We study some learnability problems in the family of Categorial Dependency Grammars (CDG), a class of categorial grammars defining dependency structures. CDG is a formal system, where types are attached to words, combining the classical categorial grammars’ elimination rules with valency pairing rules defining non-projective (discontinuous) dependencies; very importantly, the elimination rules are naturally extended to the so called “iterated dependencies” expressed by a specific type constructor and related elimination rules. This paper first reviews key points on negative results: even the rigid (one type per word) CDG cannot be learned neither from function/argument structures, nor even from dependency structures themselves. Such negative results prove the impossibility to define a learning algorithm for these grammar classes. Nevertheless, we show that the CDG satisfying reasonable and linguistically valid conditions on the iterated dependencies are incrementally learnable in the limit from dependency structures. We provide algorithms and also discuss these aspects for recent variants of the formalism that allow the inference of CDG from linguistic treebanks.

我们研究了类别依赖性语法（CDG）系列中的一些可学习性问题，该类别是定义依赖性结构的一类分类语法。CDG是一个形式系统，其中将类型附加到单词上，将经典类别语法的消除规则与定义非投影（不连续）依赖项的效价配对规则相结合；非常重要的是，消除规则自然会扩展到由特定类型构造函数和相关消除规则表示的所谓的“迭代依赖项”。本文首先回顾了负面结果的关键点：既不能从功能/参数结构中也不能从依赖结构本身中学习甚至是严格的CDG（每个单词一个类型）。这样的负面结果证明不可能为这些语法类别定义学习算法。尽管如此，我们表明，在迭代依赖项上满足合理和语言有效条件的CDG可从依赖项结构的极限中逐步学习。我们提供了算法，还讨论了形式主义的最新变体的这些方面，这些变体允许从语言树库中推断CDG。