Independence with Lower and Upper Probabilities
  It is shown that the ability of the interval probability representation to
capture epistemological independence is severely limited. Two events are
epistemologically independent if knowledge of the first event does not alter
belief (i.e., probability bounds) about the second. However, independence in
this form can only exist in a 2-monotone probability function in degenerate
cases i.e., if the prior bounds are either point probabilities or entirely
vacuous. Additional limitations are characterized for other classes of lower
probabilities as well. It is argued that these phenomena are simply a matter of
interpretation. They appear to be limitations when one interprets probability
bounds as a measure of epistemological indeterminacy (i.e., uncertainty arising
from a lack of knowledge), but are exactly as one would expect when probability
intervals are interpreted as representations of ontological indeterminacy
(indeterminacy introduced by structural approximations). The ontological
interpretation is introduced and discussed.
