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Language and Grammar

Studies in Mathematical Linguistics and Natural Language

edited by Claudia Casadio, Philip J. Scott, and Robert A.G. Seely

The application of logic to grammar is a fundamental issue in philosophy and has been investigated by such renowned philosophers as Leibniz, Bolzano, Frege, and Husserl. Language and Grammar examines categorial grammars and type-logical grammars, two linguistic theories that play a significant role in this area of study yet have been overshadowed until recently. The prominent scholars contributing to this volume also explore the impact of the Lambek program on linguistics and logical grammar, producing, ultimately, an exciting and important resource that demonstrates how type-logical grammars are promising future models of reasoning and computation.

Claudia Casadio is associate professor of logic and philosophy at the Universitá degli Studi G. d'Annunzio in Chieti, Italy. Philip J. Scott is professor of mathematics at the University of Ottawa. Robert A.G. Seely is professor of mathematics at McGill University in Montreal.


  • Contributors vii
  • Introduction: the Lambek Program xi C. Casadio, P.J. Scott, R.A.G. Seely
  • I Language 1
    • 1 The Categorial Fine-Structure of Natural Language 3 Johan van Benthem
    • 2 Excursions in Natural Logic 31 Edward Keenan
  • II Grammar 53
    • 3 Characterization of Atomicity in Lambek Calculus and Bilinear Logic 55 Mati Pentus
    • 4 Lambek Calculus with Nonlogical Axioms 77 Wojciech Buszkowski
    • 5 Onthe Expressive Power of the Lambek Calculus Extended with a Structural Modality 95 Philippe de Groote
    • 6 The Lambek Calculus with Brackets 113 Mario Fadda and Glyn Morrill
    • 7 What are Pregroups? 129 J. Lambek
    • 8 OnSubgroups of the Lambek Pregroup 137 Michael Barr
    • 9 Pregroups and Type-Logical Grammar: Searching for Convergence 141 Michael Moortgat and Richard T. Oehrle
  • III Language and Grammar 161
    • 10 Categorial Grammar for Minimalism 163 Alain Lecomte
    • 11 On Tree Languages Generated by Categorial Grammars 189 Maciej Kandulski
    • 12 Subject Predicate Order in Classical Sanskrit 211 Brendan S. Gillon
    • 13 A Computational Approach to the Noun in Burushaski 225 Daniele Bargelli
    • 14 Geometry of Language and Linguistic Circuitry 237 Glyn Morrill
  • Index 265


ISBN (Paperback): 1575864886 (9781575864884)
ISBN (Cloth): 1575864878 (9781575864877)
ISBN (Electronic): 157586942X (9781575869421)

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