A new family of categorial grammars is proposed, defined by enriching basic
categorial grammars with a conjunction operation. It is proved that the
formalism obtained in this way has the same expressive power as conjunctive
grammars, that is, context-free grammars enhanced with conjunction. It is also
shown that categorial grammars with conjunction can be naturally embedded into
the Lambek calculus with conjunction and disjunction operations. This further
implies that a certain NP-complete set can be defined in the Lambek calculus
with conjunction. We also show how to handle some subtle issues connected with
the empty string. Finally, we prove that a language generated by a conjunctive
grammar can be described by a Lambek grammar with disjunction (but without
conjunction).

提出了一种新的范畴语法家族，通过丰富基本的范畴语法，引入了一个连接操作。证明了这种方式得到的形式与带有连接的上下文无关文法具有相同的表达能力。还证明了带有连接的范畴语法可以自然地嵌入到带有连接和析取操作的 Lambek 演算中。这进一步意味着可以在带有连接的 Lambek 演算中定义一个特定的 NP 完全集。还展示了如何处理与空字符串相关的一些微妙问题。最后，证明了由连词语法生成的语言可以由不带有连接但具有析取的 Lambek 语法描述。

合取类别文法与添加剂的 Lambek 文法

Conjunctive categorial grammars and Lambek grammars with additives

We introduce the logical grammar emdebbing (LGE), a model inspired by
pregroup grammars and categorial grammars to enable unsupervised inference of
lexical categories and syntactic rules from a corpus of text. LGE produces
comprehensible output summarizing its inferences, has a completely transparent
process for producing novel sentences, and can learn from as few as a hundred
sentences.

我们介绍了逻辑语法嵌入（LGE），这是一种受到预群组语法和范畴语法启发的模型，可从文本语料库中无监督推断词汇类别和句法规则。LGE 产生易懂的输出来总结其推断，具有完全透明的生成新句子的过程，并且可以从少至一百个句子中学习。

学习语法的逻辑词嵌入

A logical word embedding for learning grammar

It is known that different categorial grammars have surface representation in
a fragment of first order multiplicative linear logic. We show that the
fragment of interest is equivalent to the recently introduced {\it extended
tensor type calculus}. This provides the former not only with some alternative
syntax and intuitive geometric representation, but also with an intrinsic
deductive system, which has been absent.

通过将对角线方法扩展到一个张量范畴中，我们展示了表征不同范畴语法的一个一阶乘性线性逻辑子集相当于最近引入的扩展张量类型演算，它不仅提供了先前的某些替代语法和直观几何表示，还具有本质的演绎系统。