15-815 Automated Theorem Proving
Lecture 23: Equality Elimination

In this lecture we discuss the technique of equality elimination, whereby a given set of clauses is transformed until symmetry, transitivity, and congruence axioms are no longer needed. This is somewhat reminiscent of the inverse method, and has been used for reasoning both in the forward and backward directions.

It is an interesting open question how to apply equality elimination techniques to intuitionistic reasoning, but the general structure of the method seems promising.

In order to make reasoning with the resulting inference rules more directed, equality elimination is combined with ordering constraints on the variables instantiations in a sequent. By far the most popular ordering are recursive path orderings which can be generated from a total order on the function symbols and constants in a given theorem proving problem. We show the lexicographic path ordering as a particular example.

[DP01] Nachum Dershowitz and David A. Plaisted.
Handbook of Automated Reasoning, Vol.1, pp 537-610, Elsevier Science and MIT Press, 2001.
[BGV98] Leo Bachmair, Harald Ganzinger, and Andrei Voronkov.
Elimination of Equality via Transformation with Ordering Constraints.
Proceedings of the 15th International Conference on Automated Deduction, C.Kircher and H.Kirchner, eds., pp.175-190, Springer-Verlag LNAI 1421, 1998.

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Frank Pfenning