15-815 Automated Theorem Proving
Lecture 25: Congruence Closure

An important component for many decision procedures, as used in theorem provers, is congruence closure which efficiently solves the question if a set of ground equations implies other ground equations. We choose an abstract presentation due to Bachmair, Tiwari, and Vigneron [BTV03] which relates congruence to (ground) completion. We also discuss how congruence closure may be used in the context of a proof-checking system.

[BTV03] Leo Bachmair, Ashish Tiwari, and Laurent Vigneron.
Abstract Congruence Closure.
Journal of Automated Reasoning, 31:129-168, 2003.

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