In section 2 we define link grammars more formally
and explain the notation and terminology used throughout the rest of
the paper. In section 3 we describe the
workings of a small link grammar for English. Our 
algorithm
is described in section 4, and the data
structures and heuristics that make it run fast are described in
section 5. In section 6
we explain the relationship between link grammars, dependency syntax,
and categorial grammars. We show how to automatically construct a
link grammar for a given categorial grammar. This construction allows
our efficient parsing algorithms and heuristics to be applied to
categorial grammars. Section 7 mentions several
other research projects that are based on link grammars.
Space limitations prevent us from presenting details of a number of other aspects of our work. The following paragraphs mention a few of these. More details on all of these matters are contained in our technical report [14].
There are a number of common English phenomena that are not handled by our current system. Our technical report contains a list of these, along with the reason for this state of affairs. The reasons range from the fact that ours is a preliminary system to the fact that some phenomena simply do not fit well into the link grammar framework.
Coordinating conjunctions such as and pose a problem for link grammars. This is because in a sentence like The dog chased and bit Mary there should logically be links between both dog and bit and chased and Mary. Such links would cross. We have devised a scheme that handles the vast majority of uses of such conjunctions and incorporated it into our program. The existence of such a conjunction in a sentence modifies the grammar of the words in it. The same parsing algorithm is then used on the resulting modified grammar.
Certain other constructs are difficult to handle only using the basic link grammar framework. One example is the non-referential use of it: It is likely that John will go is correct, but The cat is likely that John will go is wrong. It is possible - but awkward - to distinguish between these with a link grammar. To deal with this (and a number of other phenomena), we extended the basic link grammar formalism with a post-processor that begins with a linkage, analyzes its structure, and determines if certain conditions are satisfied. This allows the system to correctly judge a number of subtle distinctions (including that mentioned here).