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

Abstract

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.

DOI: 10.1007/s10472-012-9294-x

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Cite this paper

@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} }