Productive use of failure in inductive proof

Journal of Automated Reasoning

Volumn 16, Issue 1-2, 1996, Pages 79-111

  Ireland, Andrew ^a,b   Bundy, Alan ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

Automated theorem proving; Mathematical induction; Proof patching

Indexed keywords

ARTIFICIAL INTELLIGENCE; AUTOMATION; HEURISTIC METHODS; MATHEMATICAL TECHNIQUES; PROBLEM SOLVING; USER INTERFACES;

EUREKA STEPS; INDUCTIVE REASONING; MATHEMATICAL INDUCTION; PROOF PATCHING; RIPPLING;

THEOREM PROVING;

EID: 0030100852     PISSN: 01687433     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00244460     Document Type: Article

References (21)

1. Aubin, R.: Some generalization heuristics in proofs by induction, in G. Huet and G. Kahn (eds), Actes du Colloque Construction: Amélioration et vérification de Programmes, Institut de recherche d'informatique et d'automatique, 1975.
2. Boyer, R. S. and Moore, J. S.: A Computational Logic, Academic Press, New York, 1979. ACM monograph series.
3. Bouhoula, A. and Rusinowitch, M.: Automatic case analysis in proof by induction, in Proc. 13th IJCAI, Int. Joint Conf. Artificial Intelligence, 1993.
4. Bundy, A., Stevens, A., van Harmelen, F., Ireland, A., and Smaill, A.: Rippling: A heuristic for guiding inductive proofs, Artificial Intelligence 62 (1993), 185-253. Also available from Edinburgh as DAI Research Paper No. 567.
5. Bundy, A.: The use of explicit plans to guide inductive proofs, in R. Lusk and R. Overbeek (cds), 9th Conf. Automated Deduction, Springer-Verlag, 1988, pp. 111-120. Longer version avilable from Edinburgh as DAI Research Paper No. 349.
6. Bundy, A., van Harmelen, F., Horn, C., and Smaill, A.: The Oyster-Clam system, in M. E. Stickel (ed.), 10th Int. Conf. Automated Deduction, Lecture Notes in Artificial Intelligence 449, Springer-Verlag, 1990, pp. 647-648. Also available from Edinburgh as DAI Research Paper No. 507.
7. Bundy, A., van Harmelen, F., Smaill, A., and Ireland, A.: Extensions to the rippling-out tactic for guiding inductive proofs, in M. E. Stickel (ed.), 10th Int. Conf. Automated Deduction, Lecture Notes in Artificial Intelligence 449, Springer-Verlag, 1990, pp. 132-146. Also available from Edinburgh as DAI Research Paper No. 459.
8. Bundy, A. and Welham, B.: Using meta-level inference for selective application of multiple rewrite rules in algebraic manipulation, Artificial Intelligence 16(2) (1981), 189-212. Also available from Edinburgh as DAI Research Paper No. 121.
9. Basin, D. and Walsh, T.: Difference matching, in Deepak Kapur (ed.), 11th Conf. Automated Deduction, Saratoga Springs, NY, USA, June 1992. Published as Springer Lecture Notes in Artificial Intelligence 607, pp. 295-309.
10. Gentzen, G.: The Collected Papers of Gerhard Gentzen, edited by M. E. Szabo, North-Holland, Amsterdam, 1969.
11. Gordon, M. J., Milner, A. J., and Wadsworth, C. P.: Edinburgh LCF - A Mechanised Logic of Computation, Lecture Notes in Computer Science 78, Springer-Verlag, 1979.
12. Hardy, G. H.: Mathematical proof, MIND: A Quarterly Review of Psychology and Philosophy, 38(149) (January 1929), 1-25.
13. Hesketh, J. T: Using middle-out reasoning to guide inductive theorem proving, PhD thesis, University of Edinburgh, 1991.
14. Hutter, D. and Kohlhase, M.: A Colored Version of the λ-Calculus, Seki-report sr-95-05, University of Saarland, 1995.
15. Hutter, D.: Guiding inductive proofs, in M. E. Stickel (ed.), 10th Int. Conf. Automated Deduction, Lecture Notes in Artificial Intelligence 449, Springer-Verlag, 1990, pp. 147-161.
16. Ireland, A.: The use of planning critics in mechanizing inductive proofs, in A. Voronkov (ed.), Int. Conf. Logic Programming and Automated Reasoning, LPAR 92, St. Petersburg, Lecture Notes in Artificial Intelligence 624, Springer-Verlag, 1992, pp. 178-189. Also available from Edinburgh as DAI Research Paper No. 592.
17. Monroy, R., Bundy, A., and Ireland, A.: Proof plans for the correction of false conjectures, in F. Pfenning (ed.), 5th Int. Conf. Logic Programming and Automated Reasoning, LPAR 94, Lecture Notes in Artificial Intelligence 822, Springer-Verlag, 1994, pp. 54-68. Also available from Edinburgh as Research Paper No. 681.
18. Miller, D. and Nadathur, G.: An overview of λProlog, in R. Bowen and K. Kowalski (eds), Proc. 5th Int. Logic Programming Conf./5th Symp. on Logic Programming, MIT Press, 1988.
19. Manna, Z. and Waldinger, R.: The Logical Basis for Computer Programming, Vol. 1. Deductive Reasoning, Addison/Wesley, Reading, MA, 1985.
20. Thomas, M. and Jantke, K. P.: Inductive inference for solving divergance in Knuth-Bendix, in K. P. Jantke (ed.), Analogical and Inductive Inference, Proc. AII'89, Springer-Verlag, 1989, pp. 288-303.
21. Walsh, T.: A divergence critic, in Alan Bundy (ed.), 12th Conf. Automated Deduction, Lecture Notes in Artificial Intelligence 814, Springer-Verlag, Nancy, France, 1994.