MPI-INF/SWS Research Reports 1991-2021

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On kernels, defaults and even graphs

Dimopoulos, Yannis and Magirou, Vangelis and Papadimitriou, Christos

June 1993, 11 pages.

Status: available - back from printing

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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  AUTHOR = {Dimopoulos, Yannis and Magirou, Vangelis and Papadimitriou, Christos},
  TITLE = {On kernels, defaults and even graphs},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-93-226},
  MONTH = {June},
  YEAR = {1993},
  ISSN = {0946-011X},