Dependency structures are structures that are able to represent the
syntactic structure of natural language sentences. Dependency structures
are simple and independent of any grammar formalism or generating device.
This makes it possible to interpret the outcome of many grammar formalisms
as dependency structures and to compare structures of different formalisms
on a common base.
Dependency structures are not restricted to projective analyses. In the
talk I will present two measures for the level of non-projectivity of
dependency structures: the gap-degree and well-nestedness. With these two
measures it is possible to characterise the dependency structures that
correspond to derivations of Tree Adjoining Grammar (TAG). Furthermore,
this characterisation offers a way to measure the expressivity of TAG
compared to other grammar formalisms.