A New SLDNF-Tree

The concepts of Sldnf-derivation, Sldnf-refutation and Sldnf-tree deal with negation resolved by means of Negation as Failure rule and generalize those of Sld-derivation, Sld-refutation and Sldtree. The definitions given by Lloyd in [41, even though perfectly suitable to obtain the theoretical results of soundness and (a restricted form of) completeness of the Negation as Failure rule, are not applicable to all program and goal. In fact, a negative literal 7 A, by definition, can be chosen only if either a finitely failed Sldnf-tree or an Sldnf-refutation exists for A. As a consequence, we have no possibility to model, by means of an Sldnf-tree, many computational behaviours that, even if they can be considered somewhat “pathological”, are very common. Moreover, it is impossible to give an effect& fairness concept for this kind of Sldnf-tree because it involves an a priori