The Mathematics of Language (Studies in Generative Grammar, Vol 63)

This book studies language(s) and linguistic theories from a mathematical point of view. Starting with ideas already containedin Montague's work, it develops the mathematical foundations of present day linguistics. It equips the reader with all thebackground necessary to understand and evaluate theories as diverse as Montague Grammar, Categorial Grammar, HPSG and GB. The mathematical tools are mainly from universal algebra and logic, but no particular knowledge is presupposed beyond a certainmathematical sophistication that is in any case needed in order to fruitfully work within these theories. The presentation focuses onabstract mathematical structures and their computational properties, but plenty of examples from different natural languagesare provided to illustrate the main concepts and results. In contrast to books devoted to so-called formal language theory,languages are seen here as semiotic systems, that is, as systems of signs. A language sign correlates form with meaning. Using theprinciple of compositionality it is possible to gain substantial insight into the interaction between form and meaning in natural languages.

This book constitutes the proceedings of the 12th Biennial Meeting on Mathematics in Language, MOL 12, held in Nara, Japan, in September 2011.

Presented in this volume are 12 carefully selected papers, as well as the paper of the invited speaker Andreas Maletti. The papers cover such diverse topics as formal languages (string and tree transducers, grammar-independent syntactic structures, probabilistic and weighted context-free grammars, formalization of minimalist syntax), parsing and unification, lexical and compositional semantics, statistical language models, and theories of truth.