History and prospects for first-order automated deduction

Abstract

On the fiftieth anniversary of the appearance of Robinson’s resolution paper [57], it is appropriate to consider the history and status of theorem proving, as well as its possible future directions. Here we discuss the history of first-order theorem proving both before and after 1965, with some personal reflections. We then generalize model-based reasoning to first-order provers, and discuss what it means for a prover to be goal sensitive. We also present a way to analyze asymptotically the size of the search space of a first-order prover in terms of the size of a minimal unsatisfiable set of ground instances of a set of first-order clauses.