Journal of Automated Reasoning

, Volume 5, Issue 3, pp 293–307 | Cite as

Weak Generalized Closed World Assumption

  • Arcot Rajasekar
  • Jorge Lobo
  • Jack Minker
Article

Abstract

Explicit representation of negative information in logic programs is not feasible in many applications such as deductive databases and artificial intelligence. Defining default rules which allow implicit inference of negated facts from positive information encoded in a logic program has been an attractive alternative to the explicit representation approach. There is, however, a difficulty associated with implicit default rules. Default rules such as the CWA and the GCWA, which closely model logical negation, are in general computationally intractable. This has led to the development of weaker definitions of negation such as the Negation-As-Failure (NF) and the Support-For-Negation (SN) rules which are computationally simpler. These are sound implementations of the CWA and the GCWA, respectively. In this paper, we define an alternative rule of negation based upon the fixpoint definition of the GCWA. This rule, called the Weak Generalized Closed World Assumption (WGCWA), is a weaker definition of the GCWA that allows us to implement a sound negation rule, called the Negation-As-Finite-Failure (NAFF), similar to the NF-rule and less cumbersome than the SN-rule. We present three definitions of the NAFF. Two declarative definitions similar to those for the NF-rule and one procedural definition based on SLI-resolution.

Key words

Explicit representation default rules Weak Generalized Closed World Assumption 

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References

  1. 1.
    K. R. Apt, ‘Introduction to Logic Programming’. In J. van Leeuwen (ed.) Handbook of Theoretical Computer Science, North Holland. To appear.Google Scholar
  2. 2.
    K. R. Apt and M. H.van Emden, ‘Contributions to the Theory of Logic Programming’, J. ACM 29, 841–862 (1982).Google Scholar
  3. 3.
    K. L. Clark, ‘Negation as Failure’, In H. Gallaire and J. Minker (eds) Logic and Data Bases, pp. 293–322. Plenum Press, New York, 1978.Google Scholar
  4. 4.
    H. Gallaire and J. Minker (eds) Logic and Databases. Plenum Press, New York, 1978.Google Scholar
  5. 5.
    R. A. Kowalski and D. Kuehner, ‘Linear Resolution with Selection Function’, Artificial Intelligence, 2 227–260 (1971).Google Scholar
  6. 6.
    J. W. Lloyd, Foundations of Logic Programming. Springer-Verlag, 1984.Google Scholar
  7. 7.
    J.-L. Lassez and M. J. Maher, ‘Closure and Fairness in the Semantics of Programming Logic’, Theoretical Computer Sci. 29, 167–184 (1984).Google Scholar
  8. 8.
    J. Minker, ‘On Indefinite Databases and the Closed World Assumption’, In Lecture Notes in Computer Science 138, pp. 292–308, Springer-Verlag, 1982.Google Scholar
  9. 9.
    J. Minker and A. Rajasekar, ‘A Fixpoint Semantics for Disjunctive Logic Programs’, To appear in Journal of Logic Programming.Google Scholar
  10. 10.
    J. Minker and A. Rajasekar, ‘Procedural Interpretation of Non-Horn Logic Programs’, In E. Lusk and R. Overbeek (eds), Proc. 9th International Conference on Automated Deduction, pp. 278–293, Argonne, IL, May 23–26, 1988.Google Scholar
  11. 11.
    J. Minker and G. Zanon, ‘An Extension to Linear Resolution with Selection Function’, Information Processing Letters 14, 191–194 (June 1982).Google Scholar
  12. 12.
    R. Reiter, ‘On Closed World Data Bases’. In H. Gallaire and J. Minker (eds), Logic and Data Bases, pp. 55–76, Plenum Press, New York, 1978.Google Scholar
  13. 13.
    K. A. Ross and R. W. Topor, Inferring Negative Information from Disjunctive Databases, Journal of Automated Reasoning 4, 397–424 (1988).Google Scholar
  14. 14.
    J. C. Shepherdson, ‘Negation in Logic Programming’. In J. Minker (ed.) Foundations of Deductive Databases and Logic Programming. pp. 19–88, Morgan Kaufman Pub., 1988.Google Scholar
  15. 15.
    M. H.van Emden and R. A. Kowalski, ‘The Semantics of Predicate Logic as a Programming Language’, J. ACM 23, 733–742 (1976).Google Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Arcot Rajasekar
    • 1
  • Jorge Lobo
    • 1
  • Jack Minker
    • 2
    • 3
  1. 1.Department of Computer ScienceUniversity of MarylandCollege ParkUSA
  2. 2.Department of Computer ScienceUniversity of MarylandCollege ParkUSA
  3. 3.Institute for Advanced Computer StudiesUniversity of MarylandCollege ParkUSA

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