## Motivation

We consider two contrasting approaches to language:

- The symbolic approach provided by Lambek's pregroups, in which the compositional structure of language is a central element.
- The distributional approach in which words are assigned meanings in some high dimensional real vector space, typically based on some statistical analysis.

We observe that both pregroups and the category of real finite dimensional vector spaces in which distributional models live are compact monoidal categories. This observation allows us to connect sentence structure to corresponding linear maps. These linear maps can then be use to derive the meaning vector for a given sentence from the meanings of its component parts, opening up scope for a compositional, distribution theory of meaning.

The compact structure of the categories involved allows us to use string diagrams analyse the flow of meaning in language constructs. Our abstract categorical perspective allows us to exploit analogies with quantum computation in our approach to language, and enables alternative concrete models of meaning beyond vector spaces.

## Papers

- J. Lambek. The mathematics of sentence structure. American Mathematics Monthly, 65, 1958.
- J. Lambek. Type grammar revisited. Logical Aspects of Computational Linguistics, 1582, 1999.
- J. Lambek. Compact monoidal categories from linguistics to physics. In B. Coecke, editor, New structures for physics, Lecture Notes in Physics, pages 451–469. Springer, 2010.
- J. Lambek. Iterated Galois connections in arithmetics and linguistics. Galois Connections and Applications, Mathematics and its Applications, 565, 2004.
- Bob Coecke, Mehrnoosh Sadrzadeh, Stephen Clark, "Mathematical Foundations for Distributed Compositional Model of Meaning" 2010
- Mehrnoosh Sadrzadeh, Stephen Clark, Bob Coecke, "The Frobenius anatomy of word meanings I: subject and object relative pronouns", 2014
- Mehrnoosh Sadrzadeh, Stephen Clark, Bob Coecke, "The Frobenius anatomy of word meanings II: possessive relative pronouns", 2014
- Dimitri Kartsaklis, Mehrnoosh Sadrzadeh, Stephen Pulman, Bob Coecke, "Reasoning about Meaning in Natural Language with Compact Closed Categories and Frobenius Algebras", 2014
- Dimitri Kartsaklis, Mehrnoosh Sadrzadeh, "A Study of Entanglement in a Categorical Framework of Natural Language", 2014
- Bob Coecke, Edward Grefenstette, Mehrnoosh Sadrzadeh, "Lambek vs. Lambek: Functorial Vector Space Semantics and String Diagrams for Lambek Calculus", 2013
- Robin Piedeleu, Dimitri Kartsaklis, Bob Coecke, Mehrnoosh Sadrzadeh, "Open System Categorical Quantum Semantics in Natural Language Processing", 2015

## People

- Bob Coecke
- Mehrnoosh Sadrzadeh
- Martha Lewis
- Dan Marsden
- Dimitri Kartsaklis
- William Zeng
- Robin Piedeleu
- Edward Grefenstette