Abstract
The application of logical-mathematical methods to the analysis of natural language is a fundamental issue in leading fields of linguistic analysis such as theoretical and computational linguistics, philosophy of language and cognitive linguistics. The theoretical background of the volume edited by C. Casadio and J. Lambek is founded on the idea of a “logical grammar”, elaborated by well known philosophers like Leibniz, Frege and Husserl, from which categorial grammars and type logical grammars have been developed. The collection Computational Algebraic Approaches to Natural Language is devoted to a particular kind of type logical grammar, called Pregroup Grammar. A pregroup is a partially ordered monoid in which each element has both a left and a right adjoint, and is freely generated by a partially ordered set of basic types. A pregroup grammar for a language is obtained by assigning basic and derived types to the words in the dictionary of that language and by computing grammaticality and sentencehood of strings of words by means of simple calculations. Starting from these basic assumptions, the volume collects the contributions of prominent scholars who discuss some relevant theoretical issues and explore the possibilities offered by the application of the theory of pregroups to a variety of natural languages, including English, French, Japanese, Italian, Persian, Polish, and also a computational treatment of Biblical Hebrew conjugation. The result is a singular cross-linguistic geography demonstrating how important a contribution a type logical approach can offer to the study of natural languages.

Claudia Casadio is full professor of Logic and Philosophy of Science, at the University “G. d'Annunzio” in Chieti, Italy.

Joachim Lambek is Professor Emeritus of Mathematics, at the McGill University in Montreal, Canada.

Information
Type: Collection
Language(s): English
Year: 2008
Number of page(s): 300
Code (printed): ISBN 978-88-7699-125-7
Code (electronic): ISBN 978-88-7699-126-4 - Open Access Publication

Book Sections
Wojciech Buszkowski, Katarzyna Moroz (2008) Pregroup grammars and context-free grammars. In: Computational Algebraic Approaches to Natural Language. Polimetrica Publisher, Italy, pp. 1-22.

Edward P. Stabler (2008) Tupled pregroup grammars. In: Computational Algebraic Approaches to Natural Language. Polimetrica Publisher, Italy, pp. 23-52.

Anne Preller, Violaine Prince (2008) Pregroup grammars with linear parsing of the French verb phrase. In: Computational Algebraic Approaches to Natural Language. Polimetrica Publisher, Italy, pp. 53-84.

Denis Béchet, Alexander Dikovsky, Annie Foret, Emmanuelle Garel (2008) Introduction of option and iteration into pregroup grammars. In: Computational Algebraic Approaches to Natural Language. Polimetrica Publisher, Italy, pp. 85-108.

Kumi Cardinal (2008) Japanese verbal nouns: a computational approach. In: Computational Algebraic Approaches to Natural Language. Polimetrica Publisher, Italy, pp. 109-120.

Mehrnoosh Sadrzadeh (2008) Pregroup analysis of Persian sentences. In: Computational Algebraic Approaches to Natural Language. Polimetrica Publisher, Italy, pp. 121-144.

Aleksandra Kiślak-Malinowska (2008) Polish language in terms of pregroups. In: Computational Algebraic Approaches to Natural Language. Polimetrica Publisher, Italy, pp. 145-172.

Telyn Kusalik (2008) Product pregroups as an alternative to inflectors. In: Computational Algebraic Approaches to Natural Language. Polimetrica Publisher, Italy, pp. 173-190.

Gregory M. Kobele (2008) Agreement bottlenecks in Italian. In: Computational Algebraic Approaches to Natural Language. Polimetrica Publisher, Italy, pp. 191-212.

Daniele Porello (2008) Linguistic applications of Non-commutative Logic. In: Computational Algebraic Approaches to Natural Language. Polimetrica Publisher, Italy, pp. 213-232.

Joachim Lambek (2008) Reflections on English personal pronouns. In: Computational Algebraic Approaches to Natural Language. Polimetrica Publisher, Italy, pp. 233-256.

Joachim Lambek, Noson S. Yanofsky (2008) A computational approach to Biblical Hebrew conjugation. In: Computational Algebraic Approaches to Natural Language. Polimetrica Publisher, Italy, pp. 257-294.