SLDNFA: An Abductive Procedure for Normal Abductive Programs

The abductive procedure SLDNFA is presented for normal abductive programs. The procedure is a natural extension of SLDNF-resolution and incorporates both abduction and negation as failure. The main diierence between our approach and existing procedures is the treatment of non-ground abductive goals. The soundness of SLD-NFA wrt 3-valued completion semantics is proven. Also a completeness theorem is provided (where completeness here refers to a speciic notion of generating all minimal abductive solutions). Several variants of SLDNFA are given, which generate even more solutions. For these procedures, more powerful completeness theorems can be formulated. The research presented here, provides a simple framework of abductive procedures, in which a number of parameters can be set, in order to t the abduction procedure to the application under consideration.

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