A circumscriptive theorem prover

  • Matthew L. Ginsberg
Implementing Circumscription
Part of the Lecture Notes in Computer Science book series (LNCS, volume 346)


In [6], a generalization of first-order logic was introduced that led to the development of an effective theorem prover for some simple sorts of default reasoning. In this paper, we show that these ideas can also be used to construct a theorem prover for a wide class of circumscriptive theories.

The ideas to be discussed have been implemented, and the resulting system has been applied to the canonical birds flying example, to a non-separable circumscription [9], and to the Yale shooting problem. In all of these cases, the implementation returns the circumscriptively correct answer.


Partial Order Theorem Prover Conjunctive Query Default Rule Default Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    W. F. Clocksin and C. S. Mellish. Programming in Prolog. Springer-Verlag, Berlin, 1981.Google Scholar
  2. [2]
    J. de Kleer. An assumption-based truth maintenance system. Artificial Intelligence, 28:127–162, 1986.Google Scholar
  3. [3]
    M. Gelfond and V. Lifschitz. Compiling circumscriptive theories into logic programs. In Proceedings of the Seventh National Conference on Artificial Intelligence, 1988.Google Scholar
  4. [4]
    M. Gelfond, H. Przymusinska, and T. Przymusinski. The extended closed world assumption and its relationship to parallel circumscription. In Proceedings of ACM SIGACT-SIGMOD Symposium on Principles of Database Systems, pages 133–139, 1986.Google Scholar
  5. [5]
    M. R. Genesereth. An overview of meta-level architecture. In Proceedings of the Third National Conference on Artificial Intelligence, pages 119–124, 1983.Google Scholar
  6. [6]
    M. L. Ginsberg. Multivalued logics: A uniform approach to reasoning in artificial intelligence. Computational Intelligence, 4, 1988.Google Scholar
  7. [7]
    M. L. Ginsberg. A New Approach to Implicit Quantification. Technical Report 87-7, Logic Group, Stanford University, 1987.Google Scholar
  8. [8]
    S. Hanks and D. McDermott. Nonmonotonic logics and temporal projection. Artificial Intelligence, 33:379–412, 1987.Google Scholar
  9. [9]
    V. Lifschitz. Computing circumscription. In Proceedings of the Ninth International Joint Conference on Artificial Intelligence, pages 121–127, 1985.Google Scholar
  10. [10]
    J. McCarthy. Applications of circumscription to formalizing common sense knowledge. Artificial Intelligence, 28:89–116, 1986.Google Scholar
  11. [11]
    J. McCarthy. Circumscription — a form of non-monotonic reasoning. Artificial Intelligence, 13:27–39, 1980.Google Scholar
  12. [12]
    T. C. Przymusinski. Query-answering in circumscriptive and closed-world theories. In Proceedings of the Fifth National Conference on Artificial Intelligence, pages 186–190, 1986.Google Scholar
  13. [13]
    R. Reiter. On closed world data bases. In H. Gallaire and J. Minker, editors, Logic and Data Bases, pages 119–140, Plenum, New York, 1978.Google Scholar
  14. [14]
    R. Reiter and G. Criscuolo. On interacting defaults. In Proceedings of the Seventh International Joint Conference on Artificial Intelligence, pages 270–276, 1981.Google Scholar
  15. [15]
    R. Reiter and J. de Kleer. Foundations of assumption-based truth maintenance systems: Preliminary report. In Proceedings of the Sixth National Conference on Artificial Intelligence, pages 183–188, 1987.Google Scholar
  16. [16]
    S. Russell. The Compleat Guide to MRS. Technical Report STAN-CS-85-1080, Stanford University, June 1985.Google Scholar
  17. [17]
    Y. Shoham. A semantical approach to nonmonotonic logics. In Proceedings of the Tenth International Joint Conference on Artificial Intelligence, pages 388–393, 1987.Google Scholar
  18. [18]
    D. E. Smith and M. R. Genesereth. Ordering conjunctive queries. Artificial Intelligence, 26(2):171–215, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Matthew L. Ginsberg
    • 1
  1. 1.Computer Science DepartmentStanford UniversityStanfordUSA

Personalised recommendations