Table Of ContentRepresentation and
Inference for
Natural Language
, A First Course in
\ Computational Semantics
\ Patrick Blackburn
\ Johan Bos
Representation and Inference
for Natural Language
CSLI Studies in Computational Linguistics
This series covers all areas of computational linguistics and language
technology, with a special emphasis on work which has direct relevance
to practical applications, makes formal advances, and incorporates
insights into natural language processing from other fields, especially
linguistics and psychology. Books in this series describe groundbreaking
research or provide an accessible and up-to-date overview of an area for
nonspecialists. Also included are works documenting freely available
resources for language processing, such as software, grammars,
dictionaries, and corpora.
Series edited by Ann Copestake
CSU Studies in
Computational Linguistics
Representation and Inference
for Natural Language
A First Course in
Computational Semantics
Patrick Blackburn & Johan Bos
\ Q T T Center for the Study of
lV O JL/1 Language and Information
PUBLICATIONS Stanford, California
Copyright © 2005
CSLI Publications
Center for the Study of Language and Information
Leland Stanford Junior University
Printed in the United States
09 08 07 06 05 1 2 3 4 5
Library of Congress Cataloging-in-Publication Data
Blackburn, Patrick, 1959-
Representation and inference for natural language : a first course in
computational semantics / by Patrick Blackburn and Johan Bos.
p. cm. - (CSLI studies in computational linguistics)
Includes bibliographical references and index.
ISBN-13: 978-1-57586-495-2 (cloth cover : alk. paper)
ISBN-10: 1-57586-495-9 (cloth cover : alk. paper)
ISBN-13: 978-1-57586-496-9 (pbk. : alk. paper)
ISBN-10: 1-57586-496-7 (pbk. : alk. paper)
1. Semantics—Data processing. I. Bos, Johannes. II. Title. III. Scries.
P325.5.D38B59 2005
40l'.43'0285-dc22 2004029974
CIP
oo The acid-free paper used in this book meets the minimum requirements
of the American National Standard for Information Sciences—Permanence
of Paper for Printed Library Materials, ANSI Z39.48-1984.
CSLI was founded in 1983 by researchers from Stanford University, SRI
International, and Xerox PARC to further the research and development of
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CSLI Publications reports new developments in the study of language,
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Contents
Preface vii
Introduction xi
1 First-Order Logic 1
1.1 First-Order Logic 1
1.2 Three Inference Tasks 19
1.3 A First-Order Model Checker 29
1.4 First-Order Logic and Natural Language 44
2 Lambda Calculus 55
2.1 Compositionality 55
2.2 Two Experiments 59
2.3 The Lambda Calculus 66
2.4 Implementing Lambda Calculus
2.5 Grammar Engineering 86
3 Underspecified Representations 105
3.1 Scope Ambiguities 105
3.2 Montague’s Approach 109
3.3 Storage Methods 112
3.4 Hole Semantics 127
vi / Representation and Inference for Natural Language
4 Propositional Inference 155
4.1 From Models to Proofs 155
4.2 Propositional Tableaus 158
4.3 Implementing Propositional Tableau 168
4.4 Propositional Resolution 174
4.5 Implementing Propositional Resolution 185
4.6 Theoretical Remarks 191
5 First-Order Inference 203
5.1 A First-Order Tableau System 204
5.2 Unification 209
5.3 Free-Variable Tableaus 215
5.4 Implementing Free-Variable Tableaus 219
5.5 First-Order Resolution 225
5.6 Implementing First-Order Resolution 231
5.7 Off-the-Shelf Theorem Provers 235
5.8 Model Building 242
6 Putting It All Together 259
6.1 Baby Curt 259
6.2 Rugrat Curt 264
6.3 Clever Curt 267
6.4 Sensitive Curt 272
6.5 Scrupulous Curt 277
6.6 Knowledgeable Curt 281
6.7 Helpful Curt 293
A Running the Software - FAQ 309
B Propositional Logic 311
C Automated Reasoning for First-Order Logic 315
D Notation 319
References 321
Author Index 335
Prolog Index 339
Subject Index 343
Preface
This book developed out of courses on computational semantics that
the authors jointly taught at the Department of Computational Lin
guistics, University of the Saarland, Saarbriicken, Germany, in 1995 and
1998, and at ESSLLI’97, the 9th European Summer School in Logic,
Language and Information, Aix-en-Provence, France, in August 1997.
