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Mathematical foundations for a compositional distributional model of meaning
| Venue: | LINGUISTIC ANALYSIS (LAMBEK FESTSCHRIFT |
| Citations: | 86 - 18 self |
BibTeX
@INPROCEEDINGS{Coecke_mathematicalfoundations,
author = {Bob Coecke and Mehrnoosh Sadrzadeh and Stephen Clark},
title = { Mathematical foundations for a compositional distributional model of meaning},
booktitle = {LINGUISTIC ANALYSIS (LAMBEK FESTSCHRIFT},
year = {},
pages = {345--384},
publisher = {}
}
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Abstract
We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, for which we rely on the algebra of Pregroups, introduced by Lambek. This mathematical framework enables us to compute the meaning of a well-typed sentence from the meanings of its constituents. Concretely, the type reductions of Pregroups are ‘lifted’ to morphisms in a category, a procedure that transforms meanings of constituents into a meaning of the (well-typed) whole. Importantly, meanings of whole sentences live in a single space, independent of the grammatical structure of the sentence. Hence the inner-product can be used to compare meanings of arbitrary sentences, as it is for comparing the meanings of words in the distributional model. The mathematical structure we employ admits a purely diagrammatic calculus which exposes how the information flows between the words in a sentence in order to make up the meaning of the whole sentence. A variation of our ‘categorical model ’ which involves constraining the scalars of the vector spaces to the semiring of Booleans results in a Montague-style Boolean-valued semantics.
Keyphrases
mathematical foundation compositional distributional model whole sentence mathematical framework mathematical structure distributional model well-typed sentence grammatical type arbitrary sentence type reduction diagrammatic calculus single space compositional theory distributional theory grammatical structure montague-style boolean-valued semantics categorical model vector space model booleans result
