Generalized Quantifiers: Linguistic and Logical Approaches

308 Pages·1987·6.447 MB·English

by  Jon Barwise (auth.), Peter Gärdenfors (eds.)

GENERALIZED QUANTIFIERS
STUDIES IN LINGUISTICS AND PHILOSOPHY
formerly Synthese Language Library
Managing Editors:
ROBIN COOPER, University of Wisconsin
ELISA BET ENGDAHL, University of Wisconsin
RICHARD GRANDY, Rice University
Editorial Board:
EMMON BACH, University of Massachusetts at Amherst
JON BARWISE, CSLI, Stanford
JOHAN VAN BENTHEM, Mathematics Institute, University o[ Amsterdam
DA VID DOWTY, Ohio Stale University, Columbus
GERALD GAZDAR, University ofS ussex, Brighton
EWAN KLEIN, University of Edinburgh
BILL LADUSA W, University of California at Santa Cruz
SCOTT SOAMES, Princeton University
HENRY THOMPSON, University of Edinburgh
VOLUME 31
GENERALIZED
QUANTIFIERS
Linguistic and Logical Approaches
Edited by
PETER GARDENFORS
Department ofP hilosophy, Lund University
D. REIDEL PUBLISHING COMPANY
A MEMBER OF THE KLUWER ACADEMIC PUBLISHERS GROUP
DORDRECHT I BOSTON I LANCASTER I TOKYO
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TABLE OF CONTENTS
PREFACE vii
JON BARWISE / Noun Phrases, Generalized Quantifiers and
Anaphora 1
JOHAN van BENTHEM / Towards a Computational Semantics 31
ROBIN COOPER / Preliminaries to the Treatment of Gener-
alized Quantifiers in Situation Semantics 73
LARS G. JOHNSEN / There-Sentences and Generalized
Quantifiers 93
EDWARD L. KEENAN / Unreducible n-ary Quantifiers in
Natural Language 109
GODEHARD LINK / Generalized Quantifiers and Plurals 151
SEBASTIAN LOEBNER / Natural Language and Generalized
Quantifier Theory 181
JAN TORE L0NNING / Collective Readings of Definite and
Indefinite Noun Phrases 203
MATS ROOTH / Noun Phrase Interpretation in Montague
Grammar, File Change Semantics, and Situation Semantics 237
DAG WESTERST AHL / Branching Generalized Quantifiers
and Natural Language 269
LIST OF CONTRIBUTORS 299
BIBLIOGRAPHY FOR GENERALIZED QUANTIFIERS AND
NATURAL LANGUAGE 300
INDEX OF NAMES 304
INDEX OF SUBJECTS 306
v
PREFACE
Some fifteen years ago, research on generalized quantifiers was con
sidered to be a branch of mathematical logic, mainly carried out by
mathematicians. Since then an increasing number of linguists and
philosophers have become interested in exploring the relevance of
general quantifiers for natural language as shown by the bibliography
compiled for this volume. To a large extent, the new research has been
inspired by Jon Barwise and Robin Cooper's path-breaking article
"Generalized Quantifiers and Natural Language" from 1981.
A concrete sign of this development was the workshop on this topic
at Lund University, May 9-11, 1985, which was organized by Robin
Cooper, Elisabet Engdahl, and the present editor. All except two of the
papers in this volume derive from that workshop. Jon Barwise's paper
in the volume is different from the one he presented in connection with
the workshop. Mats Rooth's contribution has been added because of its
close relationship with the rest of the papers. The articles have been
revised for publication here and the authors have commented on each
other's contributions in order to integrate the collection.
The organizers of the workshop gratefully acknowledge support
from the Department of Linguistics, the Department of Philosophy and
the Faculty of Humanities at Lund University, the Royal Swedish
Academy of Sciences (through the Wallenberg Foundation), the
Swedish Institute, and the Letterstedt Foundation.
