 Barwise, Gabbay, and Hartonas (1995, 1996), appeal to the associative Lambek calculus in order to model, that is to give a semantics for, information flow itself. They define an information network \(\mathbf{N}\) as a quadruple such that \(\mathbf{N} := \langle S, C, \mapsto, \circ\rangle\), where \(S\) is a set of information states (called “sites” by the authors), \(C\) is a set of information channels, \(\mapsto\) is a ternary accessibility relation on \(S \times C \times S\), and \(\circ\) is an associative binary composition operator on \(C\). For information to flow, there must be some way in which channels compose so that information can flow from one channel to another. The authors specify the following constraint on serial channel composition. For all channels \(a\) and \(b\):