There is a large body of work based on the idea that linguistic analysis can be done by drawing links between words. These are variously called dependency systems [5], dependency syntax [10], dependency grammar [4][3], or word grammar [7][6].
In dependency grammar, a grammatical sentence is endowed with a dependency structure, which is very similar to a linkage. This structure, as defined by Melcuk [10], consists of a set of planar directed arcs among the words that form a tree. Each word (except the root word) has an arc out to exactly one other word, and no arc may pass over the root word. In a linkage (as opposed to a dependency structure) the links are labeled, undirected, and may form cycles, and there is no notion of a root word.
Gaifman [5] was the first to actually give a formal method of expressing a dependency grammar. He shows that his model is context-free.
Melcuk's definition of a dependency structure, and Gaifman's proof that dependency grammar is context free imply that there is a very close relationship between these systems and link grammars. This is the case.
It is easy to take a dependency grammar in Gaifman's notation and generate a link grammar that accepts the same language. In this correspondence, the linkage that results from parsing a sentence is the same as the corresponding dependency structure. This means that our algorithm for link parsing can easily be applied to dependency grammars. The number of disjuncts in the resulting link grammar is at most quadratic in the number of rules in the dependency grammar. None of the algorithms that have been described for dependency parsing [7][15][3] seem to bear any resemblance to ours. It is therefore plausible to conjecture that our algorithms and techniques could be very useful for directly parsing dependency grammars.
Gaifman's result shows that it is possible to represent a link grammar as a dependency grammar (they're both context-free). But this correspondence is of little use if the parsed structures that result are totally different.
One problem with constructing a dependency grammar that is in direct correspondence with a given link grammar is that a linkage in a link grammar my have cycles, whereas cycles are not allowed in dependency grammar. If we restrict ourselves to acyclic linkages, we run into another problem. This is that there is an exponential blow-up in the number of rules required to express the same grammar. This is because each disjunct of each word in the link grammar requires a separate rule in the dependency grammar.
Gaifman's model is not lexical. The method classifies the words into categories. One word can belong to many categories. Roughly speaking, for each disjunct that occurs in the dictionary, there is a category of all words that have that disjunct. The notation is therefore in a sense orthogonal to the link grammar notation.
We are not aware of any notation for dependency systems that is lexical, or that is as terse and well suited for a natural language grammar as link grammars. There has been work on creating dependency grammars for English [3][7], but we are not aware of an implementation of a dependency grammar for any natural language that is nearly as sophisticated as ours.