The Mathematics of Language

Mathematical linguistics is concerned with the study of mathematical properties of natural languages and linguistic theories. Since the mathematical properties of interest to mathematical linguists are usually from theoretical computer science (complexity classes, language hierarchies, formal learnability), mathematical linguistics can be considered as an area of theoretical computational linguistics. However, since statistical methods are rarely used in mathematical linguistics, its relationship to current practices in computational linguistics is somewhat limited. While the introduction of logic in linguistic research has originally come from semantics, this line of work did not really use sophisticated meta-results. One of the main developments in mathematical linguistics in the last decade has been the introduction of sophisticated logical methods to the study of natural language syntax, for instance the use of cut-elimination and interpolation theorems in categorial grammar or Büchi’s theorem relating finite automata and monadic second-order logic in model theoretic syntax. The book under review is written by one of the main contributors to the logical turn in mathematical linguistics, and so it is not surprising that it is its main focus