Mathematical Foundations for a Compositional Distributional Model of Meaning
Mathematical Foundations for a Compositional Distributional Model of Meaning
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发表时间：
2010-03
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通讯作者：
B. Coecke;M. Sadrzadeh;S. Clark
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作者：
B. Coecke;M. Sadrzadeh;S. Clark
我们提出了一个数学框架，用于统一向量空间模型方面的意义分布理论，以及语法类型的组合理论，为此我们依赖于 Lambek 引入的预群代数。这个数学框架使我们能够根据句子成分的含义来计算类型正确的句子的含义。具体来说，预群的类型约简被“提升”为范畴中的态射，这是一个将成分的含义转换为（类型良好的）整体的含义的过程。重要的是，整个句子的含义存在于一个空间中，与句子的语法结构无关。因此，内积可以用于比较任意句子的含义，就像它用于比较分布模型中单词的含义一样。我们采用的数学结构允许纯粹的图解演算，它揭示了信息如何在句子中的单词之间流动，以构成整个句子的含义。我们的“分类模型”的一种变体涉及将向量空间的标量限制为布尔值的半环，从而产生蒙塔古风格的布尔值语义。
We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, for which we rely on the algebra of Pregroups, introduced by Lambek. This mathematical framework enables us to compute the meaning of a well-typed sentence from the meanings of its constituents. Concretely, the type reductions of Pregroups are `lifted' to morphisms in a category, a procedure that transforms meanings of constituents into a meaning of the (well-typed) whole. Importantly, meanings of whole sentences live in a single space, independent of the grammatical structure of the sentence. Hence the inner-product can be used to compare meanings of arbitrary sentences, as it is for comparing the meanings of words in the distributional model. The mathematical structure we employ admits a purely diagrammatic calculus which exposes how the information flows between the words in a sentence in order to make up the meaning of the whole sentence. A variation of our `categorical model' which involves constraining the scalars of the vector spaces to the semiring of Booleans results in a Montague-style Boolean-valued semantics.