Lund, August 1986 PETER OARDENFORS
vii
JON BARWISE
NOUN PHRASES, GENERALIZED QUANTIFIERS
AND ANAPHORA
1. INTRODUCTION
In this paper, I discuss some relations between the generalized quan
tifier model of natural language quantification given in Barwise and
Cooper (1981) (hereinafter [BC]), on the one hand, and the approach
taken in Barwise and Perry (1983) (hereinafter [BP]), on the other. The
discussion focuses on problems of anaphora and its interaction with the
theory of quantification embedded in these two accounts. However, I
am also forced to touch on the issue of just what we are up to in giving
a model-theoretic account of semantics, one that uses some artificial
language like first-order logic or the language L(s s) presented here.
In [BC], Cooper and I proposed a model of noun phrase interpreta
tion where NPs are always interpreted as sets of sets of individuals. In
[BPI, Perry and I only treated in detail a restricted form of NP, what we
called "singular noun phrases," following the philosopher's use of
"singular term." These include names, definite descriptions and indefi
nite descriptions. Such NPs were assigned both meanings (relations
between situations and individuals) and various sorts of interpretations,
the most specific being as individuals. None of these correspond closely
with the generalized quantifier approach. In Chapter 11 we suggested
that something more like the generalized quantifier approach would be
more appropriate for "general" NPs, those containing determiners like
every, no, and the like, but did not go into any detail.
The original motivation for treating singular and general NPs differ
ently in [BPI stemmed from the simple observation that singular NPs
can be used both to describe individuals, as well as to refer to individ
uals. You cannot use general NPs to do either. Thus, for example, you
can use a singular NP, but not a general NP, as an appositive relative
clause. This seemed like an important distinction that should not be
blurred by forcing them both into the same semantic mold. More
recently, though, I have come to feel that this same distinction is
important for understanding the difference in anaphoric effect of the
two sorts of NPs. In this paper, then, I will attempt to show that
1
Peter Garden/ors (ed.), Generalized Quantifiers, 1-29.
Copyright ©.1987 by D. Reidel Publishing Company.
2 JON BARWISE
something very much like the generalized quantifier approach is a good
model for general NPs, but that something like the one Perry and I used
is better for accounting for the anaphoric effect of singular NPs.
To be more specific, I propose to replace the binary semantic
distinction of free and bound variables inherited from first-order logic,
and used in most model theory since, including Montague grammar and
the model theory of [BC], by a ternary semantic distinction: free,
restrained, and captured. I will give a precise definition of these notions
for a formal language presented below, but here is the basic idea.
Suppose a is a (use of some) pronoun in an utterance u of some
j
expression {:J. Roughly, we will say that aj is captured if aj does not
refer to or designate anything, but rather, the role it plays in the inter
pretation of {:J is completely and solely determined by a generalized
quantifier, that is, by the interpretation of some general noun phrase of
{:J, a noun phrase which must be non-referring. By contrast, a is free if
j
the referent a of a is up to the speaker, except for considerations of
j j
gender and discourse function, but is not in any way controlled by the
interpretation of other noun phrases of {:J. Otherwise, we say that a is
j
restrained; this will be so just in case it refers to or describes some
object aj, but aj is restrained by the interpretation of some singular
noun phrase in {:J.
Of course to make these informal definitions do any work, they must
be made precise, and in a way that explains properties of natural
language quantification and anaphora that have appeared problematic
on the first-order logic model. This will involve us in some fundamental
revisions of this model, and so of generalized quantifiers themselves.
The most basic change is that we must view the utterance of an expres
sion more dynamically, as having an effect on the environment shared
by speaker and hearer, the effect being represented by various sorts
of changes in variable assignments. Regarding generalized quantifiers,
we must make them more flexible and powerful, since the original
generalized quantifier approach does no better than more traditional
accounts with anaphoric phenomena like "donkey" sentences (see
below). One of my aims here is to show how to improve the generalized
quantifiers framework so that it will handle such phenomena without
recourse to an extra level of explicit syntactic representations of the
kind used in Kamp's (1981) DRS theory.
