Abstract
This paper investigates analogy-driven proof plan construction in inductive theorem proving. Given a proof plan of a source theorem, we identify constraints of second-order mappings that enable a replay of the source plan to produce a similar plan for the target theorem. In addition, the analogical replay is controlled by justifications that have to be satisfied in the target. Our analogy procedure, ABALONE, is implemented on top of the proof planner, CLaM. Employing analogy has extended the problem solving horizon of CLaM: with analogy, some theorems could be proved that CLAM could not prove automatically.
The first author was supported by the HC&M grant CHBICT930806 whilst visiting Ed inburgh and the SFB 378 and the second author by an EPSRC studentship. Computing facilities were in part provided by EPSRC grant GR/J/80702
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References
R.S. Boyer and J.S. Moore. A Computational Logic. Academic Press, London, 1979.
A. Bundy, ‘The use of explicit plans to guide inductive proofs', in Proc. 9th International Conference on Automated Deduction (CADE), eds., E. Lusk and R. Overbeek, volume 310 of Lecture Notes in Computer Science, pp. 111–120, Argonne, (1988). Springer.
A. Bundy, Stevens A, F. Van Harmelen, A. Ireland, and A. Smaill, ‘A heuristic for guiding inductive proofs', Artificial Intelligence, 63, 185–253, (1993).
A. Bundy, F. van Harmelen, J. Hesketh, and A. Smaill, ‘Experiments with proof plans for induction', Journal of Automated Reasoning, 7, 303–324, (1991).
J.G. Carbonell, ‘Derivational analogy: A theory of reconstructive problem solving and expertise acquisition', in Machine Learning: An Artificial Intelligence Approach, eds., R.S. Michalsky, J.G. Carbonell, and T.M. Mitchell, 371–392, Morgan Kaufmann Publ., Los Altos, (1986).
R. Curien, Outils pour la Preuve par Analogie, Ph.D. dissertation, Universite Henri Poincare-Nancy, January 1995.
M. Gordon, R. Milner, and C.P. Wadsworth, Edinburgh LCF: A Mechanized Logic of Computation, Lecture Notes in Computer Science 78, Springer, Berlin, 1979.
D. Hutter, ‘Guiding inductive proofs', in Proc. of 10th International Conference on Automated Deduction (CADE), ed.. M.E. Stickel, volume Lecture Notes in Artificial Intelligence 449. Springer, (1990).
D. Hutter, 'synthesis of induction orderings for existence proofs', in Proc. of 12th International Conference on Automated Deduction (CADE), ed., A. Bundy, Lecture Notes in Artificial Intelligence 814, pp. 29–41. Springer, (1994).
Th. Kolbe and Ch. Walther, ‘Reusing proofs', in Proceedings of ECAI-94, Amsterdam, (1994).
E. Melis, ‘A model of analogy-driven proof-plan construction', in Proceedings of the 14th International Joint Conference on Artificial Intelligence, pp. 182–189, Montreal, (1995).
E. Melis, ‘When to Prove Theorems by Analogy?', in KI-96: Advances in Artificial Intelligence. 20th Annual German Conference on Artificial Intelligence, pp. 259–271, Lecture Notes in Artificial Intelligence 1137, Springer, (1996).
E. Melis and J. Whittle, ‘Internal Analogy in Inductive Theorem Proving', in Proceedings of the 13th Conference on Automated Deduction (CADE-96), eds., M.A. McRobbie and J.K. Slaney, Lecture Notes in Artificial Intelligence, 1104, pp. 92–105. Springer, (1996).
E. Melis and J. Whittle, ‘Analogy as a Control Strategy in Theorem Proving', in Proceedings of the 10th Florida International AI Conference (FLAIRS-97), (1997).
J.C. Munyer, Analogy as a Means of Discovery in Problem Solving and Learning, Ph.D. dissertation, University of California, Santa Cruz, 1981.
S. Owen, Analogy for Automated Reasoning, Academic Press, 1990.
S. Vadera, ‘Proof by analogy in Mural', Formal Aspects of Computing, 7, 183–206, (1995).
J. Whittle, ‘Analogy in CLAM'', MSc.thesis, University of Edinburgh, Dept. of AI, Edinburgh, (1995). Also available at http://www.dai.ed.ac.uk/daidb/students/jonathw/publications.html
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Melisi, E., Whittle, J. (1997). External analogy in inductive theorem proving. In: Brewka, G., Habel, C., Nebel, B. (eds) KI-97: Advances in Artificial Intelligence. KI 1997. Lecture Notes in Computer Science, vol 1303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3540634932_8
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DOI: https://doi.org/10.1007/3540634932_8
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