 Impossible worlds are useful within this approach because these would-be possibilities often turn out to be impossible. Our beliefs are often (covertly) inconsistent with one another. Moreover, our knowledge and belief is not closed under (classical) logical consequence: we do not know or believe all consequences of what we know or believe. It is hard to accommodate these features using only possible worlds. Possible worlds models usually generate the problem of logical omniscience (see  epistemic logic),  which we will discuss in  section 5.3.