Abstract
Uncertainty can be formalized in three increasingly stronger frameworks based on possible worlds: qualitative (Kripke structures), quantitative (Dempster - Shafer distributions) and hierarchical (two-level probabilities). It is possible then to compare and connect in a systematic way all the methods proposed in these frameworks for knowledge updating and decision-making. It is shown that the Gärdenfors procedure for belief revision under qualitative uncertainty defines a specific qualitative possibility distribution and that several revision rules can be exhibited correspondingly for quantitative and hierarchical uncertainty. It is also shown that Gilboa-Schmeidler's non-additive probabilistic expected utility is identical with two-level probabilistic expected utility when the decision-maker has infinite aversion to second level uncertainty.
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