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Computation of Stable Models and Its Integration with Logical Query Processing
October 1996 (vol. 8 no. 5)
pp. 742-757

Abstract—The well-founded semantics and the stable model semantics capture intuitions of the skeptical and credulous semantics in nonmonotonic reasoning, respectively. They represent the two dominant proposals for the declarative semantics of deductive databases and logic programs. However, neither semantics seems to be suitable for all applications. We have developed an efficient implementation of goal-oriented effective query evaluation under the well-founded semantics. It produces a residual program for subgoals that are relevant to a query, which contains facts for true instances and clauses with body literals for undefined instances. This paper presents a simple method of stable model computation that can be applied to the residual program of a query to derive answers with respect to stable models. The method incorporates both forward and backward chaining to propagate the assumed truth values of ground atoms, and derives multiple stable models through backtracking. Users are able to request that only stable models satisfying certain conditions be computed. A prototype has been developed that provides integrated query evaluation under the well-founded semantics, the stable models, and ordinary Prolog execution. We describe the user interface of the prototype and present some experimental results.

[1] K.R. Apt and M.H. van Emden, "Contributions to the Theory of Logic Programming," J. ACM, vol. 29, no. 3, pp. 841-862, July 1982.
[2] C. Bell, A. Nerode, R.T. Ng, and V.S. Subrahmanian, "Implementing Stable Semantics by Linear Programming," Proc. Second Int'l Workshop Logic Programming and Nonmonotonic Reasoning, pp. 23-42, 1993.
[3] C. Bell, A. Nerode, R.T. Ng, and V.S. Subrahmanian, "Mixed Integer Programming Methods for Computing Nonmonotonic Deductive Databases," J. ACM, vol. 41, no. 6, pp. 1,178-1,215, 1994.
[4] N. Bidoit and P. Legay, "Well!: An Evaluation Procedure for all Logic Programs," Proc. Intl. Conf. Database Theory, pp. 335-348, 1990.
[5] R. Bol and L. Degerstedt, "Tabulated Resolution for Well Founded Semantics, Intl. Logic Programming Symp, Oct. 1993.
[6] W. Chen, "Constructive Negation of General Logic Programs," Aug. 1993.
[7] W. Chen, "Query Evaluation of Alternating Fixpoint Logic," ACM Trans. Database Systems, vol. 20, no. 3, pp. 239-287, 1995.
[8] W. Chen and D.S. Warren, "A Goal-Oriented Approach to Computing Well Founded Semantics," J. Logic Programming, vol. 17, 1993.
[9] W. Chen and D.S. Warren, "Query Evaluation Under the Well Founded Semantics," The 12th ACM Symp Principles of Database Systems, 1993.
[10] W. Chen and D.S. Warren, "Towards Effective Evaluation of General Logic Programs," Technical Report 93-CSE-11, Dept. of Computer Science and Engineering, Southern Methodist Univ., 1993.
[11] W. Chen and D.S. Warren, The SLG System, Aug., 1993, available by anonymous FTP from seas.smu.edu or cs.sunysb.edu.
[12] J. Dix, "Semantics of Logic Programs: Their Intuitions and Formal Properties, An Overview," FTPable from ftp.ms.uky.edu as /pub/lpnmr/overview.ps, Feb. 1994.
[13] P.M. Dung, "Negation as Hypotheses: An Abductive Foundation for Logic Programming," Intl. Conf. Logic Programming, June 1991.
[14] K. Eshghi, "Computing Stable Models by Using the ATMS", Nat'l Conf. Artificial Intelligence, pp. 272-277, 1990.
[15] K. Eshghi and R.A. Kowalski, "Abduction Compared with Negation by Failure," Intl. Conf. Logic Programming, pp. 235-254, 1989.
[16] M. Gelfond, "On Stratified Autoepistemic Theories," Nat'l Conf. Artificial Intelligence, pp. 207-211, 1987.
[17] M. Gelfond and V. Lifschitz, "The Stable Model Semantics for Logic Programming," R.A. Kowalski and K.A. Bowen, eds., Joint Intl. Conf. and Symp. Logic Programming, pp. 1,070-1,080, 1988.
[18] S. Greco, C. Zaniolo, and S. Ganguly, "Greedy by Choice," Proc. 11th ACM PODS Symp. Principles of Database Systems, pp. 105-113, 1992.
[19] K. Inoue and C. Sakama, "Transforming Abductive Logic Programs to disjunctive programs," Intl. Conf. Logic Programming, 1993.
