The Heine-Borel Challenge Problem. In Honor of Woody Bledsoe

Journal of Automated Reasoning

Volumn 20, Issue 3, 1998, Pages 255-282

  Melis, Erica ^a  

^a SAARLAND UNIVERSITY   (Germany)

Author keywords

Analogy; Challenge problems

Indexed keywords

COMPUTATIONAL METHODS; PROBLEM SOLVING; TOPOLOGY;

ANALOGICAL THEOREM PROVING; HEINE-BOREL THEOREM;

THEOREM PROVING;

EID: 0032095668     PISSN: 01687433     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1005843328643     Document Type: Article

References (34)

1. Bledsoe, W. W., Boyer, Robert S. and Henneman, W. H.: Computer proofs of limit theorems, Artificial Intelligence 3(1) (1972), 27-60.
2. Bledsoe, W.: Non-resolution theorem proving, Artificial Intelligence 9 (1977), 1-35.
3. Bledsoe, W. W.: The use of analogy in automatic proof discovery, Tech. Rep. AI-158-86, Microelectronics and Computer Technology Corporation, Austin, TX, 1986.
4. Bledsoe, W.: Challenge problems in elementary analysis, Journal of Automated Reasoning 6 (1990), 341-359.
5. Bledsoe, W. W.: Heine-Borel Theorem Analogy Example, Technical Report Memo ATP 124, University of Texas Computer Science Dept., Austin, TX, 1994.
6. Bledsoe, W. W.: A precondition prover for analogy, BioSystems 34 (1995), 225-247.
7. Bledsoe, W. W.: Abduction Rules, Technical Report Memo ATP 126, University of Texas Computer Science Dept., Austin, TX, August 1995.
8. Boyer, R. S. and Moore, J. S.: Integrating decision procedures into heuristic theorem provers: A case study of linear arithmetic, Machine Intelligence 11 (1988), 83-124.
9. Bundy, A.: The use of explicit plans to guide inductive proofs, in E. Lusk and R. Overbeek (eds), Proc. 9th International Conference on Automated Deduction (CADE-9) Vol. 310, Lecture Notes in Computer Science, Springer, Argonne, 1988, pp. 111-120.
10. Bundy, A., van Harmelen, F., Hesketh, J. and Smaill, A.: Experiments with proof plans for induction, J. Automated Reasoning 7 (1991), 303-324.
11. Carbonell, J. G.: Derivational analogy: A theory of reconstructive problem solving and expertise acquisition, in R. S. Michalsky, J. G. Carbonell, and T. M. Mitchell (eds), Machine Learning: An Artificial Intelligence Approach, Morgan Kaufmann Publ., Los Altos, 1986, pp. 371-392.
12. Benzmueller, C., Cheikhrouhou, L. O., Fehrer, D., Fiedler, A., Huang, X., Kerber, M., Kohlhase, M., Konrad, K., Meier, A., Melis, E., Schaarschmidt, W., Siekmann, J. and Sorge, V.: OMEGA: Towards a mathematical assistant, in Proc. 14th International Conference on Automated Deduction (CADE), Springer, Townsville, 1997.
13. Curien, R.: Outils pour la Preuve par Analogie, PhD thesis, Université Henri Poincaré, Nancy, 1995.
14. Deussen, P.: Halbgruppen und Automaten, Vol. 99 of Heidelberger Taschenbücher, Springer, Berlin, 1971.
15. Gordon, M., Milner, R. and Wadsworth, C. P.: Edinburgh LCF: A Mechanized Logic of Computation, Vol. 78 of Lecture Notes in Computer Science. Springer, Berlin, 1979.
16. Hadamard, J.: The Psychology of Invention in the Mathematical Field, Princeton Univ. Press, Princeton, 1945.
17. Huang, X., Kerber, M., Kohlhase, M. and Richts, J.: Methods - the basic units for planning and verifying proofs, in Proceedings of Jahrestagung für Künstliche Intelligenz KI-94, Springer, Saarbrücken, 1994.
18. Kling, R. E.: A paradigm for reasoning by analogy, Artificial Intelligence 2 (1971), 147-178.
19. Kolbe, Th. and Walther, Ch.: Reusing proofs, in Proceedings of 11th European Conference on Artificial Intelligence (ECAI-94), Amsterdam, 1994.
20. Kolbe, Th. and Walther, Ch.: Patching proofs for reuse, in N. Lavrac and S. Wrobel (eds), Proceedings of the 8th European Conference on Machine Learning 1995, Kreta, 1995.
21. McCune, W. W.: OTTER 2.0 users guide, Technical Report ANL-90/9, Argonne National Laboratory, Mathematics and Computer Science Division, Argonne, Illinois, 1990.
22. Melis, E.: Analogies between Proofs - a Case Study, SEKI-Report SR-93-12, University of Saarbrücken, Saarbrücken, 1993. Available from http://jswww.ags.uni-sb.de/pub/seki/index.html.
23. Melis, E.: Change of Representation in Theorem Proving by Analogy, SEKI-Report SR-93-07, University of Saarbrücken, Saarbrücken, 1993. Available from http://jswww.ags.uni-sb.de/pub/seki/index.html.
24. Melis, E.: Analogy in CLAM, Technical Report DAI Research Paper No 766, University of Edinburgh, AI Dept., Dept. of Artificial Intelligence, Edinburgh, 1995. Available from http://jswww.cs.uni-sb.de/~melis/.
25. Melis, E.: A model of analogy-driven proof-plan construction, in Proceedings of the 14th International Joint Conference on Artificial Intelligence, Montreal, 1995, pp. 182-189.
26. Munyer, J. C.: Analogy as a Means of Discovery in Problem Solving and Learning, PhD thesis, University of California, Santa Cruz, 1981.
27. Melis, E. and Veloso, M.: Analogy makes proofs feasible, in D. Aha (ed.), AAAI-Workshop on Case-Based Reasoning, Seattle, 1994, pp. 13-17.
28. Owen, S.: Analogy for Automated Reasoning, Academic Press, New York, 1990.
29. Polya, G.: How to Solve It, Princeton University Press, 1945.
30. Polya, G.: Mathematics and Plausible Reasoning, Princeton University Press, 1954.
31. Sehn, A. C.: DECLAME - eine deklarative Sprache zur Repräsentation von Methoden, Master's thesis, Universität des Saarlandes, 1995, published as SEKI Working Paper SWP-95-02.
32. van der Waerden, B. L.: Wie der Beweis der Vermutung von Baudet gefunden wurde, Abh. Math. Sem. Univ. Hamburg 28 (1964).
33. Veloso, M. M.: Flexible strategy learning: Analogical replay of problem solving episodes, in Proc. of the Twelfth National Conference on Artificial Intelligence 1994, Seattle, WA, 1994.
34. Wang, R.: The Use of Analogy in the PC System, Computer Science Department Memo, Univerity of Texas at Austin, May 1991.