Abstract
Inductive theorem provers often diverge. This paper describes a critic which monitors the construction of inductive proofs attempting to identify diverging proof attempts. The critic proposes lemmas and generalizations which hopefully allow the proof to go through without divergence. The critic enables the system SPIKE to prove many theorems completely automatically from the definitions alone.
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References
R. Aubin. Mechanizing Structural Induction. PhD thesis, University of Edinburgh, 1976.
D. Basin and T. Walsh. Difference matching. In D. Kapur, editor, 11th Conference on Automated Deduction, pages 295–309. Springer Verlag, 1992. Lecture Notes in Computer Science No. 607.
D. Basin and T. Walsh. Difference unification. In Proceedings of the 13th IJCAI. International Joint Conference on Artificial Intelligence, Chambery, France, 1993.
A. Bouhoula, and M. Rusinowitch. Automatic Case Analysis in Proof by Induction. In Proceedings of the 13th IJCAI. International Joint Conference on Artificial Intelligence, Chambery, France, 1993.
R.S. Boyer and J.S. Moore. A Computational Logic. Academic Press, 1979. ACM monograph series.
A. Bundy, A. Stevens, F. van Harmelen, A. Ireland, and A. Smaill. Rippling: A heuristic for guiding inductive proofs. Artificial Intelligence, 62:185–253, 1993.
N. Dershowitz and E. Pinchover. Inductive Synthesis of Equational Programs. In Proceedings of the 8th National Conference on AI, pages 234–239. American Association for Artificial Intelligence, 1990.
M. Hermann. Crossed term rewriting systems. CRIN Report 89-R-003, Centre de Recherche en Informatique de Nancy, 1989.
A. Ireland. The Use of Planning Critics in Mechanizing Inductive Proof. In Proceedings of LPAR'92. Springer-Verlag, 1992. Lecture Notes in Artificial Intelligence 624.
A. Ireland and A. Bundy. Using failure to guide inductive proof. Technical report 613, Dept. of Artificial Intelligence, University of Edinburgh, 1992.
H. Kirchner. Schematization of infinite sets of rewrite rules. Application to the divergence of completion processes. In Proceedings of RTA'87, pages 180–191, 1987.
M. Protzen. Disproving conjectures. In D. Kapur, editor, 11th Conference on Automated Deduction, pages 340–354. Springer Verlag, 1992. Lecture Notes in Computer Science No. 607.
M. Thomas and K.P. Jantke. Inductive Inference for Solving Divergence in Knuth-Bendix Completion. In Proceedings of International Workshop AII'89, pages 288–303, 1989.
M. Thomas and P. Watson. Solving divergence in Knuth-Bendix completion by enriching signatures. Theoretical Computer Science, 112:145–185, 1993.
T. Walsh, A. Nunes, and A. Bundy. The use of proof plans to sum series. In D. Kapur, editor, 11th Conference on Automated Deduction, pages 325–339. Springer Verlag, 1992. Lecture Notes in Computer Science No. 607.
T. Yoshida, A. Bundy, I. Green, T. Walsh, and D. Basin. Coloured rippling: the extension of a theorem proving heuristic. Technical Report, Dept. of Artificial Intelligence, University of Edinburgh, 1993.
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© 1994 Springer-Verlag Berlin Heidelberg
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Walsh, T. (1994). A divergence critic. In: Bundy, A. (eds) Automated Deduction — CADE-12. CADE 1994. Lecture Notes in Computer Science, vol 814. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58156-1_2
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DOI: https://doi.org/10.1007/3-540-58156-1_2
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Online ISBN: 978-3-540-48467-7
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