Reflecting on the above, one can say that the extensions of the syntactic calculus reviewed here are motivated by the desire to find a proper balance between expressivity and computational tractability: on the side of expressivity, an adequate typelogical framework should be able to recognize patterns beyond the strictly context-free; ideally, one would like to keep such expressivity compatible with a polynomial derivability problem.  Among contemporary ‘lexicalized’ grammar formalisms, there is a remarkable convergence on systems that meet these requirements: the so-called ‘mildly context-sensitive’ systems (Joshi, Vijay-Shanker, and Weir 1991).  Where can we situate the typelogical systems discussed here with respect to recognizing capacity and complexity?