# Grammar Equations

arXiv: https://arxiv.org/abs/2106.07485 · HTML: https://mlsanity.com/paper/2106.07485/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 24 references that are in the map.
- First posted on arXiv 14 Jun 2021.

## Builds on (most cited first, 10 of 10)

- [Foundations for Near-Term Quantum Natural Language Processing](https://mlsanity.com/paper/2012.03755/) (2020)
- [The Frobenius anatomy of word meanings I: subject and object relative pronouns](https://mlsanity.com/paper/1404.5278/) (2014)
- [The Mathematics of Text Structure](https://mlsanity.com/paper/1904.03478/) (2019)
- [A CCG-Based Version of the DisCoCat Framework](https://mlsanity.com/paper/2105.07720/) (2021)
- [The Frobenius anatomy of word meanings II: possessive relative pronouns](https://mlsanity.com/paper/1406.4690/) (2014)
- [A Study of Entanglement in a Categorical Framework of Natural Language](https://mlsanity.com/paper/1405.2874/) (2014)
- [Meaning updating of density matrices](https://mlsanity.com/paper/2001.00862/) (2020)
- [An alternative Gospel of structure: order, composition, processes](https://mlsanity.com/paper/1307.4038/) (2013)
- [Internal Wiring of Cartesian Verbs and Prepositions](https://mlsanity.com/paper/1811.05770/) (2018)
- [Lambek pregroups are Frobenius spiders in preorders](https://mlsanity.com/paper/2105.03038/) (2021)

## Built on by (most cited first, 7 of 7)

- [Compositionality as we see it, everywhere around us](https://mlsanity.com/paper/2110.05327/) (2021)
- [Distilling Text into Circuits](https://mlsanity.com/paper/2301.10595/) (2023)
- [Language-independence of DisCoCirc's Text Circuits: English and Urdu](https://mlsanity.com/paper/2208.10281/) (2022)
- [Talking Space: inference from spatial linguistic meanings](https://mlsanity.com/paper/2109.06554/) (2021)
- [A Pipeline For Discourse Circuits From CCG](https://mlsanity.com/paper/2311.17892/) (2023)
- [Quantum Methods for Managing Ambiguity in Natural Language Processing](https://mlsanity.com/paper/2504.00040/) (2025)
- [Efficient Generation of Parameterised Quantum Circuits from Large Texts](https://mlsanity.com/paper/2505.13208/) (2025)

## Abstract (arXiv)

Diagrammatically speaking, grammatical calculi such as pregroups provide wires between words in order to elucidate their interactions, and this enables one to verify grammatical correctness of phrases and sentences. In this paper we also provide wirings within words. This will enable us to identify grammatical constructs that we expect to be either equal or closely related. Hence, our work paves the way for a new theory of grammar, that provides novel `grammatical truths'. We give a nogo-theorem for the fact that our wirings for words make no sense for preordered monoids, the form which grammatical calculi usually take. Instead, they require diagrams -- or equivalently, (free) monoidal categories.