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Oxford Quantum Talks Archive

Three compact closed categories for natural language processing

Anne Preller, University of Montpellier
Flowin'Cat 2010, October 2010, University of Oxford

Pregroup grammars are based on compact bilinear logic, a simplification of the Syntactic Calculus. Categorical semantics for pregroup grammars in compact closed 2-categories [1] has diagrams of information-flow analogue to those of categorical quantum mechanics [2]. In this talk, I try to show how three different compact closed categories capture different aspects of natural language processing. They are the category of finite functions in 2-sorted first order logic, the category of finite-dimensional semi-modules over a real interval and the category of finite-dimensional complex Hilbert-spaces. Functors that preserve the compact closed structure embed the category of two-sorted functions into the category of semi-modules and the category of Hilbert spaces.

[video] [streaming video] [slides]