Abstract
Turi [20] introduced the important notion of a constrained atom: an atom with associated equality and disequality constraints on its arguments. A set of constrained atoms is a constrained interpretation. We show how non-ground representations of both the stable model and the well-founded semantics may be obtained through Turi's approach. As a practical consequence, the well-founded model (or the set of stable models) may be partially pre-computed at compile-time, resulting in the association of each predicate symbol in the program to a constrained atom. Algorithms to create such models are presented. Query processing reduces to checking whether each atom in the query is true in a stable model (resp. well-founded model). This amounts to showing the atom is an instance of one of some constrained atom whose associated constraint is solvable. Various related complexity results are explored, and the impacts of these results are discussed from the point of view of implementing systems that incorporate the stable and well-founded semantics.
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C. Baral and V.S. Subrahmanian. Dualities Between Alternative Semantics for Logic Programming and Non-Monotonic Reasoning, J. Automated Reasoning, 10:399–420, 1993.
C. Bell, A. Nerode, R. Ng and V.S. Subrahmanian. (1994) Computation and Implementation of Non-Monotonic Deductive Databases, JACM, 41(6):1178–1215, 1994.
H. Comon, P. Lescanne. Equational Problems and Disunification, J. Symbolic Computation, 7:371–425, 1989.
J. Dix and M. Müller. Implementing Semantics of Disjunctive Logic Programs Using Fringes and Abstract Properties, Proc. LPNMR '93, (eds. L.-M. Pereira and A. Nerode), pp 43–59, 1993.
J. Dix and F. Stolzenburg. Computation of Non-Ground Disjunctive Well-Founded Semantics with Constraint Logic Programming. In J. Dix, L. M. Pereira, and T. C. Przymusinski, eds, Proc. WS Non-Monotonic Extensions of Logic Programming (at JICSLP '96), pp 143–160, 1996. CS-Report 17/96, Univ. Koblenz.
M.C. Fitting. A Kripke-Kleene Semantics for Logic Programming, J. Logic Programming, 4:295–312, 1985.
M. Gabbrielli, G. Levi. Modeling Answer Constraints in Constraint Logic Programs, Proc. ICLP, 1991, pp.238–251.
D. Johnson, A Catalogue of Complexity Classes. In: Handbook of TCS, 1990.
M. Gelfond and V. Lifschitz. The Stable Model Semantics for Logic Programming, in: Proc. 5th JICSLP, pp 1070–1080, 1998.
M. Gelfond and V. Lifschitz. Classical Negation in Logic Programs and Disjunctive Databases, New Generation Computing, 9:365–385, 1991.
G. Gottlob, S. Marcus, A. Nerode, G. Salzer, and V.S. Subrahmanian. A Non-Ground Realization of the Stable and Well-Founded Semantics, Theoretical Computer Science, 166:221–262, 1996.
V. Kagan, A. Nerode, and V. Subrahmanian. Computing Minimal Models by Partial Instantiation. Theoretical Computer Science, 155:15–177, 1996.
J.W. Lloyd. Foundations of Logic Programming, Springer Verlag, 1987.
M. Maher. Complete Axiomatization of the algebra of finite, rational and infinite trees, in Proc. 3rd IEEE LICS, 1988.
W. Marek, A. Nerode, J. Remmel. On Logical Constraints in Logic Programming, Proc. LPNMR '95 (eds. W. Marek, A. Nerode, and M. Truszczyński), LNCS 928, pp 44–56, 1995.
N. McCain and H. Turner. Language Independence and Language Tolerance in Logic Programs, Proc. ICLP, 1994.
T. Sato and F. Motoyoshi. A Complete Top-down Interpreter for First Order Programs, Proc. ILPS '91, pp 37–53. MIT Press, 1991.
P. Stuckey. Constructive Negation for Constraint Logic Programming, Proc. LICS'91, pp 328–339. IEEE Computer Science Press, 1991.
V.S. Subrahmanian, D. Nau and C. Vago. WFS+Branch and Bound=Stable Models, IEEE TDKE, 7(3):362–377, 1995.
D. Turi. Extending S-Models to Logic Programs with Negation, Proc. ICLP '91, pp 397–411, 1991.
A. van Gelder, K. Ross and J. Schlipf. Well-founded Semantics for General Logic Programs, JACM, 38(3):620–650, 1991.
A. van Gelder. The Alternating Fixpoint of Logic Programs with Negation, Proc. 8th ACM Symp. on Principles of Database Systems, pp 1–10.
M. Vardi. The On the Complexity of Bounded-Variable Queries, Proc. 14th ACM Symp. on Theory of Computing, San Francisco, pp. 137–146, 1982.
S. Vorobyov. An Improved Lower Bound for the Elementary Theories of Trees. In J. K. S. M. A. McRobbie, ed, Proc. 13th Conference on Automated Deduction (CADE '96), LNCS 1104, pp. 275–287, 1996.
S. Vorobyov. Existential Theory of Term Algebras is in Quasi-Linear Non-Deterministic Time. Manuscript, February 1997.
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Eiter, T., Lu, J., Subrahmanian, V.S. (1997). Computing non-ground representations of stable models. In: Dix, J., Furbach, U., Nerode, A. (eds) Logic Programming And Nonmonotonic Reasoning. LPNMR 1997. Lecture Notes in Computer Science, vol 1265. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63255-7_14
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DOI: https://doi.org/10.1007/3-540-63255-7_14
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