Formal Aspects of Computing

, Volume 2, Issue 1, pp 207–225 | Cite as

Chain properties of rule closures

  • Miki Hermann


This article introduces a generalisation of the crossed rule approach to the detection of Knuth-Bendix completion procedure divergence. It introduces closure chains, which are special rule closures constructed by means of particular substitution operations and operators, as a suitable formalism for progress in this direction. Supporting substitution algebra is developed first, followed by considerations concerning rule closures in general, concluding with an investigation of closure chain properties. Issues concerning the narrowing process are not discussed here.

Key words

Term rewriting systems Knuth-Bendix completion procedure Divergence 


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Copyright information

© BCS 1990

Authors and Affiliations

  • Miki Hermann
    • 1
  1. 1.Centre de Recherche en Informatique de NancyCNRS and INRIA-Lorraine, Campus ScientifiqueVandœuvre-lès-NancyFrance

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