Beardon et. al. have concluded in their book [3] that there appears no simple universal way of representing the meaning of sentences in a natural language. The three main canonical NLP problems do not cover all language phenomena, even in English. Grammar formalism may not be able to provide all supports for handling natural language phenomena. In computational linguistics, Aho has concluded three different ways towards a specification of a language [1]:
In recent years, researchers have been studied NLP problems from different perspectives with different approaches. Many aspects have been discussed in [2]. In this survey, we put our emphasis on grammar formalisms, particularly, the formalisms that extend the descriptive power of context-free grammars to handle NLP problems. Grammar formalism is widely recognized as the fundamental structure of NLP. The attempt of finding grammar systems to generate the syntactic structure of a language is still going on, and most of the researches in this field are focused on deriving grammars or recognizing hierarchy of grammar formalisms. We believe that the development in terms of grammars is a way towards integrating some or more information from language semantics. Like Example 4 in Section 4, the relationship of n = m+l is more of some semantic information than syntax (or both). Clearly, context-free grammars are incapable to handle such information. Example 5 from [5] demonstrates another example of how this kind of information can be generated by GIGs.
Example 5. (Coordination)
, 
, 
,
, 
,
, 
,
, 
,
, 
.
The sentence ``Who did you visit and talk to'' can thus be generated by:
The coordination between ``visit'' and ``talk to'' in above example is ensured by the indices as we normally put ``visit'' in front of ``talk to''. The parsing tree structure in Figure 1 gives a graphic representation of this dependency.
Figure 1: Coordination example parsing tree structure.
In conclusion, GIGs are still unable to generate many other NLP problems such as 5 counting dependency language , or higher dependency languages, which has been classified in MCSLs [8]. The popular geometric hierarchy of grammar levels specified in MCSLs has been used to formalize grammars to fit different language requirements. Overall, the grammar formalism studies have been highly abstracted either computationally or mathematically. The practical application on natural languages have not been experimented. The development tasks of applying those grammars would be a long process ahead.