Reasoning with Uncertain Inputs in Possibilistic Networks

Graphical belief models are compact and powerful tools for representing and reasoning under uncertainty. Possibilistic networks are graphical belief models based on possibility theory. In this paper, we address reasoning under uncertain inputs in both quantitative and qualitative possibilistic networks. More precisely, we first provide possibilistic counterparts of Pearl's methods of virtual evidence then compare them with the possibilistic counterparts of Jeffrey's rule of conditioning. As in the probabilistic setting, the two methods are shown to be equivalent in the quantitative setting regarding the existence and uniqueness of the solution. However in the qualitative setting, Pearl's method of virtual evidence which applies directly on graphical models disagrees with Jeffrey's rule and the virtual evidence method. The paper provides the precise situations where the methods are not equivalent. Finally, the paper addresses related issues like transformations from one method to another and commutativity.