Computation of non-ground disjunctive well-founded semantics with constraint logic programming
Impressive work has been done in the last years concerning the meaning of negation and disjunction in logic programs, but most of this research concentrated on propositional programs only. While it suffices to consider the propositional case for investigating general properties and the overall behaviour of a semantics, we feel that for real applications and for computational purposes an implementation should be able to handle first-order programs without grounding them.
In this paper we present a theoretical framework by defining a calculus of program transformations that apply directly to rules with variables and function symbols. Our main results are that (1) this calculus is confluent for arbitrary programs, (2) for finite ground programs it is equivalent to a terminating calculus introduced by Brass and Dix (1995), and (3) it approximates a generalisation of D-WFS for arbitrary programs.
We achieve this by transforming program rules into rules with equational constraints thereby using heavily methods and techniques from constraint logic programming. In particular, disconnection-methods play a crucial role. In principle, any constraint theory known from the field of constraint logic programming can be exploited in the context of non-monotonic reasoning, not only equational constraints over the Herbrand domain. However, the respective constraint solver must be able to treat negative constraints of the considered constraint domain.
In summary, this work yields the basis for a general combination of two paradigms: constraint logic programming and non-monotonic reasoning.
Keywordsconstraint logic programming equational constraints dis-junctive logic programming well-founded semantics non-monotonic reasoning
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- [AD94]Chandrabose Aravindan and Phan Minh Dung. Partial deduction of logic programs wrt well-founded semantics. New Generation Computing, 13:45–74, 1994.Google Scholar
- [ADN97]Chandrabose Aravindan, Jürgen Dix, and Ilkka Niemelä. The DisLoP-project. Technical Report TR 1/97, University of Koblenz, Department of Computer Science, Rheinau 1, January 1997.Google Scholar
- [BD94]Stefan Brass and Jürgen Dix. A disjunctive semantics based on unfolding and bottom-up evaluation. In Bernd Wolfinger, editor, Innovationen bei Rechen-und Kommunikationssystemen, (IFIP '94-Congress, Workshop FG2: Disjunctive Logic Programming and Disjunctive Databases), pages 83–91, Berlin, 1994. Springer.Google Scholar
- [BD95a]Stefan Brass and Jürgen Dix. A General Approach to Bottom-Up Computation of Disjunctive Semantics. In J. Dix, L. Pereira, and T. Przymusinski, editors, Nonmonotonic Extensions of Logic Programming, LNAI 927, pages 127–155. Springer, Berlin, 1995.Google Scholar
- [BD95b]Stefan Brass and Jürgen Dix. Disjunctive Semantics based upon Partial and Bottom-Up Evaluation. In Leon Sterling, editor, Proceedings of the 12th Int. Conf. on Logic Programming, Tokyo, pages 199–213. MIT Press, June 1995.Google Scholar
- [BD96]Stefan Brass and Jürgen Dix. Characterizing D-WFS: Confluence and Iterated GCWA. In L.M. Pereira J.J. Alferes and E. Orlowska, editors, Logics in Artificial Intelligence (JELIA '96), LNCS 1126, pages 268–283. Springer, 1996. (Extended version will appear in the Journal of Automated Reasoning in 1997.).Google Scholar
- [BD97a]Stefan Brass and Jürgen Dix. Characterizations of the Disjunctive Stable Semantics by Partial Evaluation. Journal of Logic Programming, forthcoming, 1997. (Extended abstract appeared in: Characterizations of the Stable Semantics by Partial Evaluation LPNMR, Proceedings of the Third International Conference, Kentucky, pages 85–98, 1995. Springer.).Google Scholar
- [BD97b]Stefan Brass and Jürgen Dix. Semantics of Disjunctive Logic Programs Based on Partial Evaluation. Journal of Logic Programming, accepted for publication, 1997. (Extended abstract appeared in: Disjunctive Semantics Based upon Partial and Bottom-Up Evaluation, Proceedings of the 12-th International Logic Programming Conference, Tokyo, pages 199–213, 1995. MIT Press.).Google Scholar
- [CL89]Hubert Comon and Pierre Lescanne. Equational problems and disunification. Journal of Symbolic Computation, 7:371–425, 1989.Google Scholar
- [Col86]Alain Colmerauer. Theoretical model of Prolog II. In Michel van Canegham and David H.D. Warren, editors, Logic programming and its applications, pages 3–31. Ablex Publishing Corporation, Norwood, NJ, 1986.Google Scholar
- [CW95]Weidong Chen and David S. Warren. Computing of Stable Models and its Integration with Logical Query Processing. IEEE Transactions on Knowledge and Data Engineering, 17:279–300, 1995.Google Scholar
- [DF96]J. Dix and U. Furbach. The DFG-Project DisLoP on Disjunctive Logic Programming. Computational Logic, 2:89–90, 1996.Google Scholar
- [DLMW96]Jürgen Dix, Donald Loveland, Jack Minker, and David. S. Warren. Disjunctive Logic Programming and databases: Nonmonotonic Aspects. Technical Report Dagstuhl Seminar Report 150, IBFI GmbH, Schloß Dagstuhl, 1996.Google Scholar
- [ECR95]ECRC GmbH, München. ECLiPSe 3.5: User Manual — Extensions User Manual, 1995.Google Scholar
- [EGLS96]T. Eiter, G. Gottlob, J. Lu, and V. S. Subrahmanian. Computing Non-Ground Representations of Stable Models. Technical report, University of Maryland, 1996.Google Scholar
- [KSS91]David B. Kemp, Peter J. Stuckey, and Divesh Srivastava. Magic Sets and Bottom-Up Evaluation of Well-Founded Models. In Vijay Saraswat and Kazunori Ueda, editors, Proceedings of the 1991 Int. Symposium on Logic Programming, pages 337–351. MIT, June 1991.Google Scholar
- [Mah88]Michael J. Maher. Complete axiomatizations of the algebras of finite, rational and infinite trees. In Proceedings of the 3rd Annual Symposium on Logic in Computer Science, pages 348–359. Computer Society Press, 1988.Google Scholar
- [Mah93]Michael J. Maher. A logic programming view of CLP. In David S. Warren, editor, Proceedings of the 10th International Conference on Logic Programming, pages 737–753. MIT Press, Cambridge, MA, London, England, 1993. Budapest, 1993.Google Scholar
- [SS95]Chiaki Sakama and Hirohisa Seki. Partial Deduction of Disjunctive Logic Programs: A Declarative Approach. In Logic Program Synthesis and Transformation — Meta Programming in Logic, LNCS 883, pages 170–182, Berlin, 1995. Springer. Extended version to appear in Journal of Logic Programming.Google Scholar
- [ST96]Frieder Stolzenburg and Bernd Thomas. Analysing rule sets for the calculation of banking fees by a theorem prover with constraints. In Proceedings of the 2nd International Conference on Practical Application of Constraint Technology, pages 269–282, London, 1996. Practical Application Company.Google Scholar
- [Stu91]Peter J. Stuckey. Constructive negation for constraint logic programming. In Proceedings of the 6th Annual Symposium on Logic in Computer Science, pages 328–339, 1991.Google Scholar