The Decidability of the First-Order Theory of the Knuth-Bendix Order in the Case of Unary Signatures

  • Konstantin Korovin
  • Andrei Voronkov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2556)


We show that the first-order theory of any Knuth-Bendix order in the case of the signatures consisting of unary function symbols and constants is decidable. Our decision procedure uses interpretation of unary terms as trees and uses decidability of the weak monadic second-order theory of binary trees. One area of applications of our result is automated deduction, since using the first-order theory of the Knuth-Bendix orders we can decide an important class of ordering constraints. umaiy uccs.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Konstantin Korovin
    • 1
  • Andrei Voronkov
    • 1
  1. 1.University of ManchesterManchester

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