# Cobordisms and commutative categorial grammars

arXiv: https://arxiv.org/abs/2107.08728 · HTML: https://mlsanity.com/paper/2107.08728/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 21 references that are in the map.
- First posted on arXiv 19 Jul 2021.

## Builds on (most cited first, 1 of 1)

- [The Frobenius anatomy of word meanings I: subject and object relative pronouns](https://mlsanity.com/paper/1404.5278/) (2014)

## Built on by (most cited first, 2 of 2)

- [First order linear logic and tensor type calculus for categorial grammars](https://mlsanity.com/paper/2112.15253/) (2021)
- [Making first order linear logic a generating grammar](https://mlsanity.com/paper/2206.08955/) (2022)

## Abstract (arXiv)

We propose a concrete surface representation of abstract categorial grammars in the category of word cobordisms or cowordisms for short, which are certain bipartite graphs decorated with words in a given alphabet, generalizing linear logic proof-nets. We also introduce and study linear logic grammars, directly based on cobordisms and using classical multiplicative linear logic as a typing system.