 Intuitively such a formula means that the value of \(x_{n+1}\) depends only on the values of \(x_1 ,\ldots ,x_n\). The semantics of \(\mathbf{DL}\) cannot be formulated relative to single variable assignments like that of \(\mathbf{FO}\): we cannot explicate what it means for the value of \(x_{n+1}\) to depend on those of \(x_1 ,\ldots ,x_n\) with reference to a single assignment on the variables \(x_1 ,\ldots ,x_{n+1}\). For example, consider the assignment described below: 