# First order linear logic and tensor type calculus for categorial grammars

arXiv: https://arxiv.org/abs/2112.15253 · HTML: https://mlsanity.com/paper/2112.15253/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 13 references that are in the map.
- First posted on arXiv 31 Dec 2021.

## Builds on (most cited first, 4 of 4)

- [Extended Lambek calculi and first-order linear logic](https://mlsanity.com/paper/1305.6238/) (2013)
- [Hybrid Type-Logical Grammars, First-Order Linear Logic and the Descriptive Inadequacy of Lambda Grammars](https://mlsanity.com/paper/1405.6678/) (2014)
- [On embedding Lambek calculus into commutative categorial grammars](https://mlsanity.com/paper/2005.10058/) (2020)
- [Cobordisms and commutative categorial grammars](https://mlsanity.com/paper/2107.08728/) (2021)

## Abstract (arXiv)

We study relationship between first order multiplicative linear logic (MLL1), which has been known to provide representations to different categorial grammars, and the recently introduced extended tensor type calculus (ETTC). We identify a fragment of MLL1, which seems sufficient for many grammar representations, and establish a correspondence between ETTC and this fragment. The system ETTC, thus, can be seen as an alternative syntax and intrinsic deductive system together with a geometric representation for the latter. We also give a natural deduction formulation of ETTC, which might be convenient.