] J. Minker. On indefinite databases and the closed world assumption. In Lecture Notes in Computer Science 138, pages 292-308. SpringerVerlag, 1982.
• [MLR91] J. Minker, J.Lobo, and A. Rajasekar. Circumscription and disjunctive logic programming. In V. Lifschitz, editor, Artificial Intelligence and Mathematical Theory of Computation, pages 281-304. Academic Press, 1991.
• [Moo85] R.C. Moore. Semantical considerations on non-monotonic logic. Artificial Intelligence 25, pages 75-94, 1985.
• [MS91] W. Marek and V.S. Subrahmanian. The relationship between stable, supported, default and auto-epistemic semantics for general logic programs. Theoretical Computer Science, 1991. (accepted for publication), (Preliminary version in: Proc. 6th Intl. Conf. on Logic Programming).
• [MT89] W. Marek and M. Truszczynski. Stable semantics for logic programs and default theories. 1989.
• [MZ82] J. Minker and G. Zanon. An Extension to Linear Resolution with Selection Function. Information Processing Letters, 14(3):191-194, June 1982.
• [Prz88a] T. C. Przymusinski. On the declarative semantics of deductive databases and logic programming. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, chapter 5, pages 193-216. Morgan Kaufmann Pub., Washington, D.C., 1988.
• [Prz88b] T.C. Przymusinski. Perfect Model Semantics. In R.A. Kowalski and K.A. Bowen, editors, Proc. 5th International Conference and Symposium on Logic Programming, pages 1081-1096, Seattle, Washington, August 15-19 1988.
• [Prz90] T. Przymusinski. Stationary semantics for disjunctive logic programs and deductive databases. In S. Debray and M. Hermenegildo, editors, Proc. of the North American Conference on Logic Programming, pages 40-62, Austin, Texas, October 1990.
• [Rei80a] R. Reiter. Equality and domain closure in first order data bases. Journal of the ACM, 27(2):235-249, 1980.
• [Rei80b] R. Reiter. A Logic for Default Reasoning. Artificial Intelligence, 13(1 and 2):81-132, April 1980.
• [YH85] A. Yahya and L.J. Henschen. Deduction in Non-Horn Databases. J. Automated Reasoning, 1(2):141-160, 1985.