[20] N. Leone, M. Romeo, P. Rullo, and D. Saccà, "Effective Implementation of Negation in Database Logic Query Languages," P. Atzeni, ed., LOGIDATA+: Deductive Databases with Complex Objects, Lecture Notes in Computer Science 701, pp. 159-175. Springer-Verlag, 1993.
[21] J.W. Lloyd, Foundations of Logic Programming, Springer Series in Symbolic Computation, second ed. New York: Springer-Verlag, 1987.
[22] W. Marek and M. Truszczynski, "Autoepistemic Logic," J. ACM, vol. 38, no. 3, pp. 588-619, 1991.
[23] S. Naqvi and S. Tsur, A Logical Language for Data and Knowledge Bases.New York: Computer Science Press, 1989.
[24] L.M. Pereira, J.N. Aparicio, and J.J. Alferes, "Derivation Procedures for Extended Stable Models," Intl. Joint Conf. Artificial Intelligence, pp. 863-868, 1991.
[25] S.G. Pimental and J.L. Cuadraro, "A Truth Maintenance System Based on Stable Models," North American Conf. Logic Programming, pp. 274-290, 1989.
[26] T.C. Przymusinski, "Every Logic Program has a Natural Stratification and an Iterated Least Fixed Point Model," ACM SIGACT-SIGMOD-SIGART Symp. Principles of Database Systems, pp. 11-21, 1989.
[27] T.C. Przymusinski, "The Well-Founded Semantics Coincides with the Three-Valued Stable Semantics," Fundamenta Informaticae, vol. 13, pp. 445-463, 1990.
[28] R. Ramakrishnan, D. Srivastava, and S. Sudarshan, "Controlling the Search in Bottom-Up Evaluation," Joint Intl. Conf. and Symp. Logic Programming, pp. 273-287, 1992.
[29] R. Ramesh and W. Chen, "A Portable Method of Integrating slg resolution into Prolog Systems," Intl. Logic Programming Symp, 1994.
[30] K.A. Ross, "A Procedural Semantics for Well-Founded Negation in Logic Programs," J. Logic Programming, vol. 13, no. 1, pp. 1-22, 1992.
[31] K.A. Ross, The Semantics of Deductive Databases, PhD thesis, Dept. of Computer Science, Stanford Univ., Aug. 1991.
[32] D. Saccà, "The Expressive Power of Stable Models for Datalog Queries with Negation," Proc. Workshop Structural Complexity and Recursion-Theoretic Methods in Logic Programming, pp. 150-162, Nov. 1993.
[33] D. Saccà and C. Zaniolo, "Stable Models and Non-determinism for Logic Programs with Negation," ACM SIGACT-SIGMOD-SIGART Symp. Principles of Database Systems, pp. 205-217, 1990.
[34] K. Sagonas, T. Swift, and D.S. Warren, "XSB as an Efficient Deductive Database Engine," 1994.
[35] K. Satoh and N. Iwayama, "A Query Evaluation Method for Abductive Logic Programming," Joint Intl. Conf. and Symp. Logic Programming, 1992.
[36] J.S. Schlipf, "The Expressive Powers of the Logic Programming Semantics (extended abstract)," ACM SIGACT-SIGMOD-SIGART Symp. Principles of Database Systems, pp. 196-204, 1990.
[37] J.S. Schlipf, "A Survey of Complexity and Undecidability Results in Logic Programming," Proc. Workshop Structural Complexity and Recursion-Theoretic Methods in Logic Programming, pp. 93-102, Nov. 1993.
[38] P. Stuckey and S. Sudarshan, "Well-Founded Ordered Ssearch," Proc. 13th Conf. Foundations of Software Technology and Theoretical Computer Science, 1993. LNCS 761.
[39] V.S. Subrahmanian, D. Nau, and C. Vago, "WFS + Branch and Bound = Stable Models," IEEE Trans. Knowledge and Data Eng., vol. 7, no. 3, pp. 362-377, 1994.
[40] A. Van Gelder, "The Alternating Fixpoint of Logic Programs with Negation," J. Computer and System Sciences, vol. 47, pp. 185-221, 1993.
[41] A. van Gelder,K. Ross, and J.S. Schlipf,"The well-founded semantics for general logic programs," J. ACM, vol. 38, no. 3, pp. 620-650, July 1991.
[42] A. Van Gelder and R.W. Topor, "Safety and Translation of Relational Calculus Queries," ACM Trans. Database Systems, vol. 16, no. 2, pp. 235-278, June 1991.

Index Terms:
Alternating fixpoint logic, deductive database, logic programming, nonmonotonic reasoning, logical query evaluation, stable model semantics, well-founded semantics.
Citation:
Weidong Chen, David Scott Warren, "Computation of Stable Models and Its Integration with Logical Query Processing," IEEE Transactions on Knowledge and Data Engineering, vol. 8, no. 5, pp. 742-757, Oct. 1996, doi:10.1109/69.542027
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