A scheme for weakened negative introspection in autoepistemic reasoning

  • Tomi Janhunen
  • Ilkka Niemelä
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 713)


A novel scheme for weakened negative introspection in autoepistemic reasoning is proposed. The scheme is formulated proof-theoretically in terms of enumerations of formulae. The resulting sets of conclusions, cautious expansions, are a generalization of Moore style stable expansions such that each set of premises has a cautious expansion. A finitary characterization is provided for the cautious expansions. Excluding weakly grounded expansions, i.e. considering only xxN-grounded cautious expansions, is shown to imply attractive properties not present in, e.g., Moore style autoepistemic logic. For every set of premises, the intersection of the xxN-grounded cautious expansions is a cautious expansion which is the unique least xxN-grounded cautious expansion under a natural partial order of expansions. The least xxN-grounded cautious expansion can be constructed as the least fixed point of a monotonic operator. Using the finitary characterization the decidability of decision problems related to cautious expansions is established and the decision problems are related to the polynomial time hierarchy. A comparison indicates that the new principle is stronger than other similar proposals and than that used in the well-founded semantics.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bonatti, P.: Autoepistemic logics as a unifying framework for the semantics of logic programs. In Proceedings of the 1992 Joint International Conference and Symposium on Logic Programming, Washington, D.C., USA, November 1992.Google Scholar
  2. 2.
    Elkan, C.: A rational reconstruction of nonmonotonic truth maintenance systems. Artificial Intelligence, 43:219–234, 1990.Google Scholar
  3. 3.
    Etherington, D.: Formalizing nonmonotonic reasoning systems. Artificial Intelligence, 31:41–85, 1987.Google Scholar
  4. 4.
    Gelfond, M. and Lifschitz, V.: The stable model semantics for logic programming. In Proceedings of the 5th International Conference on Logic Programming, pages 1070–1080, Seattle, USA, August 1988. The MIT Press.Google Scholar
  5. 5.
    Gottlob, G.: Complexity results for nonmonotonic logics. Journal of Logic and Computation, 2(3):397–425, June 1992.Google Scholar
  6. 6.
    Kalinski, J.: Autoepistemic expansions with incomplete belief introspection. In Proceedings of the 1st International Workshop on Nonmonotonic and Inductive Logic, pages 223–232, Karlsruhe, Germany, December 1990. Springer-Verlag. Lecture Notes in Artificial Intelligence 543.Google Scholar
  7. 7.
    Kalinski, J.: Weak autoepistemic reasoning. Presented at the European Workshop on Theoretical Foundations of Knowledge Representation and Reasoning held in conjunction with ECAI'92, August 3–4, Vienna, Austria, 1992.Google Scholar
  8. 8.
    Konolige, K.: On the relation between default and autoepistemic logic. Artificial Intelligence, 35:343–382, 1988.Google Scholar
  9. 9.
    Marek, W. and Truszczyński, M.: Relating autoepistemic and default logics. In Proceedings of the 1st International Conference on Principles of Knowledge Representation and Reasoning, pages 276–288, Toronto, Canada, May 1989.Google Scholar
  10. 10.
    Marek, W. and Truszczyński, M.: Modal logic for default reasoning. Annals of Mathematics and Artificial Intelligence, 1:275–302, 1990.Google Scholar
  11. 11.
    Moore, R.: Semantical considerations on nonmonotonic logic. Artificial Intelligence, 25:75–94, 1985.Google Scholar
  12. 12.
    Niemelä, I.: Constructive tightly grounded autoepistemic reasoning. In Proceedings of the 12th International Joint Conference on Artificial Intelligence, pages 399–404, Sydney, Australia, August 1991. Morgan Kaufmann Publishers.Google Scholar
  13. 13.
    Niemelä, I.: On the decidability and complexity of autoepistemic reasoning. Fundamenta Informaticae, 17(1,2):117–155, 1992.Google Scholar
  14. 14.
    Przymusinska, H. and Przymusinski, T.: Stationary default extensions. In Working Notes of the 4th International Workshop on on Nonmonotonic Reasoning, pages 179–193, Plymouth, Vermont, USA, May 1992.Google Scholar
  15. 15.
    Przymusinski, T.: Autoepistemic logics of closed beliefs and logic programming. In Proceedings of the 1st International Workshop on Logic Programming and Non-monotonic Reasoning, pages 3–20, Washington, D.C., USA, July 1991. The MIT Press.Google Scholar
  16. 16.
    Reiter, R.: A logic for default reasoning. Artificial Intelligence, 13:81–132, 1980.Google Scholar
  17. 17.
    Van Gelder, A., Ross, K., and Schlipf, J.: The well-founded semantics for general logic programs. Journal of the ACM, 38(3):620–650, July 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Tomi Janhunen
    • 1
  • Ilkka Niemelä
    • 1
  1. 1.Department of Computer Science, Digital Systems LaboratoryHelsinki University of TechnologyEspooFinland

Personalised recommendations