Abduction in 3-Valued Logic

Abstract

Eshghi 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 a newly proposed integrity constraint allows atoms to be underivable from the theory and the abducibles. In correlation with the newly proposed integrity constraint, we present a phase of derivations augmented to Eshghi and Kowalski's abductive procedure, by which abductive unsucceeding derivations are adjusted as detections of underivability. By dealing with alternating fixpoint semantics as in[Van Gelder 93], in relation with our constraint, we see, with respect to our constraint, the soundness of Eshghi and Kowalski's abductive procedure. The motive of considering such a adjusty derivation comes up from a relaxation that there may be some atom which is not a logical consequence of P^* ∪ Δ and whose negation is neither a logical consequence. Finally the purpose of the paper is(1)to relax the constraint that all the(ground)atom or its negation should be the logical consequence of the union of a given theory and abducibles, and to get a constraint in which some atom may not be cared, (2)to extend Eshghi and Kowalski's abductive procedure to the one with an adjusty derivation phase, sound with respect to our constraint.