The notion of SLDNF-resolution gives a theoretical foundation for implementation of logic programming languages. However, a major drawback of SLDNF-resolution is that for negative queries it can not produce answers other than yes or no. Thus, only a limited class of negative queries can be handled. This thesis defines an extension of SLDNF-resolution, called SLDFA-resolution, that allows to produce the same kind of answers for negative queries as for positive ones. The extension is applicable for every normal program. A proof of its soundness with respect to the completion semantics with the (weak) domain closure axiom is given.