Grammar formalisms are a method of formalising, understanding and representing syntatic structures. They model the syntax and provide a rigid, comprehensive and parsable notion of grammaticality in a given language.
However, as a sub-field of natural language processing and computational linguistics, research in grammar formalisms has been rapidly declining if it can not be used in an application: to the point where the study of the formal notion of language syntax, as a theoretical study, has lost interest in the community.
Case in point: One of the only known *ACL workshops for formalisms was known as TAG+ and was held once every two to three years after 1998. Looking at the statistics of the number of papers in the workshop proceedings, we see that after 2004, there has been a rapid and noticeable decline in the number of papers, and 2012 onwards, a majority of the papers became about developing taggers, super-taggers and discourse structure (though languages like Arabic and Hungarian stayed in the mix). TAG+ has not been held since 2017.
I understand that the nature of NLP is changing, and it has becomes about solving problems rather than investigating theories, and that the nature of theoretical study now expected would probably lean towards analyzing the neural blackboxes rather than theoretical insights into language structure. In the meantime, hoards of low resource languages with informally written grammars (and almost no data for the extremely specific NLP tasks), will get pushed farther and farther away from being included into the computational linguistics circles in the systematic manner that they used to.
Telugu, Tamil and Malayalam are some examples of such languages. A potential direction of future research could be to understand the viability of lexicalized grammars for representing the syntax of these morphologically rich languages, and understanding that syntactic formalism need to inculcate both dependency as well as morphological information to provide insight into the “structure” underlying the language and formalizing it.