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LOGIC, LANGUAGE AND REASONING TRENDS IN LOGIC Studia Logica Library VOLUME 5 Managing Editor Ryszard W6jcicki, Institute of Philosophy and Sociology, Polish Academy of Sciences, Warsaw, Poland Editors Petr Hajek, Institute of Computer Sciences, Academy of Sciences of the Czech Republic, Prague, Czech Republic David Makinson, Ville d'Avray, France Daniele Mundici, Department of Computer Sciences, University of Milan, Italy Krister Segerberg, Department of Philosophy, Uppsala University, Uppsala, Sweden Alasdair Urquhart, Department of Philosophy, University of Toronto, Canada Assistant Editor Jacek Malinowski, Box 61, UPT 00-953, Warszawa 37, Poland SCOPE OF THE SERIES Trends in Logic is a bookseries covering essentially the same area as the journal Studia Logica - that is, contemporary formal logic and its applica tions and relations to other disciplines. These include artificial intelligence, informatics, cognitive science, philosophy of science, and the philosophy of language. However, this list is not exhaustive, moreover, the range of appli cations, comparisons and sources of inspiration is open and evolves over time. LOGIC, LANGUAGE AND REASONING Essays in Honour of Dov Gabbay Edited by HANS JÜRGEN OHLBACH s King College, London, United Kingdom and UWEREYLE University 0/ Stuttgart, Stuttgart, Germany .... " SPRINGER SCIENCE+BUSINESS MEDIA, B.V. A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-94-010-5936-7 ISBN 978-94-011-4574-9 (eBook) DOI 10.1007/978-94-011-4574-9 Printed on acid-free paper All Rights Reserved © 1999 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1999 Softcover reprint of the hardcover 1s t edition 1999 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. Photograph by Elsbeth Mastenbroek Reproduced with kind permission Preface This volume is dedicated to Dov Gabbay who celebrated his 50th birthday in October 1995. Dov is one of the most outstanding and most productive researchers we have ever met. He has exerted a profound influence in major fields of logic, linguistics and computer science. His contributions in the areas of logic, language and reasoning are so numerous that a comprehensive survey would already fill half of this book. Instead of summarizing his work we decided to let him speak for himself. Sitting in a car on the way to Amsterdam airport he gave an interview to Jelle Gerbrandy and Anne-Marie Mineur. This recorded conversation with him, which is included gives a deep insight into his motivations and into his view of the world, the Almighty and, of course, the role of logic. In addition, this volume contains a partially annotated bibliography of his main papers and books. The length of the bibliography and the broadness of the topics covered there speaks for itself. The authors of the papers in this volume are, by far, not all of his close col leagues and friends. Therefore this book can only be the first in a series of books dedicated to him. Most of the articles included build on his work and present results or summarize areas where Dov has made major contributions. The fact that one cannot avoid having him as coauthor in his own festschrift confirms what he said in the interview: "I try to work in these areas in such a way that when, sooner or later, the roads come together, like on a roundabout, it will be Gabbay com ing from this way, Gabbay coming from that way ... " Hans Jiirgen Ohlbach and Uwe Reyle Vll Contributions Dov Gabbay: "I am a logic" 1 Research Themes of Dov Gabbay 13 Proofs, Labels and Dynamics in Natural Language 31 J ohan van Benthem What a Linguist Might Want From a Logic of MOST and Other 43 Generalized Quantifiers Hans Kamp Imperative History: Two-dimensional Executable Temporal Logic 73 Marcelo Finger and Mark Reynolds Diagrammatic Reasoning in Projective Geometry 99 Philippe Balbiani and Luis Farinas del Cerro On Sentences of the Kind "Sentence 'p' is About Topic t" 115 Robert Demolombe and Andrew J.I. Jones Two Traditions in the Logic of Belief: Bringing them Together 135 Krister Segerberg Elimination of Predicate Quantifiers 149 Andreas Nonnengart, Hans Jiirgen Ohlbach and Andrzej Szalas Labelled Natural Deduction 173 Ruy J. G. B. de Queiroz and Dov M. Gabbay A General Reasoning Scheme for Underspecified Representations 251 Esther Konig and Uwe Reyle Deductive Systems and Categories in Linguistics 279 Joachim Lambek Towards a Procedural Model of Natural-language Interpretation 295 Crossover: A Case Study Ruth Kempson IX Transformation Methods in LDS 335 Krysia Broda, Marcello D'A gostino and Alessandra Russo Labelled Deduction in the Composition of Form and Meaning 377 Michael Moortgat Formalisms for Non-formal Languages 401 Julius M. Moravcsik Names Index 417 Index 422 ix DOV GABBAY: "I AM A LOGIC" JELLE GERBRANDY AND ANNE-MARJE MINEUR An Interview with Dov Gabbayl Based on the assumption that the Almighty has created a coherent being, that He has sprinkled a little logic in our minds, Dov M. Gabbay is working hard on getting theories on language, logic and information to converge. With that in mind, he publishes handbooks on all kinds of logic, he is an editor of the Journal of Logic and Computation and he is involved in the International Society for Pure and Applied Logic. When the roads come together, he wants to be on every one of them. 