When designing these courses, we found no single source containing all
the material we wanted to present. At that time, the only notes exclu
sively devoted to computational semantics that we knew of were Cooper
et al. (1993), probably the first systematic introduction to modern com
putational semantics. Like the present book, these notes are Prolog
based, and cover some of the same ground, often using interestingly
different tools and techniques. However we wanted to teach the subject
in a way that emphasized inference, underspecification, and grammar
engineering and architectural issues. By the end of the 1990s we had a
first version of the book, influenced by Pereira and Shieber (1987) and
Johnson and Kay (1990) for semantic construction, and Fitting (1996)
for inference, which partially realised these goals.
The project then took on a life of its own: it expanded and grew
in a variety of (often unexpected) directions. Both the programs and
text were extensively rewritten, some parts several times. We first pre
sented a mature, more-or-less stable, version of the newer material at
ESSLLI’01, the 13th European Summer School for Logic, Language, and
Information, Helsinki, Finland, in August 2001. We then presented it
in a more refined form at NASSLLI’02, the 2nd North American Sum
mer School for Logic, Language, and Information, Indiana University,
Bloomington, Indiana, USA, in June 2002. And finally, many years after
we started, we have ended up with the kind of introduction to compu
tational semantics that we wanted all along. It has taken us a long
time to get there, but the journey was a lot of fun. We hope that this
vii
viii / Representation and Inference for Natural Language
comes through, and that the book will be a useful introduction to the
challenging and fascinating area known as computational semantics.
Acknowledgments
The path to the finished book has been long and winding, and we
have accumulated many debts of gratitude along the way. First of all,
we would like to thank Manfred Pinkal and our ex-colleagues at the
Department of Computational Linguistics, University of the Saarland,
Saarbriicken, Germany; the department was a stimulating environment
for working on computational semantics, and the ideal place to start
writing this book. Special thanks to David Milward, who during his stay
at Saarbriicken developed the test suite for /^-conversion, and allowed
us to make use of it. We would also like to thank all our ex-students
from the University of the Saarland, and in particular Judith Baur,
Aljoscha Burchardt, Gerd Fliedner, Malte Gabsdil, Kristina Striegnitz,
Stefan Thater, and Stephan Walter, for their enthusiasm and support.
Conversations with Harry Bunt, Paul Dekker, Andreas Franke,
Claire Gardent, Hans Kamp, Martin Kay, Michael Kohlhase, Alexan
der Koller, Karsten Konrad, Alex Lascarides, Christof Monz, Reinhard
Muskens, Malvina Nissim, Maarten de Rijke, and Henk Zeevat were
helpful in clarifying our goals. We’re grateful to Stephen Anthony,
David Beaver, Mary Dalrymple, Stina Ericsson, Norbert Fuchs, Bjorn
Gamback, Durk Gardenier, Michel Genereux, John Kirk, Ewan Klein,
Emiel Krahmer, Torbjorn Lager, Shalom Lappin, Staffan Larsson, Ste
fan Muller, Ian Pratt-Hartmann, Rob van der Sandt, Frank Schilder,
and David Schlangen for comments on early drafts. Special thanks go
to Carlos Areces and Kristina Striegnitz for their editorial help, to Eric
Kow for Perl hints, and to Sebastien Hinderer for proof-reading.
Many members of the automated reasoning community expressed in
terest in this project and gave us various kinds of support. In particular,
we are grateful to William McCune (the author of Otter and Mace) for
his timely response to our questions, to Hans de Nivelle (the author of
Bliksem) for helping us with our first experiments in off-the-shelf theo
rem proving, and to Koen Claessen and Niklas Sorensson (the authors
of Paradox) for discussion and advice on model building. We’d also
like to thank Peter Baumgartner, Rajeev Gore, Andrew Slater, Geoff
Sutcliffe, and Toby Walsh for their helpful responses to our questions.
Preface / ix
Finally, we are grateful to Robin Cooper and Bonnie Webber, who
both taught courses based on the previous drafts of this book, and
provided us with feedback on what worked and what didn’t.
Patrick Blackburn
Johan Bos
December 2004
