  By discussing several examples, the theory of generalized functional models
is shown to be very natural for modeling some situations of reasoning under
uncertainty. A generalized functional model is a pair (f, P) where f is a
function describing the interactions between a parameter variable, an
observation variable and a random source, and P is a probability distribution
for the random source. Unlike traditional functional models, generalized
functional models do not require that there is only one value of the parameter
variable that is compatible with an observation and a realization of the random
source. As a consequence, the results of the analysis of a generalized
functional model are not expressed in terms of probability distributions but
rather by support and plausibility functions. The analysis of a generalized
functional model is very logical and is inspired from ideas already put forward
by R.A. Fisher in his theory of fiducial probability.
