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.

翻译：我们为基于软子指数的Lambek演算建立了一种向量空间语义学，并将其应用于构造寄生缺口名词短语及包含照应和省略现象的语篇单位的组合向量解释，随后在分布性句子相似度任务中对该构造进行了实验验证。与先前采用关联模态的Lambek演算不同，本文使用的演算采用模态的有界版本且具有可判定性。这种新型模态的向量空间语义学使我们能够将收缩操作有意义地定义为投影映射，并为先前仅能通过非线性映射实现的操作提供了线性理论基础。