... to the types found in G,), therefore c HaVaa) must be in Tree,. All the other types found in this tree mustbe introduced by hypotheses, and all the hypotheses introduced have tobe eliminated ... typical in learn-ability theory. The negative results for Lambek- like systemsshow that this is not the case. Even placingbounds on the complexity of the types appear-ing in the grammar may not ... limit points (to be defined in Section 3) for these classes.2 The Lambek Calculus Categorial grammar originated in (Aj-dukiewicz, 1935) and was further developed in (Bar-Hillel, 1953) and (Lambek, ...