Abstract
A standard approach to negation in logic programming is negation as failure. Its major drawback is that it cannot produce answer substitutions to negated queries. Approaches to overcoming this limitation are termed constructive negation. This work proposes an approach based on construction offailed trees for some instances of a negated query. For this purpose a generalization of the standard notion of a failed tree is needed. We show that a straightforward generalization leads to unsoundness and present a correct one.
The method is applicable to arbitrary normal programs. If finitely failed trees are concerned then its semantics is given by Clark completion in 3-valued logic (and our approach is a proper extension of SLDNF-resolution). If infinite failed trees are allowed then we obtain a method for the well-founded semantics. In both cases soundness and completeness are proved.
Similar content being viewed by others
References
Apt, K., Bol, R.: Logic programming and negation: a survey. Technical Report CS-R9402, CWI Amsterdam, 1994. To appear in Journal of Logic Programming
Apt, K.: Logic Programming. In: Leeuwen, J. van (ed.) Handbook of theoretical computer science, vol. B, chapter 10, pp. 493–574. Elsevier Science Publishers B. V. Amsterdam: 1990
Bol, R., Degerstedt, L.: Tabulated resolution for well founded semantics. In: Miller, D. (ed.) Logic programming—Proceedings of the 1993 International Symposium, pp. 199–219. The MIT Press, 1993
Barbuti, R., Mancarella, D., Pedreschi, D., Turini, F.: A transformational approach to negation in logic programming J. of Logic Programming 8(3), 201–228 (1990)
Bonnier, S., Nilsson, U., Näslund, T.: A simple fixed point characterization of three-valued stable model semantics. Information Processing Letters 40, 73–78 (1991)
Cavedon, L.: On completeness of SLDNF resolution. Master's thesis, Dept. of Computer Science, University of Melbourne, 1988. Technical Report 88/17
Chan, D.: Constructive negation based on the completed database. In: Kowalski R.A., Bowen, K.A. (eds.) Proc. Fifth International Conference and Symposium on Logic Programming, Seattle, pp. 111–125. MIT Press, 1988
Chan, D.: An extension of constructive negation and its application in coroutining. In: Lusk, E.L., Overbeek, R.A. (eds.) Proc. North American Conference on Logic Programming, Cleveland, pp. 477–493. MIT Press, 1989
Chomicki, J., Imieliński, T.: Finite representation of infinite query answers. ACM Transactions on Database Systems18 (2), 181–223 (1993)
Comon, H., Lescanne, P.: Equational problems and disunification. J. Symbolic Computation 7, 371–425 (1989)
Drabent, W., Martelli, M.: Strict completion of logic programs. New Generation Computing 9, 69–79 (1991)
Drabent, W.: On completeness of SLDNF-resolution. Submitted. Modified version of Technical Report LiTH-IDA-R-93-38, Linköping University, 1993
Drabent, W.: SLS-resolution without floundering. In: Pereira, L.M., Norode, A. (eds.) Proc. 2nd International Workshop on Logic Programming and Non-Monotonic Reasoning, pp. 82–98. MIT Press, June 1993
Ferrand, G., Deransart, P.: Proof method of partial correctness and weak completeness for normal logic programs. J. Logic Programming17, 265–278 (1993)
Fitting, M.: A Kripke-Kleene semantics for logic programs. J. of Logic Programming 2(4), 295–312 (1985)
Gelder, A. van, Ross, K., Schlipf, J.: The well-founded semantics for general logic programs. J ACM 38, 620–650 (1991)
Khabaza, T.: Negation as failure and parallelism. In: Proc. IEEE Conf. on Logic Programming, pp. 70–75. IEEE Press, 1984
Kunen, K.: Negation in logic programming. J. Logic Programming 4 289–308 (1987)
Kunen, K.: Signed data dependencies in logic programs. J. of Logic Programming 7(3), 231–245 (1989)
