A Direct Proof of the Completeness of SLDNF-Resolution

We give a direct proof of the following theorem: If a goal Gσ is a logical consequence of the partial completion of an arbitrary normal logic program P , then each fair, non-floundering SLDNF-tree T for G yields an answer substitution θ which is more general than σ. If the negation G is a logical consequence of the partial completion of P , then T is finitely failed. A tree is fair, if each negative main branch ends in failure or each literal in the branch is selected at a certain point. A tree is floundering, if it contains a positive node that consists of negative, non-ground literals only.