What You Always Wanted to Know about Rigid E-Unification

Authors:
Anatoli Degtyarev;Andrei Voronkov
Affiliations:
Computing Science Department, Uppsala University;Computing Science Department, Uppsala University
Venue:
Journal of Automated Reasoning
Year:
1998

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Abstract

This paper solves an open problem posed by a number of researchers: theconstruction of a complete calculus for matrix-based methods with rigidE-unification. The use of rigid E-unification and simultaneous rigidE-unification for such methods was proposed by Gallier et al., in 1987.After our proof of the undecidability of simultaneous rigid E-unification in1995. (Degtyarev and Voronkov, 1996d), it became clear that one should lookfor more refined techniques to deal with equality in matrix-based methods.In this article, we define a complete proof procedure for first-order logicwith equality based on an incomplete but terminating procedure for rigidE-unification. Our approach is applicable to the connection method and thetableau method and is illustrated on the tableau method.