Download PDFOpen PDF in browserComputational Coverage of TLG: Nonlinearity13 pages•Published: July 7, 2015AbstractWe study nonlinear connectives (exponentials) in the context of Type Logical Grammar(TLG). We devise four conservative extensions of the Displacement calculus with brackets, \DbC, \DbCM, \DbCb and \DbCbMr which contain the universal and existential exponential modalities of linear logic (\LL). These modalities do not exhibit the same structural properties as in \LL, which in TLG are especially adapted for linguistic purposes. The universal modality \univexp for TLG allows only the commutative and contraction rules, but not weakening, whereas the existential modality \exstexp allows the so-called (intuitionistic) mingle rule, which derives a restricted version of weakening called \emph{expansion}. We provide a Curry-Howard labelling for both exponential connectives. As it turns out, controlled contraction by \univexp gives a way to account for the so-called parasitic gaps, and controlled Mingle \exstexp iterability, in particular iterated coordination. Finally, the four calculi are proved to be Cut-Free but decidability is only proved for $\DbCb$, whereas for the rest the question of decidability remains open. Keyphrases: computational linguistics, cut elimination, exponentials, linear logic, sublinear logic In: Makoto Kanazawa, Lawrence S. Moss and Valeria de Paiva (editors). NLCS'15. Third Workshop on Natural Language and Computer Science, vol 32, pages 51-63.
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