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.

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