We use Lambek's pregroups and the framework of compositional distributional
models of language ("DisCoCat") to study translations from Japanese to English
as pairs of functors. Adding decorations to pregroups we show how to handle
word order changes between languages.

本文使用 Lambek's pregroups 和 compositional distributional models of language (DisCoCat) 框架，研究了从日语到英语的翻译，作为函子对。通过对 pregroups 添加修饰，展示了如何处理语言之间的词序变化。

一种将日语翻译为代数语言的方法

An algebraic approach to translating Japanese

Distributional semantic models provide vector representations for words by
gathering co-occurrence frequencies from corpora of text. Compositional
distributional models extend these from words to phrases and sentences. In
categorical compositional distributional semantics, phrase and sentence
representations are functions of their grammatical structure and
representations of the words therein. In this setting, grammatical structures
are formalised by morphisms of a compact closed category and meanings of words
are formalised by objects of the same category. These can be instantiated in
the form of vectors or density matrices. This paper concerns the applications
of this model to phrase and sentence level entailment. We argue that
entropy-based distances of vectors and density matrices provide a good
candidate to measure word-level entailment, show the advantage of density
matrices over vectors for word level entailments, and prove that these
distances extend compositionally from words to phrases and sentences. We
exemplify our theoretical constructions on real data and a toy entailment
dataset and provide preliminary experimental evidence.

本文介绍了基于矢量表示的分布语义模型，扩展到短语和句子，提出了分类组合分布语义学理论框架，实现了短语和句子层面的言外推理，并通过实验论证了基于密度矩阵的熵距离在词语和短语、句子层面的言外推理可行性和优越性。

组合分布式语义中的句子蕴含

Sentence Entailment in Compositional Distributional Semantics

The development of compositional distributional models of semantics
reconciling the empirical aspects of distributional semantics with the
compositional aspects of formal semantics is a popular topic in the
contemporary literature. This paper seeks to bring this reconciliation one step
further by showing how the mathematical constructs commonly used in
compositional distributional models, such as tensors and matrices, can be used
to simulate different aspects of predicate logic.
This paper discusses how the canonical isomorphism between tensors and
multilinear maps can be exploited to simulate a full-blown quantifier-free
predicate calculus using tensors. It provides tensor interpretations of the set
of logical connectives required to model propositional calculi. It suggests a
variant of these tensor calculi capable of modelling quantifiers, using few
non-linear operations. It finally discusses the relation between these
variants, and how this relation should constitute the subject of future work.

本文讨论了如何使用矩阵和张量来模拟谓词逻辑，并提出可以模拟量词的张量演算变体，最后讨论了这些变体之间的关系与未来研究的方向。