System Z: a natural ordering of defaults with tractable applications to nonmonotonic reasoning

  • Authors:

  • Judea Pearl

  • Affiliations:

  • University of California, Los Angeles

  • Venue:
  • TARK '90 Proceedings of the 3rd conference on Theoretical aspects of reasoning about knowledge
  • Year:
  • 1990

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Abstract

Recent progress towards unifying the probabilistic and preferential models semantics for non-monotonic reasoning has led to a remarkable observation: Any consistent system of default rules imposes an unambiguous and natural ordering on these rules which, to emphasize its simple and basic character, we term "Z-ordering." This ordering can be used with various levels of refinement, to prioritize conflicting arguments, to rank the degree of abnormality of states of the world, and to define plausible consequence relationships. This paper defines the Z-ordering, briefly mentions its semantical origins, and illustrates two simple entailment relationships induced by the ordering. Two extensions are then described, maximum-entropy and conditional entailment, which trade in computational simplicity for semantic refinements.