# Pregroup Grammars, their Syntax and Semantics

arXiv: https://arxiv.org/abs/2109.11237 · HTML: https://mlsanity.com/paper/2109.11237/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 47 references that are in the map.
- First posted on arXiv 23 Sep 2021.

## Builds on (most cited first, 11 of 11)

- [The Frobenius anatomy of word meanings I: subject and object relative pronouns](https://mlsanity.com/paper/1404.5278/) (2014)
- [Lambek vs. Lambek: Functorial Vector Space Semantics and String Diagrams for Lambek Calculus](https://mlsanity.com/paper/1302.0393/) (2013)
- [Towards a Formal Distributional Semantics: Simulating Logical Calculi with Tensors](https://mlsanity.com/paper/1304.5823/) (2013)
- [Evaluating Neural Word Representations in Tensor-Based Compositional Settings](https://mlsanity.com/paper/1408.6179/) (2014)
- [Compositional Distributional Semantics with Compact Closed Categories and Frobenius Algebras](https://mlsanity.com/paper/1505.00138/) (2015)
- [A Generalised Quantifier Theory of Natural Language in Categorical Compositional Distributional Semantics with Bialgebras](https://mlsanity.com/paper/1602.01635/) (2016)
- [Towards Compositional Distributional Discourse Analysis](https://mlsanity.com/paper/1811.03277/) (2018)
- [Multi-Step Regression Learning for Compositional Distributional Semantics](https://mlsanity.com/paper/1301.6939/) (2013)
- [Embedding Tarskian Semantics in Vector Spaces](https://mlsanity.com/paper/1703.03193/) (2017)
- [Exploring Semantic Incrementality with Dynamic Syntax and Vector Space Semantics](https://mlsanity.com/paper/1811.00614/) (2018)
- [A Typedriven Vector Semantics for Ellipsis with Anaphora using Lambek Calculus with Limited Contraction](https://mlsanity.com/paper/1905.01647/) (2019)

## Abstract (arXiv)

Pregroup grammars were developed in 1999 and stayed Lambek's preferred algebraic model of grammar. The set-theoretic semantics of pregroups, however, faces an ambiguity problem. In his latest book, Lambek suggests that this problem might be overcome using finite dimensional vector spaces rather than sets. What is the right notion of composition in this setting, direct sum or tensor product of spaces?