The end of Section 3.1 states, "Given L define the partial order \leq on D to be such that d \leq d' if either d,d' \in N, d,d' \in G, or d \in N and d' \in G."  The relation \leq is actually just a pre-order.  This error does not affect any of the results since the paper never uses the antisymmetric property, which the relation lacks.