## Equational Inference, Canonical Proofs, And Proof Orderings (1992)

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Venue: | Journal of the ACM |

Citations: | 30 - 11 self |

### BibTeX

@ARTICLE{Bachmair92equationalinference,,

author = {Leo Bachmair and Nachum Dershowitz},

title = {Equational Inference, Canonical Proofs, And Proof Orderings},

journal = {Journal of the ACM},

year = {1992},

volume = {41},

pages = {236--276}

}

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### Abstract

We describe the application of proof orderings---a technique for reasoning about inference systems---to various rewrite-based theorem-proving methods, including re#nements of the standard Knuth-Bendix completion procedure based on critical pair criteria; Huet's procedure for rewriting modulo a congruence; ordered completion #a refutationally complete extension of standard completion#; and a proof by consistency procedure for proving inductive theorems. # This is a substantially revised version of the paper, #Orderings for equational proofs," co-authored with J. Hsiang and presented at the Symp. on Logic in Computer Science #Boston, Massachusetts, June 1986#. It includes material from the paper #Proof by consistency in equational theories," by the #rst author, presented at the ThirdAnnual Symp. on Logic in Computer Science #Edinburgh, Scotland, July 1988#. This researchwas supported in part by the National Science Foundation under grants CCR-89-01322, CCR-90-07195, and CCR-90-24271. 1 ...