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Proof by consistency in conditional equational theories

  • Chapter 3 Extension Of Knuth-Bendix Completion
  • Conference paper
  • First Online:
Conditional and Typed Rewriting Systems (CTRS 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 516))

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Abstract

In this paper we deal with the problem of proving inductive theorems in conditional equational theories. We propose a proof by consistency method that can be employed when the theory is representable as a ground Church-Rosser conditional equational system. The method has a linear proof strategy and is shown to be sound and refutational complete, i.e. it refutes any conditional equation which is not an inductive theorem. Moreover it can handle rewrite rules as well as (unorientable) equations and therefore it will not fail when an unorientable equation comes up (as was the case in the earliest proof by consistency (inductionless induction) methods). The method extends the work on unconditional equational theories of [Bachmair 1988].

Research supported by the “Instituut tot Aanmoediging van het Wetenschappelijk onderzoek in Nijverheid en Landbouw — I.W.O.N.L.”

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Authors and Affiliations

  1. Department of Computer Science, K.U.Leuven, Celestijnenlaan 200A, B-3001, Leuven (Heverlee), Belgium

    Eddy Bevers & Johan Lewi

Authors
  1. Eddy Bevers
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  2. Johan Lewi
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S. Kaplan M. Okada

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© 1991 Springer-Verlag Berlin Heidelberg

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Bevers, E., Lewi, J. (1991). Proof by consistency in conditional equational theories. In: Kaplan, S., Okada, M. (eds) Conditional and Typed Rewriting Systems. CTRS 1990. Lecture Notes in Computer Science, vol 516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54317-1_91

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  • DOI: https://doi.org/10.1007/3-540-54317-1_91

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54317-6

  • Online ISBN: 978-3-540-47558-3

  • eBook Packages: Springer Book Archive

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