With respect to generative capacity, Buszkowski (2001) shows that the pregroup grammars are equivalent to context-free grammars. They share, in other words, the expressive limitations of the original categorial grammars. To overcome these limitations different strategies have been pursued, including lexical rules (metarules), derivational constraints, controlled forms of commutativity, and products of pregroups. The Studia Logica special issue (Buszkowski and Preller 2007) and the monograph Lambek 2008 give a good picture of current research.