Originally inspired by categorical quantum mechanics (Abramsky and Coecke,
LiCS'04), the categorical compositional distributional model of natural
language meaning of Coecke, Sadrzadeh and Clark provides a conceptually
motivated procedure to compute the meaning of a sentence, given its grammatical
structure within a Lambek pregroup and a vectorial representation of the
meaning of its parts. The predictions of this first model have outperformed
that of other models in mainstream empirical language processing tasks on large
scale data. Moreover, just like CQM allows for varying the model in which we
interpret quantum axioms, one can also vary the model in which we interpret
word meaning.
In this paper we show that further developments in categorical quantum
mechanics are relevant to natural language processing too. Firstly, Selinger's
CPM-construction allows for explicitly taking into account lexical ambiguity
and distinguishing between the two inherently different notions of homonymy and
polysemy. In terms of the model in which we interpret word meaning, this means
a passage from the vector space model to density matrices. Despite this change
of model, standard empirical methods for comparing meanings can be easily
adopted, which we demonstrate by a small-scale experiment on real-world data.
This experiment moreover provides preliminary evidence of the validity of our
proposed new model for word meaning.
Secondly, commutative classical structures as well as their non-commutative
counterparts that arise in the image of the CPM-construction allow for encoding
relative pronouns, verbs and adjectives, and finally, iteration of the
CPM-construction, something that has no counterpart in the quantum realm,
enables one to accommodate both entailment and ambiguity.

本文介绍了一种新的基于范畴论和量子力学的自然语言处理方法，通过将词汇进行向量化，并结合 Coecke, Sadrzadeh 和 Clark 提出的分配模型进行词汇的分析和理解，同时采用 Selinger 的 CPM 构造进行词汇多义性的处理，实现了有效的句子意义计算和词汇比较。

自然语言处理中的开放系统范畴量子语义学

Open System Categorical Quantum Semantics in Natural Language Processing

This invited chapter in the Handbook of Quantum Logic and Quantum Structures
consists of two parts: 1. A substantially updated version of quant-ph/0402130
by the same authors, which initiated the area of categorical quantum mechanics,
but had not yet been published in full length; 2. An overview of the progress
which has been made since then in this area.

本文主要包括两部分内容，第一部分是 AB 两位作者的 quant-ph/0402130 论文的更新版本，该论文开创了范畴量子力学领域，但是尚未完整出版；第二部分则概述了这一领域自那时以来所取得的进展情况。