- Published 2012 in Annals of Mathematics and Artificial Intelligence

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 $\Pi^0_1$ 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 $\Pi^0_1$ classes to give new complexity results for various questions about the well-founded semantics ${\mathit{wfs}}(P)$ of a finite predicate logic program P.

@article{Cenzer2012ACB,
title={A connection between the Cantor–Bendixson derivative and the well-founded semantics of finite logic programs},
author={Douglas A. Cenzer and Jeffrey B. Remmel},
journal={Annals of Mathematics and Artificial Intelligence},
year={2012},
volume={65},
pages={1-24}
}