I want to tackle something a bit more general than the relation that
holds between an anaphoric pronoun and its antecedent. Namely, I
GENERALIZED QUANTIFIERS 3
want to consider the relationship between the interpretation of any
dependent noun phrase, say a, and a noun-phrase element y on which
it depends. I will call the latter an antecedent of the former, the foi:mer
a dependent of the latter, and so be interested in the dependent/
antecedent (01 DIA, for short) relation. With this definition, the VIA
relation properly includes the anaphora/antecedent relation. Examples
of the former but not the latter are: Jon is taller than every other
logician, Jon is annoyed by every taller logician. It is clear that these
sentences can be used in such a way that the interpretation of the NPs
every other logician, every taller logician depends on the interpretation
of Jon. The general strategy we develop for anaphora/antecedent
relations takes care of this kind of dependence as well, and thinking
about the more general problem frees one from certain presuppositions
that one tends to bring to the problem from logic.
Before we turn to the various revisions in the treatment of gener
alized quantifiers and the VIA relation, I digress to discuss what it is we
are doing when we use a model theoretic language similar to first-order
logic for the study of natural language semantics.
1.1. How to Think about Artificial Languages
In order to isolate the features of situation semantics that have to do
just with the NPs and the VIA relation, I am going to define an artificial
language that embodies this part of the theory. I call this language
L(ss).
As a logician, I have found myself in somewhat of a dilemma in
recent years. One of the things logicians have become proficient at over
the past 25 years is the invention of new artificial languages, languages
intended to shed light on various kinds of mathematical activity. There
have been a lot of interesting work done and tools developed. These
give the logician a nice "tool box" for building and studying new
languages. However, at the same time, it has made some of us very
sceptical that first-order logic, or any other formal language, is part of
any theory of human language. How, then, are logicians (let alone the
rest of the world) to think about the relation between the artificial
languages they invent and the languages people actually use? Talking to
people at CSLI, especially John Etchemendy and Brian Smith, has
given me a way to resolve this dilemma by using the layman's distinc-
4 JON BARWISE
tion between a model of something and a theory of it - say a physical
model of air flow over an airplane wing and a theory of such flows.
Situation semantics is an attempt, however tentative, to spell out a
realistic semantical theory of natural language use. However, it is often
easier and more perspicuous to give a model of something than to
present a theory of it. This is how I suggest we think of artificial
languages like first-order logic (POL), Montague's intensional logic
(IL), and the logic L(ss) defined below - as models of natural
language, like a globe is a model of the earth.
As models of human language, current artificial languages are pretty
crude affairs. However, they have had their successes, and they have
certainly shed light on a number of important phenomena. Still, there is
a lot of room for improvement in these models, which is why logicians
have been studying a host of other languages. In this paper, then, rather
than talk about situation semantics as a theory, I want to use a few
ideas from situation semantics to build a language much like FOL, but
one that gives us a better model of the DIA relation of English.
1.2. Changing the FOL Model 01 Anaphora
A model is a model of something else, say some aspect of reality R,
only under some correspondence c between things of the model and
parts of R. The basic relation of artificial languages like FOL and IL is
a three place relation, that of satisfaction, a variable assignment 1
satisfies a formula ~ in a structure M, usually written:
M 1== ~[f1.
The correspondence c between these three things and parts of real
language use is usually left implicit. M corresponds to the world or
some part of it, ~ to some sentence or statement of human language,
and 1 to some interpretation of the free variables, the latter corre
sponding to certain kinds of pronouns.
While IL gives a more sophisticated treatment of noun phrases and
quantification than FOL, the basic treatment of pronouns and binding
is exactly the same. Indeed, every single logical language that I know
has basically the very same treatment of binding.1 For this reason, I will
use FOL as the foil for L(ss) in the following discussion. My semantics
for general NPs will be similar to that of IL, or more accurately, to that
of the language L(GQ) that Cooper and I defined in Barwise and
Cooper (1981).