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

Authors:
Douglas Cenzer;Jeffrey B. Remmel
Affiliations:
University of Florida, Gainesville, USA 32611-8105;University of California, San Diego, La Jolla, USA 92093
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
2012

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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.