  First-order multiplicative intuitionistic linear logic (MILL1) can be seen as
an extension of the Lambek calculus. In addition to the fragment of MILL1 which
corresponds to the Lambek calculus (of Moot & Piazza 2001), I will show
fragments of MILL1 which generate the multiple context-free languages and which
correspond to the Displacement calculus of Morrilll e.a.
