Density Matrices with Metric for Derivational Ambiguity

Abstract

Recent work on vector-based compositional natural language semantics has proposed the use of density matrices to model lexical ambiguity and (graded) entailment (e.g. Piedeleu et al 2015, Bankova et al 2016, Sadrzadeh et al 2018. Ambiguous word meanings, in this work, are represented as mixed states, and the compositional interpretation of phrases out of their constituent parts takes the form of a strongly monoidal functor sending the derivational morphisms of a pregroup syntax to linear maps in FdHilb.Our aims in this paper are twofold. First, we replace the pregroup front end by a Lambek categorial grammar with directional implications expressing a word's selectional requirements. By the Curry-Howard correspondence, the derivations of the grammar's type logic are associated with terms of the (ordered) linear lambda calculus; these terms can be read as programs for compositional meaning assembly with density matrices as the target semantic spaces.Secondly, we use the density matrix spaces to model the ubiquitous derivational ambiguity of natural language syntax, opening up the possibility of an integrated treatment of lexical and derivational forms of ambiguity.

A mathematical neural process model of language comprehension, from syllable to sentence

“…For concrete worked out example of these ideas, see (Bradley, 2018) (Sadrzadeh, Clark, & Coecke, 2013) (Grefenstette, Sadrzadeh, Clark, Coecke, & Pulman, 2010) (Grefenstette & Sadrzadeh, 2011b) (Grefenstette & Sadrzadeh, 2011a). An extension of these principles, to handle structural ambiguities such as that in the sentence -I saw the people with binoculars, (Correia, Moortgat, & Stoof, 2020) develop an approach that imbibes density matrices (or tensors) with directional properties. Therefore, in spite of words having identical syntactic and semantic properties, the structure dependent meaning changes based on syntax.…”