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The Decidability of the First-Order Theory of Knuth-Bendix Order

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Automated Deduction – CADE-20 (CADE 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3632))

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Abstract

Two kinds of orderings are widely used in term rewriting and theorem proving, namely recursive path ordering (RPO) and Knuth-Bendix ordering (KBO). They provide powerful tools to prove the termination of rewriting systems. They are also applied in ordered resolution to prune the search space without compromising refutational completeness. Solving ordering constraints is therefore essential to the successful application of ordered rewriting and ordered resolution. Besides the needs for decision procedures for quantifier-free theories, situations arise in constrained deduction where the truth value of quantified formulas must be decided. Unfortunately, the full first-order theory of recursive path orderings is undecidable. This leaves an open question whether the first-order theory of KBO is decidable. In this paper, we give a positive answer to this question using quantifier elimination. In fact, we shall show the decidability of a theory that is more expressive than the theory of KBO.

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Authors and Affiliations

  1. Computer Science Department, Stanford University, Stanford, CA, 94305-9045, USA

    Ting Zhang, Henny B. Sipma & Zohar Manna

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  1. Ting Zhang
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  2. Henny B. Sipma
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  3. Zohar Manna
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Editors and Affiliations

  1. Technical University of Catalonia, Barcelona

    Robert Nieuwenhuis

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Zhang, T., Sipma, H.B., Manna, Z. (2005). The Decidability of the First-Order Theory of Knuth-Bendix Order. In: Nieuwenhuis, R. (eds) Automated Deduction – CADE-20. CADE 2005. Lecture Notes in Computer Science(), vol 3632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11532231_10

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  • DOI: https://doi.org/10.1007/11532231_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28005-7

  • Online ISBN: 978-3-540-31864-4

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