Automated Theorem Proving and Logic Programming

Abstract We present a detailed review of the elements of automated theorem proving, emphasizing certain aspects of especial interest to the logic programming community. In particular, we focus heavily on how an automated theorem-proving program can treat equality in a natural and yet effective manner, and how such a program can use strategy to control its reasoning in a sophisticated fashion. With the objective of significantly increasing the scope of logic programming, perhaps some unusually inventive researcher can adapt various procedures we review in this article, and adapt them in a way that preserves most of the speed offered by logic programming. In turn, although our expertise rests far more in automated theorem proving, we include certain observations concerning the value of logic programming to automated theorem proving in general. In other words, a natural symbiosis between automated theorem proving and logic programming exists, which nicely completes the circle, since logic programming was born of automated theorem proving.

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