Handbook of Logic and Language

1273 Pages·1997·0.34 MB·English

by  Johan van Benthem

HANDBOOK OF LOGIC AND LANGUAGE
This Page Intentionally Left Blank
HANDBOOK OF LOGIC
AND LANGUAGE
edited by
Johan van BENTHEM
University of Amsterdam & Stanford University
Alice ter MEULEN
Indiana University, Bloomington, Indiana
m
1997 1997
ELSEVIER
AMSTERDAM • LAUSANNE • NEW YORK THE MIT PRESS
OXFORD SHANNON • TOKYO CAMBRIDGE, MASSACHUSETTS
ELSEVIER SCIENCE B.V.
Sara Burgerhartstraat 25
P.O. Box 211, 1000 AE Amsterdam, The Netherlands
Co-publishers for the United States and Canada:
The MIT Press
55 Hayward Street
Cambridge, MA 02142, U.S.A.
Library of Congress Cataloging-in-Publication Data
Handbook of logic and language / edited by Johan van Benthem, Alice
ter Meulen.
p. cm.
Includes bibliographical references and indexes.
ISBN 0-444-81714-X (Elsevier). -- ISBN 0-262-22053-9 (MIT Press)
1. Natural language processing (Computer science) 2. Logic,
Symbolic and mathematical. 3. Semantics. 4. Linguistics.
I. Benthem, J. F. A. K. van, 1949- . II. Meulen, Alice G. B. ter.
QA76.9.N38H36 1996
401'.5113--dc20 96-27559
CIP
Elsevier Science B.V. The MIT Press
ISBN: 0-444-81714-X ISBN: 0-262-22053-9
© 1997 Elsevier Science B.V. All rights reserved
No part of this pubhcation may be reproduced, stored in a retrieval system, or transmitted, in any
form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the
written permission of the Publisher, Elsevier Science B.V, Copyright & Permissions Department,
PO. Box 521, 1000 AM Amsterdam, The Netherlands.
Special regulations for readers in the U.S.A.: This publication has been registered with the
Copyright Clearance Center Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923. Information
can be obtained from the CCC about conditions under which photocopies of parts of this publication
may be made in the U.S.A. All other copyright questions, including photocopying outside the
U.S.A., should be referred to the Publisher, unless otherwise specified.
No responsibility is assumed by the Publisher for any injury and/or damage to persons or property
as a matter of products liability, negligence or otherwise, or from any use or operation of any
methods, products, instructions or ideas contained in the material herein.
This book is printed on acid-free paper.
Printed in The Netherlands
Preface
This Handbook documents the main currents in contemporary research at the interface
of logic and natural language, including its broader ramifications in computer science,
linguistic theory and cognitive science. The history of the combined study of "Logic and
Language" goes back a long way, at least until the work of the scholastic philosophers in
the Middle Ages. At the beginning of the twentieth century, the subject was revitalized
through the pioneering efforts of Gottlob Frege, Bertrand Russell, and Polish philosoph-
ical logicians such as Kazimierz Ajdukiewicz. Around 1970, the landmark achievements
of Richard Montague established a junction between state-of-the-art mathematical logic
and generative linguistic theory, following Chomskyan standards of rigor. Over the sub-
sequent decades, this enterprise of Montague Grammar has flourished, and diversified
into a number of research programs with empirical and theoretical substance. Its cur-
rent results are found in rapidly disseminated results concerning generalized quantifiers,
categories and type theories, situations and partial logic, dynamic interpretation and in-
ference, or feature structures and unification. Some of the material produced may be
found in other handbooks on semantics or computer science. But most of it is scattered
in research papers, preprints with only local accessibility, ftp-archives or limited editions
of special-purpose collections. There is not even one main journal serving this emergent
scientific community, even though "Linguistics and Philosophy", "The Journal of Philo-
sophical Logic", "Natural Language Semantics" and "The Journal of Logic, Language
and Information" collectively span a good deal of it. The current Handbook appears to
be the first in putting the logic-language interface as such at center stage. We want to
demonstrate both aspects of the interaction between logic and language, namely (1) how
logical systems are designed and modified in response to linguistic needs, and (2) how
mathematical theory arises in this process, and how it affects subsequent linguistic theory.
