 Is it possible to take formally in account the insights of Lewis’ definition of common knowledge without abandoning the possible world framework? (Sillari 2005) puts forth an attempt to give a positive answer to that question by articulating in a possible world semantics the distinction between actual belief and reason to believe. As in (Cubitt and Sugden 2003), the basic epistemic operator represents reasons to believe. The idea is then to impose an awareness structure over possible worlds, adopting the framework first introduced by Fagin and Halpern (1988). Simply put, an awareness structure associates to each agent, for every possible world, a set of events of which the agent is said to be aware. An agent entertains an actual belief that a certain event occurs if and only if she has reason to believe that the event occurs and such event is in her awareness set at the world under consideration. A different avenue to the formalization of Lewis’s account of common knowledge is offered by Paternotte (2011), where the central notion is probabilistic common belief (see section 5.2 below).