Again, I don't want to get too drawn in to the belief function discussion --
it's hard enough keeping up with all these emails. Writing a long response
would take more time than I've got. Nevertheless, I'd like to point out
that one problem with belief functions is that there is some ambiguity
about their semantics. It's not that they haven't got semantic
interpretations. Judea's probability of provability is one, but only one
among several. Another one is Philippe's TBM. Yet another is belief
functions as lower envelopes of families of probability distributions (with
plausibility functions being the corresponding upper envelopes). Yet another
is beliefs as evidence, in a sense made precise in a paper I wrote with
Ron Fagin called "Two views of belief: belief as generalized probability
and belief as evidence" (Artificial Intelligence, vol. 54, 1992,
pp.~275--317). A generalization of a point made earlier by Kathy is
that none of these semantics is necessarily appropriate for a given
application. More importantly, you can't mix and match (as people seem
to occasionally in the literature), starting out with one interpretation
and switching to another midstream. That leads you quickly to funny
answers. -- Joe
