 Although Lewis introduced the technical term ‘common knowledge,’ his analysis is about belief, rather than knowledge. Indeed, Lewis offers his solution to the second problem mentioned above by introducing a distinction between actual belief and reason to believe. Reasons to believe are interpreted as potential beliefs of agents, so that the infinite hierarchy of epistemic states becomes harmless, consisting in an infinite number of states of potential belief. The solution to the first problem is given by providing a finite set of conditions that, if met, generate the infinite series of reasons to believe. Such conditions taken together represent Lewis’ official definition of common knowledge. Notice that it would be more appropriate to speak of ‘common reason to believe,’ or, at least, of ‘common belief.’ Lewis himself later acknowledges that “[t]hat term [common knowledge] was unfortunate, since there is no assurance that it will be knowledge, or even that it will be true.” Cf. (Lewis 1978, p. 44, n.13) Disregarding the distinction between reasons to believe and actual belief, we follow (Vanderschraaf 1998) to give the details of a formal account of Lewis’s definition here, and show that Lewis’ analysis does result in the common knowledge hierarchy following from a finite set of axioms. It is however debatable whether a possible worlds approach can properly render the subtleties of Lewis’ characterization. Cubitt and Sugden (2003), for example, abandon the possible worlds framework altogether and propose a different formal interpretation of Lewis in which, among other elements, the distinction between reasons to believe and actual belief is taken into account. An attempt to reconcile the two positions can be found in (Sillari 2005), where Lewis’ characterization is formalized in a richer possible worlds semantic framework where the distinction between reasons to believe and actual believe is represented.