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Journal of Logic and Computation 1991 1(6):811-834; doi:10.1093/logcom/1.6.811
© 1991 by Oxford University Press
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Original Articles

A Complete Axiomatization of the Three valued Completion of Logic Programs

ROBERT F. STÄRK

Institut für Informatik und angewandte Mathematik, Universität Bern Längassstrasse 51, CH-3012 Bern, Switzerland

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 {varepsilon}-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.

Keywords: Logic programming; three-valued logic; negation as failure; SLDNF-resolution; sequent calculus


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