 Possible world models can also be used for contraction. In contraction, a restriction on what worlds are “possible” (compatible with the agent’s beliefs) is removed. Thus, the set of possibilities is enlarged, so that the contraction of \([K]\) by \([p]\) will result in a superset of \([K]\). Furthermore, the new possibilities should be worlds in which \(p\) does not hold, i.e., they should be worlds in which \(\neg p\) holds. In the limiting case when \([K]\) and \([\neg p]\) have a non-empty intersection, no enlargement of \([K]\) is necessary to make \(\neg p\) possible, and the original belief state will therefore be unchanged. In summary, contraction should be performed according to the following rule: