Lambek vs. Lambek: Functorial Vector Space Semantics and String Diagrams for Lambek Calculus
Bob Coecke, Edward Grefenstette, and Mehrnoosh Sadrzadeh

TL;DR
This paper explores the use of functorial vector space semantics and string diagrams to model Lambek calculus, providing a categorical framework that enhances the compositional understanding of natural language meaning.
Contribution
It demonstrates how to extend the DisCoCat model from pregroups to the original Lambek calculus using monoidal bi-closed categories and string diagrams.
Findings
Functorial passage from Lambek calculus to vector spaces is possible.
String diagrams effectively depict the flow of word meanings.
The approach generalizes the categorical semantics of natural language.
Abstract
The Distributional Compositional Categorical (DisCoCat) model is a mathematical framework that provides compositional semantics for meanings of natural language sentences. It consists of a computational procedure for constructing meanings of sentences, given their grammatical structure in terms of compositional type-logic, and given the empirically derived meanings of their words. For the particular case that the meaning of words is modelled within a distributional vector space model, its experimental predictions, derived from real large scale data, have outperformed other empirically validated methods that could build vectors for a full sentence. This success can be attributed to a conceptually motivated mathematical underpinning, by integrating qualitative compositional type-logic and quantitative modelling of meaning within a category-theoretic mathematical framework. The…
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