Dependency systems and phrase-structure systems

A language is considered here as a finite set of symbols (words of the language) together with a set of strings (finite sequences) of these symbols (sentences of the language). A grammar is a system of rules by means of which those strings which belong to the language (i.e., are sentences) are defined. Two types of grammars are dealt with-those based on dependency rules and those based on phrase-structure rules. Both of these supply the sentences that they analyze with additional structure; there is a very close relationship between these structures. Different notions of equivalence between grammars of the two types, based on structure similarities, are defined. Every dependency system has a "naturally corresponding≓ phrase-structure system but not vice versa. An effective necessary and sufficient condition for the existence of a "naturally corresponding≓ dependency system for a given phrase-structure system is given, and an effective way to construct it when it exists. Nevertheless, every set of strings defined by means of a grammar of one type is also defined by means of a grammar of the other type, which can be found effectively. However, the result above implies that there will be cases in which the second system will not be "naturally correlated≓ with the given one from a structural point of view.