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WFS + Branch and Bound = Stable Models
June 1995 (vol. 7 no. 3)
pp. 362-377

Abstract—Though the semantics of nonmonotonic logic programming has been studied extensively, relatively little work has been done on operational aspects of these semantics. In this paper, we develop techniques to compute the well-founded model of a logic program. We describe a prototype implementation and show, based on experimental results, that our technique is more efficient than the standard alternating fixpoint computation. Subsequently, we develop techniques to compute the set of all stable models of a deductive database. These techniques first compute the well-founded semantics and then use an intelligent branch and bound strategy to compute the stable models. We report on our implementation, as well as on experiments that we have conducted on the efficiency of our approach.

[1] K. Apt, H.A. Blair, and A. Walker, "Towards a Theory of Declarative Knowledge," Foundations of Deductive Databases and Logic Programming, J. Minker, ed., pp. 89-148. Morgan Kaufmann, 1988.
[2] C. Baral and V.S. Subrahmanian,“Stable and extension class theory for logic programs and default logics,” J. Automated Reasoning, vol. 8, pp. 345-366, 1992.
[3] C. Baral and V.S. Subrahmanian,“Dualities between alternative semantics for logic programming and nonmonotonic reasoning,” J. Automated Reasoning, vol. 10, pp. 399-420, 1993.
[4] C. Bell,A. Nerode,R. Ng,, and V.S. Subrahmanian,“Implementing deductive databases by linear programming,” accepted for publication in ACM Trans. Database Systems.
[5] 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.
[6] W. Chen and D.S. Warren,“A practical approach to computing the well-founded semantics,” Proc. 1992 Int’l Conf. Logic Programming, Nov. 1992.
[7] M.C. Fitting,“A Kripke-Kleene semantics for logic programming,” J. Logic Programming, vol. 4, pp. 295-312, 1985.
[8] M. Gelfond and V. Lifschitz,“The stable model semantics for logic programming,” Proc. Fifth Int’l Conf. and Symp. on Logic Programming, R.A. Kowalski and K.A. Bowen, eds., pp. 1,070-1,080, 1988.
[9] G. Gottlob,S. Marcus,A. Nerode,, and V.S. Subrahmanian,“Non-ground stable and well-founded demantics,” manuscript in preparation, 1993.
[10] V. Kagan,A. Nerode,, and V.S. Subrahmanian,“Computing definite logic programs by partial instantiation,” Annals of Pure and Applied Logic, vol. 67, pp. 161-182, 1993.
[11] V. Kagan,A. Nerode,, and V.S. Subrahmanian,“Computing minimal models by partial instantiation,” 1993, accepted for publication in Theoretical Computer Science.
[12] D. Kemp,P.J. Stuckey,, and D. Srivastava,“Magic sets and bottom-up evaluation of well-founded models,” Proc. 1991 Int’l Logic Programming Symp., V. Saraswat and K. Ueda, eds., pp. 337-351, MIT Press, 1991.
[13] D.E. Knuth, The Art of Computer Programming, vol. 1,Addison Wesley, second ed. 1973.
[14] N. Leone and P. Rullo,“Safe computation of the well-founded semantics of DATALOG queries,” Information Systems, vol. 17, no. 1, 1992.
[15] N. Leone,M. Romeo,P. Rullo,, and D. Sacca,“Effective implementation of negation in database logic query languages,” LOGIDATA+: Deductive Databases with Complex Objects, LNCS vol. 701, pp. 159-175, Springer, 1993.
[16] J.W. Lloyd, Foundations of Logic Programming, Springer Series in Symbolic Computation, second ed. New York: Springer-Verlag, 1987.
[17] W. Marek and M. Truszczynski,“Stable semantics for logic programs and default theories,” Proc. 1989 North Am. Conf. Logic Programming, E. Lusk and R. Overbeek, eds., pp. 243-256, MIT Press, 1989.
[18] 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.
[19] V.S. Subrahmanian,D.S. Nau,, and C. Vago,“WFS + branch and bound = stable models,” Tech. Report CS-TR-2935, July 1992, Univ. of Maryland. Tech. report version of this paper.
[20] A. van Gelder, "The Alternating Fixpoint of Logic Programs with Negation," Proc. ACM Symp. Principles of Database Systems, pp. 1-10, 1989.
[21] A. van Gelder, K. Ross, and J. Schlipf, "Unfounded Sets and Well-founded Semantics for General Logic Programs," Proc. Symp. Principles of Database Systems, pp. 221-230, 1988.
[22] D.S. Warren,“Computing the well-founded semantics of logic programs,” SUNY Stonybrook Tech. Report TR 91-12, June 1991.

Index Terms:
Logic programming, deductive databases, nonmonotonic reasoning, negation by failure.
Citation:
V.s. Subrahmanian, Dana Nau, Carlo Vago, "WFS + Branch and Bound = Stable Models," IEEE Transactions on Knowledge and Data Engineering, vol. 7, no. 3, pp. 362-377, June 1995, doi:10.1109/69.390244
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