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：本文构建了基于软子指数项的兰贝克演算的向量空间语义学，运用该演算为寄生空缺名词短语及包含照应和省略现象的话语单元构建组合性向量解释，并在分布式语义句子相似度任务中对此构造进行实验验证。与以往使用带相关模态词的兰贝克演算不同，本文采用的演算使用有界版本模态词且具有可判定性。这种新型模态词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，并为之前仅能通过非线性映射实现的操作提供线性理论框架。