 Another important notion, crucial in the study of social interaction, is  common knowledge.  This concept can be described as what everybody knows, everybody knows that everybody knows, everybody knows that everybody knows that everybody knows, and so on. Just as with distributed knowledge, this notion does not require the addition of further semantic components: the individual epistemic indistinguishability relations already provide everything that is needed to make the definition explicit. If one defines an epistemic relation for the “everybody knows” modality in the natural way \((R_E := \bigcup_{i \in \ttA} R_i)\), and then define \(R_C\) as the transitive closure of \(R_E\),