The discussion of the (weak and strong) generative capacity of CCG and TAG has recently been revived (Hockenmaier and Young, 2008;Koller and Kuhlmann, 2009).
koller and kuhlmann (2009) have shown that CCGs that are pure (i.e., they can only use generalized composition rules, and there is no way to restrict the instances of these rules that may be used) and first-order (i.e., all argument categories are atomic) can not generate a n b n c n .