# Vector Space Semantics for Lambek Calculus with Soft Subexponentials

arXiv: https://arxiv.org/abs/2111.11331 · HTML: https://mlsanity.com/paper/2111.11331/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 29 references that are in the map.
- First posted on arXiv 22 Nov 2021.

## Builds on (most cited first, 6 of 6)

- [Open Sesame: Getting Inside BERT's Linguistic Knowledge](https://mlsanity.com/paper/1906.01698/) (2019)
- [Evaluating Neural Word Representations in Tensor-Based Compositional Settings](https://mlsanity.com/paper/1408.6179/) (2014)
- [Undecidability of the Lambek calculus with a relevant modality](https://mlsanity.com/paper/1601.06303/) (2016)
- [A Typedriven Vector Semantics for Ellipsis with Anaphora using Lambek Calculus with Limited Contraction](https://mlsanity.com/paper/1905.01647/) (2019)
- [Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality (Extended Abstract)](https://mlsanity.com/paper/2101.10486/) (2021)
- [Anaphora and Ellipsis in Lambek Calculus with a Relevant Modality: Syntax and Semantics](https://mlsanity.com/paper/2110.10641/) (2021)

## Built on by (most cited first, 3 of 3)

- [A Quantum Natural Language Processing Approach to Pronoun Resolution](https://mlsanity.com/paper/2208.05393/) (2022)
- [Assessing the Unitary RNN as an End-to-End Compositional Model of Syntax](https://mlsanity.com/paper/2208.05719/) (2022)
- [Towards Transparency in Coreference Resolution: A Quantum-Inspired Approach](https://mlsanity.com/paper/2312.00688/) (2023)

## Abstract (arXiv)

We develop a vector space semantics for Lambek Calculus with Soft Subexponentials, apply the calculus to construct compositional vector interpretations for parasitic gap noun phrases and discourse units with anaphora and ellipsis, and experiment with the constructions in a distributional sentence similarity task. As opposed to previous work, which used Lambek Calculus with a Relevant Modality the calculus used in this paper uses a bounded version of the modality and is decidable. The vector space semantics of this new modality allows us to meaningfully define contraction as projection and provide a linear theory behind what we could previously only achieve via nonlinear maps.