Annals of Mathematics and Artificial Intelligence

, Volume 20, Issue 1, pp 1–12

On kernels, defaults and even graphs


  • Yannis Dimopoulos
    • Max‐Planck‐Institut für Informatik
  • Vangelis Magirou
    • Athens University of Economics
  • Christos H. Papadimitriou
    • CS&EE DepartmentUniversity of California at San Diego

DOI: 10.1023/A:1018972125742

Cite this article as:
Dimopoulos, Y., Magirou, V. & Papadimitriou, C.H. Annals of Mathematics and Artificial Intelligence (1997) 20: 1. doi:10.1023/A:1018972125742


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.

Copyright information

© Kluwer Academic Publishers 1997