 For any set \(A\) of sentences, let \([A]\) denote the set of possible worlds that contain \(A\) as a subset, and similarly for any sentence \(p\) let \([p]\) be the set of possible worlds that contain \(p\) as an element. If \(A\) is inconsistent, then \([A] = \varnothing\). Otherwise, \([A]\) is a non-empty set of possible worlds. (It is assumed that \(\bigcap \varnothing\) is equal to the whole language.) If \(K\) is a belief set, then \(\bigcap[K] = K\).