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A Connection between Cantor-Bendixson Derivatives and the Well-Founded Semantics of Logic Programs

We show that there is a close connection between the construction of the perfect kernel of a Π1 class via the interation of the Cantor-Bendixson derivative through the ordinals and the construction of the well-founded semantics for logic programs via Van Gelder’s alternating fixpoint construction. This connection allows us to transfer known complexity results for the perfect kernel of Π1 classes to to give new complexity results for various questions about the well-founded semantics wfs(P ) of a logic program P .