Discussion.  The basis for the DL extensions is the associative calculus L. As we saw above, a global insensitivity to phrase structure is a source of overgeneration, unless blocked by explicit island modalities.  In the development of DL nothing seems to hinge on the associativity of the base system: it would seem entirely feasible, in other words, to develop DL as an extension of a non-associative basis, allowing for the representation of constituent-structure information. In the interpreting frames, one would then start from a graded groupoid rather than a monoid. The fact that the DL framework can readily accommodate a string or tree-based point of view testifies to the versatility of the approach.