Abduction in Logic Programming as Second-Order Quantifier Elimination

It is known that skeptical abductive explanations with respect 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 application patterns and generalizations of second-order quantification, like literal projection, the globally weakest sufficient condition and circumscription, we transfer these principles in a unifying framework to abduction 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.