 Of course in many social situations, you may want to prevent common knowledge from arising, for example, if you want to keep a secret from certain others. There are also more interesting cases where everybody knows some fact, for example that a particular country possesses nuclear weapons, but where it would lead to political problems to make this fact common knowledge by making a public announcement. For a number of such social situations where maintaining privacy and ignorance are crucial, see van Eijck and Verbrugge (2009). An interesting recent development is the study of dynamic-epistemic logic-based epistemic planning, which enables us to synthesize communication protocols in order to create certain exact configurations of levels of higher-order knowledge within a group (Bolander and Andersen 2011, Löwe, Pacuit, and Witzel 2011).