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Journal of Automated Reasoning

, Volume 16, Issue 1–2, pp 79–111 | Cite as

Productive use of failure in inductive proof

  • Andrew Ireland
  • Alan Bundy
Article

Abstract

Proof by mathematical induction gives rise to various kinds of eureka steps, e.g., missing lemmata and generalization. Most inductive theorem provers rely upon user intervention in supplying the required eureka steps. In contrast, we present a novel theorem-proving architecture for supporting the automatic discovery of eureka steps. We build upon rippling, a search control heuristic designed for inductive reasoning. We show how the failure if rippling can be used in bridging gaps in the search for inductive proofs.

Key words

Automated theorem proving mathematical induction proof patching 

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Andrew Ireland
    • 1
  • Alan Bundy
    • 1
  1. 1.Department of Artificial IntelligenceUniversity of EdinburghEdinburghScotland, UK

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