带相关模态的 Lambek 演算的范畴向量空间语义
Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality
AI总结：
本文为带相关模态 !L* 的 Lambek 演算构建范畴组合分布式语义，通过量子化函子实例化到有限维向量空间，并在寄生空位短语消歧任务中评估三种余代数模态解释。
摘要：
我们为带相关模态 !L* 的 Lambek 演算发展了一种范畴组合分布式语义，该演算拥有收缩规则与置换规则的受限版本。该语义的范畴部分是一个带有余代数模态的幺半双闭范畴，非常类似于 Differential Category（微分范畴）的结构。我们通过“量子化”函子将该范畴实例化为有限维向量空间和线性映射，并研究余代数模态的三种具体解释。我们应用该模型，为 !L* 的启发性示例——即对包含寄生空位的短语进行推导——构建范畴解释和具体语义解释。具体解释的有效性通过一个消歧任务进行评估：该任务在句子消歧数据集的扩展版本上进行，将其扩展到寄生空位短语，并使用 BERT、Word2Vec 和 FastText 向量以及 Relational 张量。
英文摘要：
We develop a categorical compositional distributional semantics for Lambek Calculus with a Relevant Modality !L*, which has a limited edition of the contraction and permutation rules. The categorical part of the semantics is a monoidal biclosed category with a coalgebra modality, very similar to the structure of a Differential Category. We instantiate this category to finite dimensional vector spaces and linear maps via "quantisation" functors and work with three concrete interpretations of the coalgebra modality. We apply the model to construct categorical and concrete semantic interpretations for the motivating example of !L*: the derivation of a phrase with a parasitic gap. The effectiveness of the concrete interpretations are evaluated via a disambiguation task, on an extension of a sentence disambiguation dataset to parasitic gap phrases, using BERT, Word2Vec, and FastText vectors and Relational tensors.
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