An answer to an open problem of Urquhart

Abstract

In this paper, we answer a question raised by A. Urquhart, namely whether a polynomial simulation of three calculi for propositional formulae with  as the only connective extends to the general case with all usual connectives. The three calculi are resolution with limited extension, a Gentzen calculus G and the same calculus extended by the analytic cut rule (called G acut). It is important that neither the Gentzen systems nor resolution are restricted to tree form. We show that p-simulations only exist between G acut and resolution with limited extension, but not between G and G acut, and between G and resolution with limited extension, respectively.