Abduction in logic programming as second-order quantifier elimination

Abstract. It is known that skeptical abductive explanations with re-spect to classical logic can be characterized semantically in a natural way as formulas with second-order quantifiers. Computing explanations is then just elimination of the second-order quantifiers. By using appli-cation patterns and generalizations of second-order quantification, like literal projection, the globally weakest sufficient condition and circum-scription, we transfer these principles in a unifying framework to ab-duction with three non-classical semantics of logic programming: stable model, partial stable model and well-founded semantics. New insights are revealed about abduction with the partial stable model semantics.