Plausibility measures and default reasoning

Nir Friedman*, Joseph Y. Halpern

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

93 Scopus citations

Abstract

We introduce a new approach to modeling uncertainty based on plausibility measures. This approach is easily seen to generalize other approaches to modeling uncertainty, such as probability measures, belief functions, and possibility measures. We focus on one application of plausibility measures in this paper: default reasoning. In recent years, a number of different semantics for defaults have been proposed, such as preferential structures, ε-semantics, possibilistic structures, and κ-rankings, that have been shown to be characterized by the same set of axioms, known as the KLM properties. While this was viewed as a surprise, we show here that it is almost inevitable. In the framework of plausibility measures, we can give a necessary condition for the KLM axioms to be sound, and an additional condition necessary and sufficient to ensure that the KLM axioms are complete. This additional condition is so weak that it is almost always met whenever the axioms are sound. In particular, it is easily seen to hold for all the proposals made in the literature.

Original languageAmerican English
Pages (from-to)648-685
Number of pages38
JournalJournal of the ACM
Volume48
Issue number4
DOIs
StatePublished - Jul 2001

Keywords

  • Conditional logic
  • Default reasoning
  • Plausibility measures
  • Possibility measures
  • Preferential orderings nonmonotonic inference
  • ε-semantics
  • κ-rankings

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