Critical pair criteria for completion

Authors:
Leo Bachmair;Nachum Dershowitz
Affiliations:
Department of Computer Science SUNY at Stony Brook Stony Brook, New York 11794, U.S.A.;Department of Computer Science University of Illinois at Urbana-Champaign Urbana, Illinois 61801, U.S.A.
Venue:
Journal of Symbolic Computation
Year:
1988

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Abstract

We formulate the Knuth-Bendix completion method at an abstract level, as an equational inference system, and formalize the notion of critical pair criterion using orderings on equational proofs. We prove the correctness of standard completion and verify all known criteria for completion, including those for which correctness had not been established previously. What distinguishes our approach from others is that our results apply to a large class of completion procedures, not just to a particular version. Proof ordering techniques therefore provide a basis for the design and verification of specific completion procedures (with or without criteria).