Linear Resolution with Selection Function

Linear resolution with selection function (SL.resolution) is a restricted form of linear resolution. The main restriction is e~ected by a selection function which chooses fro:~ each clause a sit, gle literal to be resolved upon in that clause. This and other restrictions are adapted to linear resolution from Loveland's model elimination. We show that SL-resolution achieves a substantial reduction in the generation of redundant and irrelevant derivations and does so without significantly increasing the complexity o f simplest proofs. We base our argument for the increased efficiency of SL-resolution upon precise calculation of these quantities. A more far reaching advantage of SL-resolution is its suitability fo .~. ristic search. In particular, classification trees, subgoals, lemmas, and and/~./ search tret n all be used to increase the efficiency of flndino refutations. These considerations alone sug. r. :t the superiority of SL-resolution to theorem-proving procedures constructed solely for their I1euristie attraction. From comparison with other theorem-proving methods, we conjectur~ that best proof procedures for first order logic will be obtained by further elaboration of ~ ~.-resolution.