Mathematical Linguistics: A Comprehensive Overview

Abstract

Mathematical linguistics is a field of linguistic inquiry that applies mathematical methods and concepts to linguistic systems, or to a phenomenon that is observed in natural languages by providing precise tools for analyzing linguistic structures, ,patterns and processes . This field is focused on emerging formal models to describe linguistic phenomena such as syntax, phonology, semantics, discourse and pragmatics, through the use of logic, algebra and set theory Through the usage of probabilistic models and logical systems , mathematical linguistics also makes it possible to quantify ambiguity, model language variation, and predict  linguistic phenomena.  This field is aimed to rigorously and quantitatively understand of language which increases new ways to model linguistic phenomena in more logical systems. Ultimately, mathematical linguistics stands as a dynamic field which continues advancements to understand language through the intersection of mathematics and linguistics .This paper presents a comprehensive overview of mathematical linguistics, by exploring its historical development, theoretical foundations ,core concepts, key models and core areas and also emphasizes the importance of mathematical linguistics in bridging the gap between abstract formalism and actual linguistic issues. Moreover, it underlines the use of tools from set theory, logic, automata theory, and algebra to formalize syntax, semantics, morphology, discourse and phonology. Therefore, the goal of this research is to offer a unified framework for comprehending the scope and impact of mathematical linguistics.