Machine methods of proving logical arguments expressed in English

This paper describes a COMIT program that proves the validity of logical arguments expressed in a restricted form of ordinary English. Some special features include its ability to translate an input argument into logical notation in four progressively refined ways, of which the first pertains to propositional logic and the last three to first-order functional logic; and its ability in many cases to select the "correct" logical translation of an argument, i.e., the translation that yields the simplest proof. The logical evaluation part of the program uses a proof procedure algorithm that is an amalgam of the "one-literal clause rule" of DavisPutnam and the "matching algorithm" of Guard. It is particularly efficient in proving theorems whose matrices in conjunctive normal form contain one or more one-literal clauses (atomic wffs), but it will also prove theorems whose matrices contain only polyliteral clauses. The program has been run on the I.B.M. 7094 computers at M.I.T. and utilizes the time-sharing facilities provided by Project MAC and the Computation Center.