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A Complete Axiomatization of the Three-Valued Completion of Logic Programs

We prove the completeness of extended SLDNF-resolution for the new class of e-programs with respect to the three-valued completion of a logic program. Not only the class of allowed programs but also the class of definite programs are contained in the class of e-programs. To understand better the three-valued completion of a logic program we introduce a formal system for three-valued logic in which one can derive exactly the three-valued consequences of the completion of a logic program. The system is proof theoretically interesting, since it is a fragment of Gentzen's sequent calculus LK.