'Like a roundabout, it will be Gabbay coming from this way, Gabbay coming from that way ... ' We had to accompany him to the airport to have our interview, but then again, some people deserve the 'Superstar approach '. Gabbay is now working at Imperial College in London, though officially on sabbatical to study Labelled Deductive Systems. Biography - 'This is what I want to do'. I was born in 1945, and I grew up in Israel. I started my university studies in '63, I studied mathematics and physics for the BSc, mathematics for the MSc - I did my Master's on many-valued logics - and then I did my PhD on non-classical logics, in 1969. I went to an extremely religious school. Take for example the way they taught physics. The teacher came to class and said: 'When God created the world, He used these equations, and then He derived everything from that'. No experiments, nothing, it was all mathematics. They taught history only because it was necessary, teaching languages was good, and they taught (mathematically) some science. Humanities - Arts, Music - they did not IThis interview is also published in Ta!, the Dutch students' magazine for computa tional linguistics. HJ. Ohlbach and U. Reyle (eds.), Logic, Language and Reasoning, 1-12. © 1999 Kluwer Academic Publishers. 2 JELLE GERBRANDY AND ANNE-MARIE MINEUR take seriously. And they taught us a lot of Bible. So I naturally became one-sided, not only in what I knew, but also in my attitude. The school attitude was: 'Here is the word of God, you concentrate on that. Don't be distracted by junk'. I don't believe that you have to follow the Bible in the same way, although I believe it is good to know some things about it. But the attitude of 'this is what I want to do, don't be distracted', was ingrained in me. At that time, this was a good attitude. A lot of my fellow students did get distracted. I didn't go to discotheques or out dancing with the girls. I made a concentrated effort. Of course, I could have gone funny at the age of forty. A part of the religious teaching was for everyone to get married, have children, and so forth. I got married in 1970. My wife is an artist, and I learned a lot from her; the fact that I can talk about things, for instance. I remember I was going out with her, before we were married, and we were walking from one part of the university to another part. My objective was to get from A to B, she wanted to stop and look at the moon, because it looked very nice. And I thought: 'What the hell would I want to look at the moon for, when I want to go to B?' Now, of course, I will look at the moon at all times with her. Then I went to Stanford, from 1970 to 1974, 1975. In Stanford I took up Dana Scott's position. When I worked in Stanford, I wanted to become a professor as fast as possible. I thought that if I worked only in one subject, intuitionistic logic for example, a large part of the department in Stanford would not be interacting with me. Then I saw that there was Logic and Language, and I started working on language with Julius Moravcsik. And I loved it. At that time I also used to go to statistics seminars in the other faculty. Probably, scientifically it was right, because now we have uncertainty, prob abilistic reasoning and so on, but from the effort point of view, it would have been too much to do. Then one day Kreisel came to me and said that G6del wanted to talk to me: 'Come to my office on Sunday'. So I went to his office on Sunday, and G6del talked to me through Kreisel. It was a very strange situation: Kreisel was sitting on the phone, talking to G6del in Ger man, G6del would ask a question, Kreisel would repeat it to me in English, I would answer, or Kreisel would answer for me. This is how I talked to G6del. Basically, what G6del said was: 'What is this young Gabbay doing? He is doing this, he is doing that, what is this? I knew what I was doing when I was sixteen'. And Kreisel said: 'Well, he's young, he's enthusiastic'. So I dropped statistics after that, but kept the language, because I was interested in that. I will get into statistics now, probably. After that, we decided to go back to Israel. So I resigned and went back to the Bar-Han University, and I stayed there until 1982. In that year I went for a year to