A Proof-Theoretic Approach to Scope Ambiguity in Compositional Vector Space Models

TL;DR

This paper introduces a proof-theoretic method combining a polarized sequent calculus with vector space models to explain scope ambiguity in quantified sentences, providing a derivational procedure for modeling this ambiguity.

Contribution

It combines a polarized sequent calculus with vector space models to systematically explain scope ambiguity in quantified sentences.

Findings

Established a derivational procedure for scope ambiguity in vector space models.

Extended the non-associative Lambek calculus to handle quantifier scope.

Provided a formal explanation for how scope ambiguity arises in compositional models.

Abstract

We investigate the extent to which compositional vector space models can be used to account for scope ambiguity in quantified sentences (of the form "Every man loves some woman"). Such sentences containing two quantifiers introduce two readings, a direct scope reading and an inverse scope reading. This ambiguity has been treated in a vector space model using bialgebras by (Hedges and Sadrzadeh, 2016) and (Sadrzadeh, 2016), though without an explanation of the mechanism by which the ambiguity arises. We combine a polarised focussed sequent calculus for the non-associative Lambek calculus NL, as described in (Moortgat and Moot, 2011), with the vector based approach to quantifier scope ambiguity. In particular, we establish a procedure for obtaining a vector space model for quantifier scope ambiguity in a derivational way.