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Abstract

We present a formal framework for ordered default reasoning which has desirable mathematical properties yet is relatively simple and can be implemented using standard theorem provers. By expressing default logic as a relation from theories to extensions we are able to formalise Brewka's prioritized default logic as a composite relation. We also decompose the extension relation by factoring out deductive closure. The resulting augmentations can be computed for decidable cases, and provide an extension membership test for composite extensions. Finally we define the equivalent formalism in autoepistemic logic.

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References

  1. [1]
    Brewka, G. Preferred Subtheories: An Extended Logical Framework for Default Reasoning. In Proc. IJCAI-89, pp. 1043–1048, Detroit, USA, 1989.Google Scholar
  2. [2]
    Etherington, D. W. Formalizing Nonmonotonic Reasoning Systems. Artificial Intelligence, 31 pp. 41–85, 1987.Google Scholar
  3. [3]
    Hanks, S. and McDermott, D. Default Reasoning, Nonmonotonic Logics, and the Frame Problem. In Proc. AAAI-86, pp. 328–333, Philadelphia, USA, 1986.Google Scholar
  4. [4]
    Konolige, K. Hierarchic Autoepistemic Theories for Nonmonotonic Reasoning. In Proc. AAAI-88, pp. 439–443, Saint Paul, USA, 1988.Google Scholar
  5. [5]
    Konolige, K. On the Relation Between Default Theories and Autoepistemic Logic. Artificial Intelligence, 35 pp. 343–382, 1988.Google Scholar
  6. [6]
    MacNish, C. PhD thesis, Department of Engineering, Cambridge, UK, 1991. In preparation.Google Scholar
  7. [7]
    MacNish, C. Hierarchical Default Logic (Extended Version). Technical Report CUED/F-INFENG/TR.52, Cambridge University Engineering Department, 1991.Google Scholar
  8. [8]
    MacNish, C. Well-behaved Reasoning with Seminormal Defaults. In Proc. 4th International Symposium on AI, CancÚn, Mexico, November 1991. To appear.Google Scholar
  9. [9]
    McCarthy, J. Applications of Circumscription to Formalising Common-Sense Knowledge. Artificial Intelligence, 28 pp. 89–116, 1986.Google Scholar
  10. [10]
    Poole, D. L. On the Comparison of Theories: Preferring the Most Specific Explanation. In Proc. IJCAI-85, pp. 144–147, Los Angeles, CA, 1985.Google Scholar
  11. [11]
    Reiter, R. A Logic for Default Reasoning. Artificial Intelligence, 13 pp. 81–132, 1980.Google Scholar
  12. [12]
    Shoham, Y. Chronological Ignorance: Experiments in Nonmonotonic Temporal Reasoning. Artificial Intelligence, 36 pp. 279–331, 1988.Google Scholar
  13. [13]
    Touretzky, D. S., Horty, J. F. and Thomason, R. H. A Clash of Intuitions: The Current State of Nonmonotonic Multiple Inheritance Systems. In Proc. IJCAI-87, pp. 476–482, Milan, Italy, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Craig MacNish
    • 1
  1. 1.Department of EngineeringUniversity of CambridgeCambridgeUK

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