Mathematical Linguistics

by

Alice G.B. ter Meulen

• LAST REVIEWED: 23 March 2012
• LAST MODIFIED: 23 March 2012
• DOI: 10.1093/obo/9780199772810-0029

Introduction

Mathematical linguistics is a field of scientific linguistic inquiry applying mathematical methods and concepts to linguistic systems, to phenomena observed in natural languages, or to the metatheory of models of grammars. Its original sources lie in Europe, where philosophers and logicians were relatively friendly toward ordinary language early in the 20th century. Later global developments quickly increased the field’s diversity and created independent research agendas on the complexity of computational processes, new ways to model linguistic phenomena in richer or more flexible logical systems, and mathematical characterizations of various notions of linguistic complexity. Neighboring disciplines include not only the foundations of mathematics and mathematical logic but also computational linguistics, philosophical logic, knowledge representation as a branch of artificial intelligence, theoretical computer science, and computational psychology. Mathematical linguistics has initially served as a foundation for computational linguistics, though its research agenda of designing machines to simulate natural language understanding is clearly more applied. Inductive methods have gained the upper hand in applied computational linguistics, whereas deductive logical methods are still very much in vogue in theoretical mathematical linguistics, with some new systems mixing both types of methods.

Handbooks

Topics of mathematical linguistics in almost every handbook in Mathematical Logic, Computational Linguistics or Cognitive Science. This section contains two selected bibliographic references to handbooks more specifically related to mathematical linguistics and its topics (Maienborn, et al. 2011; van Benthem and ter Meulen 2010).

• Maienborn, Claudia, Klaus von Heusinger, and Paul Portner, eds. 2011. Semantics: An international handbook of natural language meaning. 2 vols. Berlin: de Gruyter.

  A comprehensive survey of contemporary semantics with several excellent contributions on topics in common with mathematical linguistics.

• van Benthem, Johan, and Alice G. B. ter Meulen. 2010. Handbook of logic and language. 2d ed. Amsterdam and New York: Elsevier Science.

  State-of-the-art handbook on current research in the applications of logical systems to natural language, including topics such as categorial grammars, Montague grammar, situation theory, game-theoretic semantics, compositionality, formal learning theory, nonmonotonic logics, generalized quantifiers, presuppositions, plurals, questions, and generics. First version was published in 1997.