The derivation sketch below illustrates the interplay between logical and structural reasoning. As long as the gap subformula ◊□np carries the licensing ◊, the structural rules are applicable; as soon as it has found the appropriate structural position where it is selected by the transitive verb, it can be used as a regular np, given the type transition ◊□np ⊢ np which obviates the need for the inclusion postulate of the earlier account.  Related analyses of extraction based on the ‘!’ modality of Linear Logic can be found in (Barry et al. 1991), with the dereliction rule !A ⊢ A taking the place of ◊□A ⊢ A for gap introduction.