Plausibility Measures and Default Reasoning
N. Friedman and J. Y. Halpern
National Conf. on Artificial Intelligence (AAAI96).
See also the journal
version of this paper.
We introduce a new approach to modeling uncertainty
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, $\epsilon$-semantics,
that have been shown to be characterized by
the same set of axioms, known as the KLM properties (for Kraus, Lehmann,
Magidor). While this was viewed as a surprise, we show here that
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.
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