 As explained in Pacuit (2007), in order to show that this situation cannot be ‘represented’, the original paper (Brandenburger &amp; Keisler 2006) introduces a belief model. This structure represents each agent’s beliefs about the beliefs of the other agent. More precisely, a belief model is a two-sorted structure, one sort for each agent, with each sort representing an epistemic state that its agent might have. The model’s first component is its domain, given by the union of \(W_a\) and \(W_b\), the disjoint sets of states of Ann and Bob, respectively. The model also has a relation for each agent, \(R_a\) and \(R_b\), with \(R_auv\) (restricted to \(u \in W_a\) and \(v \in W_b)\) read as “in state u, Ann considers v possible, and analogous for \(R_bvu\). Again, the structure represents each agent’s beliefs about the beliefs of the other, so each collection \(\cU_b\) of subsets of \(W_b\) can be understood as a language for Ann (the beliefs she might have about Bob’s beliefs), and analogous for Bob; a full language is then defined as the union of a language for each agent. For the involved epistemic attitudes, Ann believes a given \(U \in \cU_b\) if and only if the set of states that she considers possible is a subset of U. On the other hand, an assumption is understood as the strongest belief, so Ann assumes a given \(U \in \cU_a\) if and only if the set of states she considers possible is exactly U.