What you always wanted to know about rigid E-unification

Abstract

This paper solves an open problem posed by a number of researchers: the construction of a complete calculus for matrix-based methods with rigid E-unification. The use of rigid E-unification and simultaneous rigid E-unification for such methods has been proposed by Gallier, Raatz and Snyder [35]. After our proof of the undecidability of simultaneous rigid E-unification [22] it has become clear that one should look for more refined techniques to deal with equality in matrix-based methods. In this article, we define a complete proof procedure for firstorder logic with equality based on an incomplete but terminating procedure for rigid E-unification. Our approach is applicable to the connection method and the tableau method and illustrated on the tableau method.KeywordsIntuitionistic LogicAutomate DeductionConnection MethodNegation Normal FormTableau MethodThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.