Soundness of abductive proof procedure with respect to constraint for non-ground abducibles

AbstractEshghi and Kowalski's abductive procedure is not, in general, sound with respect to the 2-valued stable model semantics, but sound with respect to preferred extension (Dung, 1991). We establish an abduction framework in which the integrity constraint is defined so that nonground abducibles may be extracted. By dealing with alternating fixpoint theory as in Van Gelder (1993) on the domain containing variables, we show, with respect to the proposed constraint, the soundness of a modified version of Eshghi and Kowalski's procedure where the negation as failure with non-safe rule is adopted