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A blackboard architecture for guiding interactive proofs

  • Christoph Benzmüller
  • Volker Sorge
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1480)

Abstract

The acceptance and usability of current interactive theorem proving environments is, among other things, strongly influenced by the availability of an intelligent default suggestion mechanism for commands. Such mechanisms support the user by decreasing the necessary interactions during the proof construction. Although many systems offer such facilities, they are often limited in their functionality. In this paper we present a new agent-based mechanism that independently observes the proof state, steadily computes suggestions on how to further construct the proof, and communicates these suggestions to the user via a graphical user interface. We furthermore introduce a focus technique in order to restrict the search space when deriving default suggestions. Although the agents we discuss in this paper are rather simple from a computational viewpoint, we indicate how the presented approach can be extended in order to increase its deductive power.

Keywords

Open Line Natural Deduction Support Line Active Focus Interactive Proof 
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.

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References

  1. 1.
    P. B. Andrews. An Introduction To Mathematical Logic and Type Theory: To Truth Through Proof. Academic Press, San Diego, CA, USA, 1986.Google Scholar
  2. 2.
    P. B. Andrews, M. Bishop, S. Issar, D. Nesmith, F. Pfenning, and H. Xi. Tps: A Theorem Proving System for Classical Type Theory. Journal of Automated Reasoning, 16(3):321–353, 1996.zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    C. Benzmüller, L. Cheikhrouhou, D. Fehrer, A. Fiedler, X. Huang, M. Kerber, M. Kohlhase, K. Konrad, E. Melis, A. Meier, W. Schaarschmidt, J. Siekmann, and V. Sorge. ΩMega: Towards a Mathematical Assistant. In W. McCune, editor, Proceedings of the 14th Conference on Automated Deduction (CADE-14), LNAI, Townsville, Australia, 1997. Springer Verlag, Berlin, Germany.Google Scholar
  4. 4.
    R. Engelmore and T. Morgan, editors. Blackboard Systems. Addison-Wesley, 1988.Google Scholar
  5. 5.
    L. D. Erman, F. Hayes-Roth, and R. D. Reddy. The HERSAY-II speech understanding system: Integrating knowledge to resolve uncertainty. ACM Computing Surveys, 12(2), 1980.Google Scholar
  6. 6.
    L. Erman, P. London, and S. Fickas. The Design and an Example Use of HEARSAY-III. In P. J. Hayes, editor, Proceedings of the 7th International Joint Conference on Artificial Intelligence (IJCAI '81), pages 409–415. William Kaufmann, 1981.Google Scholar
  7. 7.
    G. Gentzen. Untersuchungen über das Logische Schlie\en I und II. Mathematische Zeitschrift, 39:176–210, 405–431, 1935.MathSciNetCrossRefGoogle Scholar
  8. 8.
    M. J. C. Gordon and T. F. Melham. Introduction to HOL. Cambridge University Press, Cambridge, United Kingdom, 1993.Google Scholar
  9. 9.
    M. A. Pérez and J. L. Sibert. Focus in graphical user interfaces. In W. D. Gray, William E. Hefley, and Dianne Murray, editors, Proceedings of the International Workshop on Intelligent User Interfaces, pages 255–258. ACM Press, 1993.Google Scholar
  10. 10.
    The Oz Programming System Programming Systems Lab, DFKI, Germany, 1998. URL: http://www.ps.uni-sb.de/oz/.Google Scholar
  11. 11.
    J. Siekmann, S. M. Hess, C. Benzmüller, L. Cheikhrouhou, D. Fehrer, A. Fiedler, M. Kohlhase, K. Konrad, E. Melis, A. Meier, and V. Sorge. LΩUI: A Distributed Graphical User Interface for the Interactive Proof System Ω mega. Submitted to the International Workshop on User Interfaces for Theorem Provers, 1998.Google Scholar
  12. 12.
    J. W. Sullivan and S. W. Tyler, editors. Intelligent User Interfaces. ACM Press Frontier Series. ACM Press, New York, NY, USA, 1991.Google Scholar
  13. 13.
    L. Théry, Y. Bertot, and G. Kahn. Real Theorem Provers Deserve Real User-Interfaces. In Proceedings of The Fifth ACM Symposium on Software Development Environments (SDE5), Washington D.C., USA, December 1992. ACM Press.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Christoph Benzmüller
    • 1
  • Volker Sorge
    • 1
  1. 1.Fachbereich InformatikUniversität des SaarlandesSaarbrückenGermany

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