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A structural completeness theorem for a class of conditional rewrite rule systems

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COLOG-88 (COLOG 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 417))

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Abstract

For a class of quantifier-free logical theories, axiomatized by conditional equivalences, we prove a completeness result of the form: if a theory T from the class generates the uniquely terminating conditional rewrite rule system, and a partition T1 ∪ T2 of T satisfies certain structural properties, then an arbitrary unquantified formula Ω is a theorem of T1 ∪ T2 iff the leaves of any proof tree for Ω are theorems of T1.

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Authors and Affiliations

  1. Program Systems Institute of the USSR Academy of Sciences, 152140, Pereslavl-Zalessky, USSR

    Sergey G. Vorobyov

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  1. Sergey G. Vorobyov
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Per Martin-Löf Grigori Mints

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© 1990 Springer-Verlag Berlin Heidelberg

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Vorobyov, S.G. (1990). A structural completeness theorem for a class of conditional rewrite rule systems. In: Martin-Löf, P., Mints, G. (eds) COLOG-88. COLOG 1988. Lecture Notes in Computer Science, vol 417. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52335-9_62

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  • DOI: https://doi.org/10.1007/3-540-52335-9_62

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52335-2

  • Online ISBN: 978-3-540-46963-6

  • eBook Packages: Springer Book Archive

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