This collection is not a textbook, however. The novice to the field should consult one
of several available fine introductions with non-partisan coverage of basic assumptions,
tools and results.
The primary purpose of this Handbook is to chart the scientific territory of this research
community, serve as vademecum to its travelers and communicate its main results and
achievements to its widening audience. Our choice of topics for the twenty chapters
has been intended to demonstrate the strongest issues of 'ongoing concern', but also,
to bring some new themes to the fore. The following working principles explain the
principal architecture of this resulting volume.
vi Preface
Frameworks
"Logic and Language" used to be a loosely organized scholarly community, until a divi-
sion into different schools became visible in the eighties, perhaps due to academic pop-
ulation growth or changing funding structures. These schools embodied certain valuable
perspectives and methodologies, that we have chosen to represent here. There are the two
classical paradigms of Montague Grammar and Government Binding Theory, which are
still spawning modern manifestations to-day, such as 'dynamic' versions of the former,
and 'minimalist' versions of the latter. Next, we have added two influential enterprises
of the next generation in the 80s, viz. Discourse Representation Theory and Categorial
Grammar. Finally, we have included two principal competitors, viz. Game-Theoretical
Semantics and Situation Theory. Our sense is, however, that polemical scholarly divisions
are on the wane. The six chapters in the Frameworks Part demonstrate broad approaches,
rather than a scripture for narrow sects - and moreover, they interleave in various ways.
It is our deep conviction that the logical study of natural language benefits from such
methodological diversity, while keeping an open eye for universal topics of common
concern. After all, even in the established sciences, the existence of different stances
(say, 'discrete' or 'continuous', 'algebraic' or 'geometric') has long been a recognized
as a beneficial aspect of our human repertoire of research strategies.
General topics
In this Part, we have collected some pervasive logical and mathematical themes across
the study of linguistic phenomena. These have been chosen with various motivations in
mind. First, the above frameworks use a number of different mathematical paradigms for
their articulation. Montague Grammar and Categorial Grammar have been traditionally
associated with the well-established fields of lambda calculus and Type Theories. On
the other hand. Government Binding Theory as well as current 'unification grammars'
tend toward some form of the newly emerging field of Feature Logic. Yet other math-
ematical paradigms are relevant, too. For example, game-theoretical semantics naturally
involves mathematical game theory, and Situation Semantics has gone towards Partial
Logic, often in combination with non-wellfounded set theories. These connections are
not exclusive. For instance, the primordial formal question in linguistic semantics has
been the quest for Compositionality, which is often pursued in a framework of universal
algebra. Moreover, what is typical for mathematical approaches is the constant discovery
of new connections. For instance, feature logics turn out to have many connections with
the existing field of modal logic - and so do non-wellfounded set theories. (But even
when existing mathematical paradigms are employed, the natural language connection
may provide them with new twists.) A second source for logical theory has been the
study of specific categories of linguistic expression. For instance, a recurrent topic is
the structure of natural language quantification, which has inspired an independent the-
ory of Generalized Quantifiers. Likewise, studies of anaphora and related phenomena
(especially within discourse representation theory) have motivated a search for dynamic
procedures for evaluating expressions, which finds its expression in the new topic of log-
ical Dynamics. Thirdly, we have added some themes for other reasons. By and large, the
Preface vii
logical emphasis in the study of natural language has been semantic. But the other main
parts of logic, namely, proof theory and recursion theory, are becoming ever more rele-
vant, too. The chapter on Mathematical Linguistics and Proof Theory demonstrates the
first connection. It forms a natural pair with the Framework chapter on type-logical gram-
mars, showing how significant proof-theoretic techniques can solve outstanding problems
in mathematical linguistics, and how proof calculi and (algebraic) models are related at
a meta-theoretic level after all. The chapter on Formal Learning Theory illustrates the
second combinatorial connection, applying recursion-theoretic tools to important aspects
of linguistic competence. Another common thread in much of this work are pervasive
connections with the study of programming languages, data structures or knowledge rep-
resentation in computer science. The chapter on Nonmonotonicity in Linguistics shows
one striking instance where techniques and concerns from artificial intelligence are merg-
ing with those in "Logic and Language".
