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On the completeness of SLDENFresolution
 Michael Thielscher
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SLDENFresolution combines the negationasfailure principle for logic programs involving negation, and SLDEresolution for logic programs with an underlying equational theory. Recently, J. Shepherdson proved the soundness of this resolution principle wrt. an extended completion semantics. In this note, we investigate the particular problems of obtaining completeness which are caused by adding equational theories. As a concrete result we show to what extent the classical result for hierarchical and allowed nonequational programs can be generalized.
 Apt, K. R., Blair, H. A., and Walker, A.: Towards a theory of declarative knowledge, in J. Minker (ed.), Foundations of Deductive Databases an Logic Programming, Chapter 2, Morgan Kaufmann Publishers Inc., 1987, pp. 89–148.
 Apt, K. R., Bol, R. (1994) Logic programming and negation: a survey. J. Logic Programming 19/20: pp. 971
 Baader, F. and Siekmann, J. H.: Unification theory, in D. M. Gabbay, C. J. Hogger, and J. A. Robinson (eds), Handbook of Logic in Artificial Intelligence and Logic Programming, Oxford University Press, 1993.
 Clark, K. L. Negation as failure. In: Gallaire, H., Minker, J. eds. (1978) Logic and Data Bases. Plenum, New York, pp. 293322
 Gallier, J. H., Raatz, S. (1989) Extending SLDresolution to equational horn clauses using Eunification. J. Logic Programming 6: pp. 344
 Hölldobler, S.: Foundations of Equational Logic Programming, LNAI 353, Springer, 1989.
 Hölldobler, S., Thielscher, M. (1995) Computing change and specificity with equational logic programs. Ann. Mathematics and Artificial Intelligence 14: pp. 99133
 Jaffar, J., Lassez, J.L., and Lloyd, J.: Completeness of the negation as failure rule, in A. Bundy (ed.), Proc. Int. Joint Conf. on Artificial Intelligence (IJCAI), Karlsruhe, Germany, 1983, pp. 500–506.
 Jaffar, J., Lassez, J.L., Maher, M. J. (1984) A theory of complete logic programs with equality. J. Logic Programming 1: pp. 211223
 Jaffar, J., Maher, M. J. (1994) Constraint logic programming: a survey. J. Logic Programming 19/20: pp. 503581
 Kunen, K. (1989) Signed data dependencies in logic programs. J. Logic Programming 7: pp. 231246
 Lloyd, J. W.: Foundations of Logic Programming, Series Symbolic Computation, 2nd extended edition, Springer, 1987.
 Plotkin, G. (1972) Building in equational theories. Machine Intelligence 7: pp. 7390
 Robinson, J. A.: A review of automatic theorem proving, in Annual Symposium in Applied Mathematics, American Mathematical Society, 1967, pp. 1–18.
 Sato, T. (1990) Completed logic programs and their consistency. J. Logic Programming 9: pp. 3344
 Shepherdson, J. C. (1984) Negation as failure: a comparison of Clark's completed data base and Reiter's closed world assumption. J. Logic Programming 1: pp. 5179
 Shepherdson, J. C. (1985) Negation as failure II. J. Logic Programming 3: pp. 185202
 Shepherdson, J. C.: Negation in logic programming for general logic programs, in J. Minker (ed.), Foundations of Deductive Databases and Logic Programming, Chapter 1, Morgan Kaufmann Publishers Inc., 1987, pp. 19–88.
 Shepherdson, J. C. (1991) Correct answers to allowed programs and queries are ground. J. Logic Programming 11: pp. 359362
 Shepherdson, J. C. (1992) SLDNFresolution with equality. J. Automated Reasoning 8: pp. 297306
 Siekmann, J. H.: Unification of commutative terms, in Proc. Int. Symp. on Symbolic and Algebraic Manipulation (EUROSAM), Marseille, France, June 1979, Springer LNCS 72, pp. 531–545.
 Siekmann, J. H. (1989) Unification theory. J. Symbolic Computation 7: pp. 207274
 Stroetmann, K. (1993) A completeness result for SLDNFresolution. J. Logic Programming 15: pp. 337355
 Title
 On the completeness of SLDENFresolution
 Journal

Journal of Automated Reasoning
Volume 17, Issue 2 , pp 199214
 Cover Date
 19961001
 DOI
 10.1007/BF00244496
 Print ISSN
 01687433
 Online ISSN
 15730670
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 logic programming
 negation as failure
 unification theory
 Industry Sectors
 Authors

 Michael Thielscher ^{(1)}
 Author Affiliations

 1. TH Darmstadt, FG Intellektik, Alexanderstraße 10, D64283, Darmstadt, Germany