The categorical compositional distributional model of meaning gives the
composition of words into phrases and sentences pride of place. However, it has
so far lacked a model of logical negation. This paper gives some steps towards
providing this operator, modelling it as a version of projection onto the
subspace orthogonal to a word. We give a small demonstration of the operators
performance in a sentence entailment task.

该研究论文提出了一种关于逻辑否定的操作方法，将其建模为对于词的正交子空间的投影版本，并在句子推理任务中展示了该操作符的性能。

面向组合分布语义的逻辑否定

Towards logical negation for compositional distributional semantics

The categorical compositional distributional model of natural language
provides a conceptually motivated procedure to compute the meaning of
sentences, given grammatical structure and the meanings of its words. This
approach has outperformed other models in mainstream empirical language
processing tasks. However, until recently it has lacked the crucial feature of
lexical entailment -- as do other distributional models of meaning.
In this paper we solve the problem of entailment for categorical
compositional distributional semantics. Taking advantage of the abstract
categorical framework allows us to vary our choice of model. This enables the
introduction of a notion of entailment, exploiting ideas from the categorical
semantics of partial knowledge in quantum computation.
The new model of language uses density matrices, on which we introduce a
novel robust graded order capturing the entailment strength between concepts.
This graded measure emerges from a general framework for approximate
entailment, induced by any commutative monoid. Quantum logic embeds in our
graded order.
Our main theorem shows that entailment strength lifts compositionally to the
sentence level, giving a lower bound on sentence entailment. We describe the
essential properties of graded entailment such as continuity, and provide a
procedure for calculating entailment strength.

本文研究了分类组合分布语义学中的词汇包含问题，使用密度矩阵和量子计算中的部分知识的范畴语义思想提出了一种新的语言模型，并引入了一种新颖而强健的分级量化概念，能够有效地计算概念之间的包含关系。

组合分布语义的分级蕴涵

Graded Entailment for Compositional Distributional Semantics

Categorical compositional distributional model of Coecke et al. (2010)
suggests a way to combine grammatical composition of the formal, type logical
models with the corpus based, empirical word representations of distributional
semantics. This paper contributes to the project by expanding the model to also
capture entailment relations. This is achieved by extending the representations
of words from points in meaning space to density operators, which are
probability distributions on the subspaces of the space. A symmetric measure of
similarity and an asymmetric measure of entailment is defined, where lexical
entailment is measured using von Neumann entropy, the quantum variant of
Kullback-Leibler divergence. Lexical entailment, combined with the composition
map on word representations, provides a method to obtain entailment relations
on the level of sentences. Truth theoretic and corpus-based examples are
provided.

扩展基于类别、组成和分布的语义模型，通过将单词表示扩展为概率分布，定义对词汇蕴涵的对称和非对称相似度度量，利用量子变体对 von Neumann 熵进行度量。通过单词表示的组合映射和单词之间的蕴涵关系，提供了一种获取句子水平上的因果关系的方法。