Descriptive themes
Finally, there is a group of chapters devoted to some major empirical phenomena in
natural language that have inspired logical theory. The list is certainly not exhaustive from
a linguistic (or even a more narrowly semantic) point of view, but we did try to cover
most major areas in our chapters on Quantifiers, Temporality, Plurals and Collectives,
and Generics and Defaults. To these, we added two chapters showing that the logical
approach also extends to phenomena that are often considered part of pragmatics, such
as Presupposition and Questions.
Evidently, other principles of division are possible for all this material. Therefore, an
appended Glossary provides information about further ubiquitous notions in the field
of "Logic and Language", that cut across chapters, such as 'anaphora', 'ambiguity' or
'inference'.
This is a rapidly developing field. In future editions, we may want to include new areas
where logic and language meet, such as phonology, pragmatics and speech act theory, or
discourse modeling. Also, the area of computational linguistics has been underrepresented
(in part, to avoid overlap with other Handbooks) - so that we hardly deal with issues
of efficiency or real-time performance for logical systems. Even so, no exclusions of
principle underlie the present selection. For instance, even though our main emphasis
here is semantic, we do include proof-theoretic and recursion-theoretic themes - and we
even expect that proof-theoretic and indeed more general combinatorial concerns and
results will grow in importance in the years to come.
Another development that we foresee is a confluence of concerns between this field
and related areas within computer science and cognitive science. There are powerful
analogies between studying, say, human conversation and information exchange between
machines. Often, one common account of information structure may serve both descrip-
tive and engineering needs. Various indications of this trend can already be observed
in some of our chapters, witness the influence of dynamic programming paradigms, or
the marriage between categorial analysis and type theories or linear logics prominent in
program verification and synthesis. In the final analysis, this insight was already implicit
viii Preface
in Montague's Thesis, when he stated that he saw no difference in principle between the
study of formal and natural languages (and, we would add: programming languages).
This contact is also very much in evidence in the "European Summer Schools in
Logic, Language and Information", which have served as a meeting place for the field
for some eight years now. Their course curriculum brings together all the strands that
we have touched upon: Logic, Language, Computation, Logic and Language, Logic and
Computation, Language and Computation. We see this trend, not just as a technological
fashion, but also as a welcome broadening of the scope and applicability of logico-
linguistics - toward a general science of 'information systems' and cognitive processes.
This field is so vast, that no methodological or ideological purity seems feasible or even
desirable - and indeed, the recent literature shows ever changing constellations of syntax
and semantics, model theory and proof theory. Finally, there is also a more descriptive
perspective in this wider development. Both logical formalisms and computational ones
are artifacts of human design. But logico-linguistic theories often deal with cognitive
phenomena with independent empirical manifestations, which are also being studied by
cognitive psychologists. We predict more intensive contacts here as well. For instance,
the agenda of a semantic system might come to contain, not just the usual issues like
correctness or completeness, but also the explanation of common mistakes, or other parts
of human performance.
Our aim has been to demonstrate the interaction of logic and language, and the chap-
ters of this Handbook should be assessed as the product of that contact: not exclusively
on their linguistic or logical merit. Logico-linguistics is sui generis, even though we have
emphasized its connections to its parent disciplines, as well as some broader interdis-
ciplinary trends. Important contributions are not necessarily measured in terms of net
weight in theorems, or baskets full of fresh empirical observations. They often consist in
careful conceptual analysis, driven by empirical data, but using mathematical techniques
to construct appropriate information models. Of course, contributions of this kind occa-
sionally do affect the parent disciplines. Results obtained in generalized quantifier theory
are currently interacting with more mathematical research, and the same can be observed
or expected for other interfaces. (For instance, a case in point is that of temporal structure
in natural languages, philosophy and computer science.) But the main point remains a
certain 'feeling' and tolerance for different kinds of intellectual achievement. It is not at
all easy to find the appropriate level of abstraction for logico-linguistic research. One is
not after simplistic concrete notions like the ins and outs of 'grammatical wellformed-
ness', but rather after deeper general mechanisms in cognition and information flow, such
as 'collectivity', 'dependence' or 'polymorphism', and the cross-linguistic universals sig-
naling their presence. It seems fair to say, though, that we do not yet have any good
integrated architecture of this kind which would allow us to understand the structure and
explain the efficiency (such as it is) of human cognitive processes.
