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

  • Sergey G. Vorobyov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 417)


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.

Key words and phrases

conditional rewrite rules inference rules proof search reduction case splitting strong completeness confluency finite termination decision algorithms 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Sergey G. Vorobyov
    • 1
  1. 1.Program Systems Institute of the USSR Academy of SciencesPereslavl-ZalesskyUSSR

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