Power defaults (preliminary report)

  • Guo-Qiang Zhang
  • William C. Rounds
Regular Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1265)


We present a spectrum of default logics, using powerdomains to encode default constraints. The resulting nonmonotonic entailment relations all satisfy the law of reasoning by cases. This result is a consequence of two general theorems valid for any Scott domain: the Dichotomy Theorem and the Extension Splitting Theorem. We briefly indicate that for propositional logic, the complexity of entailment is complete for co-NP(3).


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Aït-Kaci. A Lattice-Theoretic Approach to Computation based on a Calculus of Partially Ordered Type Structures. PhD thesis, University of Pennsylvania, 1984.Google Scholar
  2. 2.
    K. R. Apt and R. N. Bol, Logic programming and negation: a survey. Technical Report CS-R9402, CWI, Amsterdam, 1994.Google Scholar
  3. 3.
    P. Buneman. Functional programming and databases. In D. Turner, editor, Research Topics in Functional Programming, pages 155–169. Addison-Wesley, 1990.Google Scholar
  4. 4.
    M. Gelfond, V. Lifschitz, H. Przymuzińska, and M. Truszczyński. Disjunctive defaults. In Proceedings of Second Annual Conference on Knowledge Representation, pages 230–237. Morgan Kaufmann, 1991.Google Scholar
  5. 5.
    G. Gottlob. Complexity results for nonmonotonic logics. In Notes on Fourth Int. Workshop on Non-monotonic Reasoning, 1992.Google Scholar
  6. 6.
    S. Kraus, D. Lehmann, and M. Magidor. Nonmonotonic reasoning, preferential models, and cumulative logics. Artificial Intelligence, 44:167–207, 1990.Google Scholar
  7. 7.
    L. Libkin. Aspects of Partial Information in Databases. PhD thesis, University of Pennsylvania, 1994.Google Scholar
  8. 8.
    W. Marek, A. Nerode, and J. Remmel. A theory of nonmonotonic rule systems. In Proceedings of 5th IEEE Symposium on Logic in Computer Science, pages 79–94, 1990.Google Scholar
  9. 9.
    F. Pereira and S. Shieber. The semantics of grammar formalisms seen as computer languages. In Proceedings of 10th International Conference on Computational Linguistics: COLING 84, 1984.Google Scholar
  10. 10.
    C. Pollard and M. A. Moshier. Unifying partial descriptions of sets. In P. Hansen, editor, Vancouver Studies in Cognitive Science: vol. I. University of British Columbia Press, 1990.Google Scholar
  11. 11.
    Raymond Reiter. A logic for default reasoning. Artificial Intelligence, 13:81–132, 1980.CrossRefGoogle Scholar
  12. 12.
    W. Rounds and G. Q. Zhang. Logical considerations on default semantics. To appear, Annals of Mathematics and Artificial Intelligence, 1997.Google Scholar
  13. 13.
    W. Rounds and G. Q. Zhang. Suggestions for a nonmonotonic feature logic. Technical Report CS-R9551, CWI, Amsterdam, 1995.Google Scholar
  14. 14.
    W. Rounds and G. Q. Zhang. Complexity of power default reasoning. In Proceedings of LICS 97, July 1997.Google Scholar
  15. 15.
    M. B. Smyth. Powerdomains. Journal of Computer and System Science, 16(1):23–36, February 1978.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Guo-Qiang Zhang
    • 1
  • William C. Rounds
    • 2
  1. 1.Department of Computer ScienceUniversity of GeorgiaAthensUSA
  2. 2.Artificial Intelligence LaboratoryUniversity of MichiganAnn ArborUSA

Personalised recommendations