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：已知不同组合语法在第一阶段乘法线性逻辑的片段中具有表面表现。我们展示了该片段与最近引入的“扩展张量类型演算”是等效的。这不仅为前者提供了一些替代语法和直观的几何表现，而且还具有一种固有的推理系统，这是缺少的。