Suppose that we have a group consisting of agents. Then we augment the language of propositional logic by knowledge operators (one for each agent), and form formulae in the obvious way. A statement like is read ``agent 1 knows ''2.1. The state that agent knows that agent knows is formalized by . A formula like is interpreted: ``if agent knows and then he knows ''.
Formally, the language of modal epistemic logic is defined as follows:
The modal depth of a formula is defined by the following conditions: for all ; ; ; and .