 A prototypical epistemic logic language is given by first fixing a set of propositional variables \(p_{1}\), \(p_{2}\),…. In applications of epistemic logic, propositional variables are given specific interpretations: For example, \(p_{1}\) could be taken to represent the proposition “there is a hen in the yard” and \(p_{2}\) the proposition “there is a dog in the yard”, etc. The propositional variables represent propositions which are represented in no finer detail in the formal language. As such, they are therefore often referred to as atomic propositions or simply atoms. Let Atom denote the set of atomic propositions.