Categorial Grammars with Iterated Types form a Strict Hierarchy of k-Valued Languages

摘要

The notion of k-valued categorial grammars where a word is associated to at most k types is often used in the field of lexicalized grammars as a fruitful constraint for obtaining several properties like the existence of learning algorithms. This principle is relevant only when the classes of k-valued grammars correspond to a real hierarchy of languages. Such a property had been shown earlier for classical categorial grammars. This paper establishes the relevance of this notion when categorial grammars are enriched with iterated types.