On kernels, defaults and even graphs
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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.
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- On kernels, defaults and even graphs
Annals of Mathematics and Artificial Intelligence
Volume 20, Issue 1-4 , pp 1-12
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- Kluwer Academic Publishers
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- 1. Max‐Planck‐Institut für Informatik, Im Stadtwald, 66123, Saarbrücken, Germany
- 2. Athens University of Economics, 76 Patission Str., 10434, Athens, Greece
- 3. CS&EE Department, University of California at San Diego, La Jolla, CA, 92093‐0114, USA