Plausibility Measures and Default Reasoning
N. Friedman and J. Y. Halpern
To appear in Journal of the ACM.
Earlier version appeared under the title Plausibility
Measures and Default Reasoning in Thirteenth
National Conf. on Artificial Intelligence (AAAI96).
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, $\epsilon$-semantics, possibilistic structures, and
$\kappa$-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.
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