It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic. We show that the fragment of interest is equivalent to the recently introduced {\it extended tensor type calculus}. This provides the former not only with some alternative syntax and intuitive geometric representation, but also with an intrinsic deductive system, which has been absent.

翻译：已知不同范畴语法在一阶乘法线性逻辑的某个片段中存在表层表示。我们证明该相关片段等价于近期提出的扩展张量类型演算。这不仅为该片段提供了替代性句法及直观的几何表示，还赋予其此前缺失的内在演绎系统。