双代数范畴组合分布语义中自然语言的广义量词理论
A Generalised Quantifier Theory of Natural Language in Categorical Compositional Distributional Semantics with Bialgebras
摘要：
范畴组合分布语义学是自然语言的一种模型，它将词的统计向量空间模型和语法的组合模型结合起来。我们正式在这个模型中的广义量词理论的自然语言，由于Barwise和库珀。其基础是一个具有双代数的紧闭范畴。我们从生成语法形式化开始，并为其开发抽象的范畴组合语义，然后将抽象设置实例化为集合和关系以及有限维向量空间和线性映射。我们证明了等价的关系实例化的真值理论语义的广义量词。向量空间实例化形式化的统计使用的话，使我们能够，第一次，原因量化的短语和句子组成的分布语义。
英文摘要：
Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier theory of natural language, due to Barwise and Cooper. The underlying setting is a compact closed category with bialgebras. We start from a generative grammar formalisation and develop an abstract categorical compositional semantics for it, then instantiate the abstract setting to sets and relations and to finite dimensional vector spaces and linear maps. We prove the equivalence of the relational instantiation to the truth theoretic semantics of generalised quantifiers. The vector space instantiation formalises the statistical usages of words and enables us to, for the first time, reason about quantified phrases and sentences compositionally in distributional semantics.
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