One Direction in Mathematical Linguistics: Generative Grammars

Abstract

My interest in mathematical linguistics stems from a curiosity about languages and a desire to be scientific in a study of them. My purpose for an SIP was to learn as much as possible about this field as I could in the ten weeks of a SIP quarter. I discovered that it was difficult to find books which were written about generative grammars on an elementary level, and so I decided to write my SIP on some.concepts and conclusions about these grammars in order.to impress the concepts in my own mind. My paper is not meant to be inclusive of all the work which linguists have done on generative grammars. Instead, I have chosen major concepts and theorems of two types of generative grammars. The theorems and concepts show the kind of methods which math linguists have developed and the kind of conclusions which they have reached. I have limited most of my considerations to generative grammars for natural languages because I was most interested in results for natural languages. Generative grammars are useful for artificial languages, and most of the concepts I will discuss can be applied to them.