Abstract
We present an expression-directed and renaming-invariant approach to linear resolution. eliminating the ‘usual’ annoyances involving the handling of variables and substitutions and culminating in strengthened forms of mgu- and lifting-lemmas. Subsequently, we give a twist to lifting ground derivations, obtaining three basic theorems on the tree of all ground derivations represented by an SLD tree. These provide fast proofs for standard theorems, results on infinite derivations, greatest fixed points, and answer the question of when these are reached after ω steps in the downward fixed-point hierarchy.
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