Proving Theorems by Pattern Recognition, II

Abstract

Theoretical questions concerning the possibilities of proving theorems by machines are considered here from the viewpoint that emphasizes the underlying logic. A proof procedure for the predicate calculus is given that contains a few minor peculiar features. A fairly extensive discussion of the decision problem is given, including a partial solution of the (x) (Ey) (z) satis fiability case, an alternative procedure for the (x) (y) (Ez) case, and a rather detailed treatment of Skolem’s case. In connection with the (x) (Ey) (z) case, an amusing combinatorial problem is suggested in Section 4.1. Some simple mathematical examples are considered in Section VI.

First published in Bell System Technical Journal, vol, 40, pp, 1–41 © 1961 AT&T. Reproduced by special permission.