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A generalised quantifier theory of natural language in categorical compositional distributional semantics with bialgebras

Published online by Cambridge University Press:  10 April 2019

Jules Hedges  and
Mehrnoosh Sadrzadeh
Jules Hedges*
Affiliation:
Department of Computer Science, University of Oxford, Oxford, UK
Mehrnoosh Sadrzadeh
Affiliation:
School of Electronic Engineering and Computer Science, Queen Mary University of London, London, UK
*
*Corresponding author. Email: julian.hedges@cs.ox.ac.uk
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Abstract

Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier theory of natural language, due to Barwise and Cooper. The underlying setting is a compact closed category with bialgebras. We start from a generative grammar formalisation and develop an abstract categorical compositional semantics for it, and then instantiate the abstract setting to sets and relations and to finite-dimensional vector spaces and linear maps. We prove the equivalence of the relational instantiation to the truth theoretic semantics of generalised quantifiers. The vector space instantiation formalises the statistical usages of words and enables us to, for the first time, reason about quantified phrases and sentences compositionally in distributional semantics.

Keywords

Compositional Distributional SemanticsCompact Closed CategoriesFrobenius and BialgebrasVector Space SemanticsGeneralised QuantifiersConservativityNatural Language Semantics
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 29 , Issue 6 , June 2019 , pp. 783 - 809
Copyright
© Cambridge University Press 2019 

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