Yannis, Dimopoulos; Vangelis, Magirou; Christos, Papadimitriou
On kernels, defaults and even graphs
Extensions in prerequisite‐free, disjunction‐free default theories have been shown to be in direct correspondence with kernels of directed graphs; hence default theories without odd cycles always have a “standard” kind of an extension. We show that, although all “standard” extensions can be enumerated explicitly, several other problems remain intractable for such theories: Telling whether a non‐standard extension exists, enumerating all extensions, and finding the minimal standard extension. We also present a new graph‐theoretic algorithm, based on vertex feedback sets, for enumerating all extensions of a general prerequisite‐free, disjunction‐free default theory (possibly with odd cycles). The algorithm empirically performs well for quite large theories.
http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.pngAnnals of Mathematics and Artificial IntelligenceSpringer Journalshttp://www.deepdyve.com/lp/springer-journals/on-kernels-defaults-and-even-graphs-psWxEKv8Sb