Abstract

This paper was motivated by a need to consider the time efficiency of Prolog programs. In the context of logic programming, we consider the minimal lengths of refutations of a goal with respect to a program. We present proofs of a number of results of this type. We are especially interested in the special case of testing for membership in a given set of terms. Concomitantly, we are led to classify sets of terms in a way appropriate for these considerations. Since our results for logic programming provide lower bounds, they will immediately imply corresponding lower bounds for pure Prolog.

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