Alternating fixpoint tailored to magic programs

We study applying the magic-sets transformation techniques to Datalog programs with negation that may not have 2-valued well-founded models. In this general setting we encounter the problem that the well-founded model of the original program does not always agree with the well-founded model of the magic program derived by commonly used left-to-right sips on the query. In order to fix this disagreement we present a novel method that is obtained by slightly and naturally tailoring Van Gelder's alternating fixpoint technique to a magic program.