This comes from an email by Jean Dezert. We have briefly discussed about it and agree this is an excellent topic for our group to discuss. I'm basically posting his email as is:
I suggest as an interesting possible topic, to study in deep the consistency and foundations of belief functions theories to warn the community about very serious problems when using them. In clear, DST is NOT a consistent generalization of Bayesian reasoning since it is incompatible with probability calculus and classical notion of pooling evidences. So we must see them as only more or less efficient approximate reasoning techniques and no legitimacy with probability calculus can serve to establish the solidity of their foundations. These conclusions are based on my own recent research results and corroborate very few papers suspecting this serious problem (see Zadeh, Pear, Gelman and Pei Wang papers for examples).
I do think that it becomes more than urgent to put this clearly in light to warn the young researchers entering in this field. So, my message is clear: we can use these techniques at our own risk. Their interest must however not be discarded because probability calculus is not well adapted to model human reasoning and that's why other techniques need to be developed. But these techniques must be consistent with common sense at least in simple examples, and it can be shown that DS rule suffers of such serious consistency problem.