A connection between the Cantor–Bendixson derivative and the well-founded semantics of finite logic programs

Results of Schlipf (J Comput Syst Sci 51:64–86, 1995 ) and Fitting (Theor Comput Sci 278:25–51, 2001 ) show that the well-founded semantics of a finite predicate logic program can be quite complex. In this paper, we show that there is a close connection between the construction of the perfect kernel of a Π^0_1 class via the iteration of the Cantor–Bendixson derivative through the ordinals and the construction of the well-founded semantics for finite predicate logic programs via Van Gelder’s alternating fixpoint construction. This connection allows us to transfer known complexity results for the perfect kernel of Π^0_1 classes to give new complexity results for various questions about the well-founded semantics 𝑤𝑓𝑠(P) of a finite predicate logic program P .