Lloyd, J.W.: Foundations of Logic Programming. Springer-Verlag, 2nd, extended edn., 1987
Lugiez, D.: A deduction procedure for first order programs. In: Levi, G., Martelli, M. (eds.) Proc. of Sixth International Conf. on Logic Programming, Lisbon, pp. 585–599. MIT Press, 1989
Maher, M.: Complete axiomatization of the algebras of finite, rational and infinite trees. In: Proc. 3rd Symposium on Logic in Computer Science, pp. 348–357 (1988)
Mancarella, P., Martini, S., Pedreschi, D.: Complete logic programs with domain closure axiom. J. of Logic Programming 5(3), 263–276 (1988)
Maluszyński, J., Näslund, T., Fail substitutions for negation as failure. In: Lusk, E.L., Overbeck, R.A. (eds.) Proc. North American Conference on Logic Programming, Cleveland, pp. 461–476. MIT Press, 1989
Näslund, T.: Sldfa-resolution. Licentiate thesis. Department of Computer and Information Science, Linköping University, 1990
Plaza, J.A.: Fully declarative logic programming. In: Programming Language Implementation and Logic Programming, Proceedings 1992, pp. 415–427. Springer, 1992 (LNCS, vol. 631)
Przymusinski, T.C.: On constructive negation in logic programming. In: Proc. North American Conference on Logic Programming, Addendum. MIT Press, 1989
Przymusinski, T.C.: On the declarative and procedural semantics of logic programs. Journal of Automated Reasoning 5, 167–205 (1989)
Przymusinski, T.C.: The well-founded semantics coincides with the three-valued stable semantics. Fundamenta Informaticae XIII(4), 445–463 (1990)
Przymusinski, T.C.: Well-founded completions of logic programs. In: Furukawa, K. (ed.) Proceedings of the Eighth International Conference on Logic Programming. Paris, pp. 726–741. MIT Press, 1991
Shepherdson, J.C.: A sound and complete semantics for a version of negation as failure. Theoretical Computer Science 65, 343–371 (1989)
Shepherdson, J.C.: Language and equality theory in logic programming. Technical Report PM-91-02, School of Mathematics, University of Bristol, 1991. Newer version of PM-88-08
Seki, H., Itoh, H.: A query evaluation method for stratified programs under the extended CWA. In: Kowalski, R.A., Bowen K.A. (eds.) Proc. of the Fifth International Conference and Symposium on Logic Programming, pp. 195–211. MIT Press, 1988
Sato, T., Motoyoshi, F.: A complete top-down interpreter for first order logic programs. In: Logic Programming, Proc. of the 1991 International Symposium, pp. 35–53. MIT Press, 1991
Sato, T., Tamaki, H.: Transformational logic program synthesis. In: Proceedings of the International Conference on Fifth Generation Computer Systems, pp. 195–201, 1984
Sato, T., Tamaki, H.: OLD-resolution with tabulation. In: Shapiro, E. (ed.) Proceedings of the third International Conference on Logic Programming, pp. 84–98. Springer, 1986. LNCS 225
Stuckey, P.: Constructive negation for constraint logic programming. In: 6th Annual IEEE Symposium on Logic in Computer Science (LICS'91), July 1991
Teusink, F.: Using SLDFA-resolution with abductive logic programs. In: ILPS'93 post-conference workshop “Logic Programming with Incomplete Information”, 1993
Wallace, M.: Negation by constraints: A sound and efficient implementation of negation in deductive databases. In: Proc. 1987 Symposium on Logic Programming, San Francisco, pp. 253–263. IEEE Computer Society Press, 1987
Wallace, M.: Tight, consistent and computable completions for unrestricted logic programs. J. of Logic Programming 15(3), 243–274 (1993)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Drabent, W. What is failure? An approach to constructive negation. Acta Informatica 32, 27–59 (1995). https://doi.org/10.1007/BF01185404
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01185404