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Oxford Quantum Talks Archive

Lambek vs Lambek - type grammars and resulting information-flows for compositional distributional meaning

Bob Coecke, University of Oxford
Flowin'Cat 2010, October 2010, University of Oxford

In recent work a recipe was proposed to compute, given the meaning vectors of words making up a sentence, a meaning vector for that sentence, by exploiting the grammatical type structure; in particular, the space in which the sentence was described can be fixed, and does not depend on the grammatical structure of the sentence (Coecke, Sardzadeh, Clark, 2010). In this proposal, one relied on the type grammars modeled by Lambek's pregroups. The mechanism of how the meanings of words interact to produce the meaning of a sentence has a purely diagrammatic form, which admits intuitive interpretation in terms of information flow. There is a remarkable resemblance with flows of information in (categorical) quantum mechanics. A great portion of this talk will be a survey of this diagrammatic idea of information flow. Our 1st new result is that the choice of the type grammar is irrelevant to the applicability of the recipe: it can also be applied for the traditional Lambek grammars in terms of residuated monoids, the even weaker Ajdukiewicz-Bar-Hillel grammars, Grishin grammars, etc. A 2nd contribution is an investigation in what the choice of a type grammar (and also, the way in which it is used) actually implies at the level of the information flows of word meanings in sentences.

[video] [streaming video] [slides]