Since the seminal work of J. A. Robinson on resolution, many lifting lemmas for simplifying proofs of completeness of resolution have been proposed in the literature. In the logic programming framework, they may also help to detect some infinite derivations while proving goals under the SLD-resolution. In this paper, we first generalize a version of the lifting lemma, by extending the relation "is more general than" so that it takes into account only some arguments of the atoms. The other arguments, which we call neutral arguments, are disregarded. Then we propose two syntactic conditions of increasing power for identifying neutral arguments from mere inspection of the text of a logic program.
In the framework of Lloyd and Shepherdson [16], partial deduction involves the creation of SLDNF-trees for a given program and some goals up to certain halting points. This paper identifies the relation between halting criteria for partial deduction and loop checking (as formalized in [1]). For simplicity, we consider only positive programs and SLD-resolution here. It appears that loop checks for partial deduction must be complete, whereas traditionally, the soundness of a loop check is more important. However, it is also shown that sound loop checks can contribute to improve partial deduction. Finally, a class of complete loop checks suitable for partial deduction is identified.  A partial evaluator for Prolog takes a program and a query and return a program specialized for all instances of that query. The intention is that the generated program will execute more efficiently than the original one for those instances.