A logic-based tractable approximation of probability

We provide a logical framework in which a resource-bounded agent can be seen to perform approximations of probabilistic reasoning. Our main results read as follows. First, we identify the conditions under which propositional probability functions can be approximated by a hierarchy of depth-bounded belief functions. Second, we show that under rather palatable restrictions, our approximations of probability lead to uncertain reasoning which, under the usual assumptions in the field, qualifies as tractable.