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Journal of Logic and Computation 1999 9(1):47-61; doi:10.1093/logcom/9.1.47
© 1999 by Oxford University Press
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A direct proof of the completeness of SLDNF-resolution

R Stärk

Institute of Informatics, University of Fribourg, Rue Faucigny 2, CH-1700 Fribourg, Switzerland. E-mail: robert.staerk@unifr.ch

We give a direct proof of the following theorem: if a goal G{sigma} 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 {theta} which is more general than {sigma}. 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.

Key words: Logic programming, negation as failure, SLDNF-resolution.


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