 Consider the waiter example in more detail. Before receiving the hard information that the soda is for you (and for the sake of the example we are assuming that the waiting is dealing with hard information here), the waiter’s knowledge-base is modelled by a pair of worlds (hereafter information states) \(x\) and \(y\) such that in \(x\) you ordered the soda and your friend the espresso, and in \(y\) you ordered the espresso and your friend the soda. After receiving the hard information that the soda is for you, \(y\) is eliminated from the waiter’s knowledge-base, leaving only \(x\). As such, the reduction of the range of possibilities corresponds to an information-gain for the waiter. Consider the truth condition for agent \(\alpha\) knows that \(\phi\), written \(K_{\alpha}\phi\):