Non-resolution theorem proving

Earlier work by Newell, Simon, Shaw, and Gelernter in the middle and late 1950s emphasized the heuristic approach, but the weight soon shifted to various syntactic methods culminating in a large effort on resolution type systems in the last half of the 1960s. It was about 1970 when considerable interest was revived in heuristic methods and the use of human supplied, domain dependent, knowledge. It is not my intention here to slight the great names in automatic theorem proving, and their contributions to all we do, but rather to show another side of it. For recent books on automatic theorem proving see Chang and Lee [19], Loveland [44], and Hayes [31]. Also see Nilsson's recent review article [61]. The word "resolution" has come to be associated with general purpose types of theorem provers which use very little domain dependent information and few if any special heuristics besides those of a syntactic nature. It has also connoted the use of clauses and refutation proofs. There was much hope in the late 60's that such systems, especially with various exciting improvements, such as set of support, model elimination, etc., would be powerful provers. But by the early 70's there was emerging a belief that resolution type systems could never really "hack" it, could not prove really hard mathematical theorems, without some extensive changes in philosophy.