A blackboard architecture for guiding interactive proofs
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.
KeywordsOpen Line Natural Deduction Support Line Active Focus Interactive Proof
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- 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
- 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.R. Engelmore and T. Morgan, editors. Blackboard Systems. Addison-Wesley, 1988.Google Scholar
- 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.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
- 8.M. J. C. Gordon and T. F. Melham. Introduction to HOL. Cambridge University Press, Cambridge, United Kingdom, 1993.Google Scholar
- 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.The Oz Programming System Programming Systems Lab, DFKI, Germany, 1998. URL: http://www.ps.uni-sb.de/oz/.Google Scholar
- 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.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.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