This paper deals with two important issues related to the handling of uncertain and causal information in a qualitative (or min-based) possibility theory framework. The first issue addresses encoding interventions using the possibilistic conditioning under uncertain inputs problem. More precisely, we analyze the min-based possibilistic counterpart of Jeffrey's rule of conditioning and point out that contrary to the probabilistic setting, this rule does not guarantee the existence of a solution satisfying the kinematics conditions. Then we show that this rule can naturally encode the concept of interventions in causal graphical models. Surprisingly enough, we show that when dealing with interventions the min-based counterpart of Jeffrey's rule provides a unique solution. The second issue deals with the efficient handling of sets of observations and interventions in min-based possibilistic networks, where we propose a solution based on a series of equivalent and efficient transformations on the initial causal graph.
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