Cut-Property and Negation as Failure

What is the semantics of Negation-as-Failure in logic programming? We try to answer this question by proof-theoretic methods. A rule based sequent calculus is used in which a sequent is provable if, and only if, it is true in all three-valued models of the completion of a logic program. The main theorem is that proofs in the sequent calculus can be transformed into SLDNF-computations if, and only if, a program has the cut-property. A fragment of the sequent calculus leads to a sound and complete semantics for SLDNFresolution with substitutions. It turns out that this version of SLDNF-resolution is sound and complete with respect to three-valued possible world models of the completion for arbitrary logic programs and arbitrary goals. Since we are dealing with possibly nonterminating computations and constructive proofs, three-valued possible world models seem to be an appropriate semantics.