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On the use of the constructive omega-rule within automated deduction

  • Session 8: Logical Frameworks
  • Conference paper
  • First Online:
Logic Programming and Automated Reasoning (LPAR 1992)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 624))

Abstract

In general, cut elimination holds for arithmetical systems with the ω-rule, but not for systems with ordinary induction. Hence in the latter, there is the problem of generalisation, since arbitrary formulae can be cut in. This makes automatic theorem-proving very difficult. An important technique for investigating derivability in formal systems of arithmetic has been to embed such systems into semi-formal systems with the ω-rule. This paper describes the outline of an implementation of such a system. Moreover, an important application is presented in the form of a new method of generalisation by means of “guiding proofs” in the stronger system, which sometimes succeeds in producing proofs in the original system when other methods fail.

The research reported in this paper was supported by an SERC studentship to the first author and by ESPRIT BRA 3245

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Author information

Authors and Affiliations

  1. Department of Artificial Intelligence, Edinburgh University, Scotland

    S. Baker, A. Ireland & A. Smaill

Authors
  1. S. Baker
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  2. A. Ireland
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  3. A. Smaill
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Editor information

Andrei Voronkov

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© 1992 Springer-Verlag Berlin Heidelberg

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Baker, S., Ireland, A., Smaill, A. (1992). On the use of the constructive omega-rule within automated deduction. In: Voronkov, A. (eds) Logic Programming and Automated Reasoning. LPAR 1992. Lecture Notes in Computer Science, vol 624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013063

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  • DOI: https://doi.org/10.1007/BFb0013063

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55727-2

  • Online ISBN: 978-3-540-47279-7

  • eBook Packages: Springer Book Archive

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