Finally, let us formulate one more disclaimer. Aristotle once observed that it is the hall-
mark of an educated mind to give any subject of investigation no more formal structure
than is germane to it. Many people have claimed that natural language is intrinsically un-
stable, and more 'artistic' then formal-mathematical in its character. From that viewpoint,
logical analysis may not have enough of a foothold, and also, it may produce at best
overly complex formalism. Evidently, the raison d'etre of the field represented here has a
Preface ix
different presupposition. There is enough stable structure in natural language to support
logical analysis and theory formation. This does not mean that every aspect of natural
language is amenable to this style of analysis. It would be tedious to produce formal
systems where a light essay would convey the main insights much more clearly. And
indeed, the chapters in this Handbook show a great diversity of literary styles, reflect-
ing the range of academic cultures meeting here. Incidentally, even the formal 'logical
style' does not involve one uniform methodology. For instance, Montague advocated
the complete formal specification of natural language fragments with fully determinate
interpretations - which to some critics may seem like their terminal dissection and clin-
ical death. But the methodology of the field has become much more diverse, as will be
amply clear from the treatment of natural language structure and its uses in our various
chapters. In this, it is quite similar to computer science, where the design of complete
systems is just one way of approaching the study of computation. And with this much
general philosophy, we invite the reader to take a look.
The diversity of perspectives that come together in this Handbook here will probably
be reflected in that of its readership. Different digestive strategies may be advisable
for linguists, logicians or computer scientists - and in any case, our chapters do not
form a linear sequence. Some Framework chapters are good introductions to the kind of
enterprise going on in this field, while those on Descriptive Topics present a lot of the
typical data that must be accounted for. From a logician's viewpoint, there are yet other
coherent subsets, including a type-theoretic track and a dynamic track. But it is by no
means impractical to simply tackle the chapters in their own order, using the Glossary
for occasional assistance.
Acknowledgement
For an enterprise of this scale to reach completion, a large number of colleagues have
generously provided their assistance, ranging from an occasional bibliographic reference,
via critical reading of early drafts or offering insightful advice on our coverage, to sub-
stantial contributions of material that went into chapter texts. Among these we would
mention: Greg Carlson, Gennaro Chierchia, the members of the FRACAS project, Josef
von Genabit, Martin Kay, Monika Kiraly, Angelika Kratzer, Manfred Krifka, Sten Lind-
strom, Godehard Link, Michael Morreau, Drew Moshier, Dick Oehrle, Barbara Partee,
Jim Rogers, Krister Segerberg, Moshe Vardi, Frank Veltman.
Various authors have profited importantly from comments and advice from their des-
ignated commentators, who are mentioned on the front leaf. We took this useful system
from the various Handbooks produced by Dov Gabbay. Some commentators have be-
come co-authors, witness several of our chapters. The Handbook and its editors have also
been strengthened by early advice and support from Stan Peters. Despite this extensive
support system, there have been set-backs. Planned chapters on "Unification Grammars",
"Intensionality" and "Conditionals" had to be dropped at a late stage, for reasons entirely
beyond the control of the editors. Some pointers to these areas have been moved into
the Glossary. Finally, it is a pleasure to record a matter of intellectual credit. The idea
for this Handbook was first conceived by Arjen Sevenster from Elsevier Science Pub-
lishers, who has been a pillar of support ever since. Elsevier has also provided funding