Abstract
The problem of analogy in theorem proving has been studied for several years now (see [5, 10, 12] for example). Those works restrict the use of analogy to proofs, disregarding the possibilities of using analogy also for counter-examples construction. Moreover, they deal with the problem of proving a new theorem once an appropriate source theorem has been provided as a guideline. We overcome these drawbacks by using a method for model construction developed in our group and by generalizing proofs (or counter-examples constructions) before including them in the database of source examples. Analogy discovery relies on partial matching between a target statement, and a source (generalized) refutation or counter-example construction, thus allowing more targets to be regarded as “analogous” to a source. It increases the power of an analogy-based prover, by recognizing subgoals within a source refutation or model building. We use in this purpose notions of graph cut sets, and incremental update of statements.
Funded by DRET-France
Funded by MRE-France
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
C. Berge. Graphes et hypergraphes. Dunod, second edition, 1970.
W. W. Bledsoe. Non-resolution theorem proving. Artificial Intelligence, 9:1–35, 1977.
C. Bourely, G. Défourneaux, and N. Peltier. Building proofs or counter-examples by analogy in a resolution framework. In J. J. Alferes, L. M. Pereira, and E. Orlowska, editors, Proceedings of JELIA 96, volume 112 of LNAI, pages 34–49. Springer, 1996.
T. Boy de la Tour and R. Caferra. Proof analogy in interactive theorem proving: A method to express and use it via second order pattern matching. In Proceedings of AAAI 87, pages 95–99. Morgan Kaufmann, 1987.
T. Boy de la Tour and C. Kreitz. Building proofs by analogy via the Curry-Howard isomorphism. In Proceedings of LPAR 92, pages 202–213. Springer, 1992.
R. Caferra and N. Zabel. A method for simultaneous search for refutations and models by equational constraint solving. Journal of Symbolic Computation, 13:613–641, 1992.
H. Comon and P. Lescanne. Equational problems and disunification. Journal of Symbolic Computation, 7:371–475, 1989.
R. Curien, Z. Qian, and Hui-Shi. Efficient second-order matching. In H. Ganzinger, editor, Proceedings of 7th Rewriting Techniques and Applications, volume 1103 of Lecture Notes in Computer Science, pages 317–331. Springer, 1996.
G. Huet. A unification algorithm for typed λ-calculus. Theorical Computer Science, 1:27–57, 1975.
T. Kolbe and C. Walther. Second-order matching modulo evaluation — A technique for reusing proofs. In C. S. Mellish, editor, Proceedings of IJCAI 95, pages 190–195. IJCAI, Morgan Kaufmann, 1995.
W. McCune. Otter 3.0 Reference Manual and Guide. Argonne National Laboratory, Aug. 1995. Revision A.
E. Melis. A model of analogy-driven proof-plan construction. In Proceedings of the 14th International Joint Conference on Artificial Intelligence, pages 182–189, Montreal, 1995.
S. Owen. Analogy for Automated Reasoning. Academic Press, 1990.
C. Suttner and G. Sutcliffe. The TPTP problem library. Technical report, TU München/James Cook University, 1996. V-1.2.1.
L. Wos, R. Overbeek, E. Lush, and J. Boyle. Automated Reasoning: Introduction and Application. McGraw-Hill, second edition, 1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Défourneaux, G., Peltier, N. (1997). Partial matching for analogy discovery in proofs and counter-examples. In: McCune, W. (eds) Automated Deduction—CADE-14. CADE 1997. Lecture Notes in Computer Science, vol 1249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63104-6_43
Download citation
DOI: https://doi.org/10.1007/3-540-63104-6_43
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63104-0
Online ISBN: 978-3-540-69140-2
eBook Packages: Springer Book Archive