Dependency Trees and the Strong Generative Capacity of CCG

We propose a novel algorithm for extracting dependencies from CCG derivations. Unlike earlier proposals, our dependency structures are always tree-shaped. We then use these dependency trees to compare the strong generative capacities of CCG and TAG and obtain surprising results: Although both formalisms generate the same string languages, their strong generative capacities are equivalent if we ignore word order, and incomparable if we take it into account.