I am an undergraduate mathematics student with a keen interest in pursuing research in the formalization of natural languages (from a more mathematical-logical approach), yet there aren't many resources that provide an overview of this very technical field. I wish to be able to provide myself a general map to navigate this subject more clearly, so I will attempt explain my basic understanding of an overview of the fields that tackle with this subject, and I'd greatly appreciate any correction or addition to my limited insight.
From my understanding, (loosely speaking) there are two prominent mathematical-logical approaches in formalizing natural languages: Categorial Grammar and Montague Semantics. While Categorial Grammar uses methods borrowed from category theory to (mainly) study the syntax of natural languages, Montague Semantics, as the name might suggest, (mainly) focuses on the semantics of natural languages by implementing methods from Lambda Calculus. In terms of subareas of each of these two fields, I have not seen much discussed in terms of the subareas of Montague Semantics; however, Categorial Grammar seems ripe with subareas (although I have heard some of the fields mentioned below are only closely related to Categorial Grammar rather than being a strict subfield of it):
- Combinatory Categorial Grammar (CCG)
- Lambek Calculus
- Type-Logical Grammar
- Pre-Group Grammar
- Proof-Theoretic Semantics
In addition to any corrections or additions, I would greatly appreciate any suggestions for resources, references or books that deal with these subjects or their prerequisites.