What is failure? An approach to constructive negation

A standard approach to negation in logic programming is negation as failure. Its major drawback is that it cannot produce answer substitutions to negated queries. Approaches to overcoming this limitation are termed constructive negation. This work proposes an approach based on construction offailed trees for some instances of a negated query. For this purpose a generalization of the standard notion of a failed tree is needed. We show that a straightforward generalization leads to unsoundness and present a correct one.The method is applicable to arbitrary normal programs. If finitely failed trees are concerned then its semantics is given by Clark completion in 3-valued logic (and our approach is a proper extension of SLDNF-resolution). If infinite failed trees are allowed then we obtain a method for the well-founded semantics. In both cases soundness and completeness are proved.