Mathematical Methods and Models in Linguistics

Abstract

In this article, relevant approaches to creating and using mathematical models in linguistics are examined. Analyzed are the types of mathematical methods used to solve linguistic tasks. Also investigated are the fundamental principles for creating mathematical models. Stressed in particular is that the approach usually applied in solving physical tasks can be effective. Its typical feature is that a universal theory explaining the interaction among a system’s functional elements on the most general level is the basis of the model. In this case, the necessary approximating dependencies are not conjectured, as is often the case, but obtained or calculated on the basis of the fundamental theory. The prospects for applying this approach in linguistics are defined. Examples of the modeling of linguistic systems and a comparative analysis of their various methods are provided. Much attention is paid to the universality of the mathematical models used to analyze linguistic material. It is noted that if the approximate dependencies used are based on a system’s general universal properties, this can significantly complicate the quantitative analysis of the data. The advantages and shortcomings of mathematical modeling in solving applied linguistic tasks are illustrated. Besides “classic” models (such as Zipf’s law for the rank distribution of words in a text), other modeling approaches are described. In particular, attention is paid to the methods of constructing mathematical models based on neural networks. In this case, the approximation of dependence is realized in the form of sequential essentially nonlinear transformations. The main disadvantage of this approach is connected with the technical complications of execution and with the absence of overt analytical dependence. The main advantage is hidden in the potential possibility of creating approximate dependencies of practically any type. As a comparison of various modeling approaches, the article provides examples of solving the same linguistic tasks using several methods.