A Human Oriented Logic for Automatic Theorem Proving

Unknown author (1972-10-01)

The automation of first order logic has received comparatively little attention from researcher intent upon synthesizing the theorem proving mechanism used by humans. The dominant point of view [15], [18] has been that theorem proving on the computer should be oriented to the capabilities of the computer rather than to the human mind and therefore one should not be afraid to provide the computer with a logic that humans might find strange and uncomfortable. The preeminence of this point of view is not hard to explain since until now the most successful theorem proving programs have been machine oriented. Nevertheless, there are at least two reasons for being dissatisfied with the machine oriented approach. First, a mathematician often is interested more in understanding the proof of a proposition than in being told that the propositions true, for the insight gained from an understanding of the proof can lead to the proof of additional propositions and the development of new mathematical concepts. However, machine oriented proofs can appear very unnatural to a human mathematician thereby providing him with little if any insight. Second, the machine oriented approach has failed to produce a computer program which even comes close to equaling a good human mathematician in theorem proving ability; this leads one to suspect that perhaps the logic being supplied to the machine is not as efficient as the logic used by humans. The approach taken in this paper has been to develop a theorem proving program as a vehicle for gaining a better understanding of how humans actually prove theorems. The computer program which has emerged from this study is based upon a logic which appears more "natural" to a human (i.e., more human oriented). While the program is not yet the equal of a top flight human mathematician, it already has given indication (evidence of which is presented in section 9) that it can outperform the best machine oriented theorem provers.