Type Logical Grammar Categorial Logic of Signs
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Type Logical Gratntnar Categorial Logic of Signs
by
GL YN V. MORRILL Department of Computer Systems and Languages, Polytechnic University of Catalonia, Spain
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SPRINGER SCIENCE+BUSINESS MEDIA, B.V.
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ISBN (eBook) ISBN 978-0-7923-3226-8 978-0-7923-3226-8ISBN ISBN 978-94-011-1042-6 978-94-011-1042-6 (eBook) DOl DOI 10.1007/978-94-011-1042-6 10.1007/978-94-011-1042-6
Printed on paper Printed on acid~free acid~free paper
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All Reserved AU Rights Rights Reserved © Science+I3usiness Media © 1994 1994Springer Springer Science+I3usiness MediaDordrecht Dordrecht
in Originally published by in1994 1994 Originally published by Kluwer KluwerAcademic AcademicPublishers Publishers Softcover reprint of 1st 1994 Softcover reprint ofthe thehardcover hardcover stedition edition 1994 No part of protected by copyright notice may be or part ofthe thematerial material protected by this this copyright notice be reproduced reproduced Of utilized in or utilized inany anyform formor orby by any anymeans, means,electronic electronic Of mechanical, mechanical, including photocopying, recording or storage and inciuding photocopying, recording Of by by any anyinformation information stOfage and retrieval system, without written permission from owner. retrieval system, without written permission fromthe thecopyright copyright owner.
To my parents, Abby and Alan
CONTENTS Notational Conventions ............................................ xi Foreword ......................................................... xiii Chapter One: Montague Grammar ................................. 1 1 Model Theoretic Semantics ............................... . .. 4 2 Grammar Terminology and Presentation ..................... 12 3 Montagovian Fragment ...................................... 19 3.1 Intensionality .......................................... 22 3.2 Object Position ........................................ 26 3.3 Quantifying-In ........................................ 28 3.4 Coordination and Relativisation ....................... 38 4 Conversion to Direct Semantics .............................. 43 Chapter Two: Logic of Types and Types of Logic .................. 47 1 The Curry-Howard Correspondence .......................... 48 1.1 Natural Deduction ..................................... 51 1.2 Gentzen Sequent Logic ................................ 53 1.3 Conjunction and Disjunction .......................... 55 2 The Structural Hierarchy .................................... 59 Chapter Three: Categorial Grammar .............................. 69 1 Non-Associative Lambek Calculus ........................... 72 2 Associative Lambek Calculus ................................ 78 3 Coordination ..........................................
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