A proof-theoretic approach to scope ambiguity in compositional vector space models

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 introduce one reading for each quantifier. We combine a polarised focussed sequent calculus for the non-associative Lambek Calculus NL as described in Moortgat and Moot (2011) with a non-compositional ap- proach to quantifier scope in vector space semantics introduced by Hedges and Sadrzadeh (2016) and (Sadrzadeh 2016). In particular, we obtain an automatic and compositional procedure for obtaining quantifier scope ambiguity in vector space models of meaning.