 Lewis presents his account of common knowledge on pp. 52–57 of Convention. Lewis does not specify what account of knowledge is needed for common knowledge. As it turns out, Lewis’ account is satisfactory for any formal account of knowledge in which the knowledge operators \(\mathbf{K}_i, i \in N\), satisfy K1, K2, and K3. A crucial assumption in Lewis’ analysis of common knowledge is that agents know they share the same “rationality, inductive standards and background information” (Lewis 1969, p. 53) with respect to a state of affairs \(A'\), that is, if an agent can draw any conclusion from \(A'\), she knows that all can do likewise. This idea is made precise in the following: