Vector Space Semantics for Lambek Calculus with Soft Subexponentials

TL;DR

This paper introduces a vector space semantics for Lambek Calculus with Soft Subexponentials, enabling compositional interpretations of complex linguistic structures and supporting distributional similarity tasks with a decidable calculus.

Contribution

It develops a new vector space semantics for a bounded version of Lambek Calculus with Soft Subexponentials, allowing linear contraction and meaningful compositional semantics.

Findings

Successful construction of vector interpretations for parasitic gap noun phrases

Application to discourse units with anaphora and ellipsis

Experimentation with distributional sentence similarity tasks

Abstract

We develop a vector space semantics for Lambek Calculus with Soft Subexponentials, apply the calculus to construct compositional vector interpretations for parasitic gap noun phrases and discourse units with anaphora and ellipsis, and experiment with the constructions in a distributional sentence similarity task. As opposed to previous work, which used Lambek Calculus with a Relevant Modality the calculus used in this paper uses a bounded version of the modality and is decidable. The vector space semantics of this new modality allows us to meaningfully define contraction as projection and provide a linear theory behind what we could previously only achieve via nonlinear maps.