A Completeness Result for SLDNF-Resolution

Because of the possibility of floundering and infinite derivations, SLDNFresolution is, in general, not complete. The classical approach [17] to get a completeness result is to restrict the attention to normal programs P and normal goals G , such that P ∪ {G} is allowed and P is hierarchical. Unfortunately, the class of all normal programs and all normal goals meeting these requirements is not powerful enough to be of great practical importance. But after refining the concept of allowedness by taking modes [12] into account, we can broaden the notion of a hierarchical program, and thereby define a subclass of the class of normal programs and normal goals which is powerful enough to compute all primitive recursive functions without losing the completeness of SLDNF-resolution.