# Interacting Conceptual Spaces I : Grammatical Composition of Concepts

arXiv: https://arxiv.org/abs/1703.08314 · HTML: https://mlsanity.com/paper/1703.08314/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2017.

## Built on by (most cited first, 13 of 13)

- [Compositionality as we see it, everywhere around us](https://mlsanity.com/paper/2110.05327/) (2021)
- [Conversational Negation using Worldly Context in Compositional Distributional Semantics](https://mlsanity.com/paper/2105.05748/) (2021)
- [Composing Conversational Negation](https://mlsanity.com/paper/2107.06820/) (2021)
- [Distilling Text into Circuits](https://mlsanity.com/paper/2301.10595/) (2023)
- [How to make qubits speak](https://mlsanity.com/paper/2107.06776/) (2021)
- [Talking Space: inference from spatial linguistic meanings](https://mlsanity.com/paper/2109.06554/) (2021)
- [A Categorical Semantics of Fuzzy Concepts in Conceptual Spaces](https://mlsanity.com/paper/2110.05985/) (2021)
- [The Conceptual VAE](https://mlsanity.com/paper/2203.11216/) (2022)
- [From Conceptual Spaces to Quantum Concepts: Formalising and Learning Structured Conceptual Models](https://mlsanity.com/paper/2401.08585/) (2023)
- [An algebraic approach to translating Japanese](https://mlsanity.com/paper/2303.05834/) (2023)
- [Taking Cognition Seriously: A generalised physics of cognition](https://mlsanity.com/paper/2108.01229/) (2021)
- [Formalising and Learning a Quantum Model of Concepts](https://mlsanity.com/paper/2302.14822/) (2023)
- [Breaking Free Transformer Models: Task-specific Context Attribution Promises Improved Generalizability Without Fine-tuning Pre-trained LLMs](https://mlsanity.com/paper/2401.16638/) (2024)

## Abstract (arXiv)

The categorical compositional approach to meaning has been successfully applied in natural language processing, outperforming other models in mainstream empirical language processing tasks. We show how this approach can be generalized to conceptual space models of cognition. In order to do this, first we introduce the category of convex relations as a new setting for categorical compositional semantics, emphasizing the convex structure important to conceptual space applications. We then show how to construct conceptual spaces for various types such as nouns, adjectives and verbs. Finally we show by means of examples how concepts can be systematically combined to establish the meanings of composite phrases from the meanings of their constituent parts. This provides the mathematical underpinnings of a new compositional approach to cognition.