English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Recent work on vector-based compositional natural language semantics hasproposed the use of density matrices to model lexical ambiguity and (graded)entailment (e.g. Piedeleu et al 2015, Bankova et al 2019, Sadrzadeh et al2018). Ambiguous word meanings, in this work, are represented as mixed states,and the compositional interpretation of phrases out of their constituent partstakes the form of a strongly monoidal functor sending the derivationalmorphisms of a pregroup syntax to linear maps in FdHilb. Our aims in this paperare threefold. Firstly, we replace the pregroup front end by a Lambekcategorial grammar with directional implications expressing a word'sselectional requirements. By the Curry-Howard correspondence, the derivationsof the grammar's type logic are associated with terms of the (ordered) linearlambda calculus; these terms can be read as programs for compositional meaningassembly with density matrices as the target semantic spaces. Secondly, weextend on the existing literature and introduce a symmetric, nondegeneratebilinear form called a "metric" that defines a canonical isomorphism between avector space and its dual, allowing us to keep a distinction between left andright implication. Thirdly, we use this metric to define density matrix spacesin a directional form, modeling the ubiquitous derivational ambiguity ofnatural language syntax, and show how this alows an integrated treatment oflexical and derivational forms of ambiguity controlled at the level of theinterpretation.

Density Matrices with Metric for Derivational Ambiguity