Linguistic applications of first order intuitionistic linear logic

In this paper we will discuss the first order multiplicative intuitionistic fragment of linear logic, MILL1, and its applications to linguistics. We give an embedding translation from formulas in the Lambek Calculus to formulas in MILL1 and show this translation is sound and complete. We then exploit the extra power of the first order fragment to give an account of a number of linguistic phenomena which have no satisfactory treatment in the Lambek Calculus.
Keywords embedding translations  first order logic  Lambek Calculus  linear logic  locality conditions  proof nets  proof theory  quantifier scoping  relativization
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    Glyn Morrill, Oriol Valentín & Mario Fadda (2011). The Displacement Calculus. Journal of Logic, Language and Information 20 (1):1-48.
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