A Hybrid System For Quantifier Scoping

Abstract

this paper has been to show that syntactic and lexical factors are well-behaved enough that non-modularity restricted to these factors is a burden which however is bearable, and worth bearing. But if all factors including infinite complex meanings are hybridized, the problems become intractable. It would be perhaps impossible to determhe even a large portion of the fun, ction flex-syn-se.m-prag. And even if it were only excruciating out not impossible, the effort would have to be largely duplicated whenever the data was extended. It's not for nothing that modularity is a hallmark of good design. (Note also, incidentally, that scoping would have to entirely follow translation, unlike Figure I.) As a working hypothesis I have adopted the second alternative. Yet the argument of section I, extended to semantic factors, suggests that if the system is to capture the complex and subtle variations in human scope judgments, these factors should be not integrated but hybridized. To back away from this because it makes the engineering too hard may be understandable, but we should not forget the joke about the guy looking for lost keys where he knows they aren't because the light is better there. Modularity may be imperative for approaching complex problems, but there is no a priori reason why the mind must be modular. Indeed Fodor (1983) has speculated that much of it may not be, and hence he is pessimistic about cognitive science

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A HYBRID SYSTEM FOR QUANTIFIER SCOPING
1. Introduction
A prominent
confronting natural language processing systems
is ambiguity of quantifier scope relations. For
example, the sentence Some target was hit by
every arrow has one reading on which the
quantified noun phrase (NP) some target has
wider scope than the quantified NP every arrow
(some particular target got hit by all the arrows),
and another reading on which every arrow has
wide scope (each arrow hit some target or other).
Many factors influence preferred scope readings.
Semantic factors, for example: in Sam served one
beer to all customers, we prefer wide scope for
all because the alternative reading entails the
unlikely scenario of patrons huddled around a
single beer mug. Syntactic factors:
embedded prepositional objects often scope over
heads, as in Every teacher at some high school
joined the union, whereas heads usually assume
scope over NPs contained in a relative clause, as
in Every teacher who is at some high school
joined the union. Lexical factors (i.e. the lexical
identity of quantifiers): e.g. each tends toward
wide scope and a toward narrow scope. Linear
order is a factor - leftmost quantifiers tend to
have wide scope - and there are others as well.
Given the relevance of different factors, a
question arises: how can a system determine a
scope reading based on the combination of
factors present in any given sentence?
The standard approach has two parts: f'wst,
assign measures to the scoping influences of
specific factors taken individually, and second,
integrate the individual measures. The first task
is performed by various "specialists". A system
may have a lexical specialist which represents the
wide scope tendency of each, a specialist which
represents the inverse scoping tendency of an
embedded prepositional object, a specialist which
represents the tendency of quantifiers to scope
according to linear order, and so on. The system
will prefer those scope orders for which
fint(fspecl, fspec 2 .... ) is optimal, where lint is
the integrating function and each fspec i is a
specialist. For example, in the system of Grosz
et. al. (1987), the specialists are called "critics."
Given a candidate scope order, the "left-right"
source of ambiguity
e.g.
ARNOLD J. CHIEN
PRC Inc.
1500 PRC Dr., 5S3; McLean, VA 22102 USA
chien arnold@po.gis.prc.com
critic deducts points for each deviation from left-
to-right scope order; the "quantifier strength"
critic (i.e. lexical specialist) uses a numerical
ranking of quantifiers to add and deduct points
depending on how closely the candidate order
respects the ranking; and so on. The integrating
function fint simply adds up the critics' points,
though Grosz et. al. allow that the critics'
judgments may need to be variously weighted in
some fashion. To my knowledge all current
systems use an "integration of specialists"
(henceforth IS) approach, though not always as
explicitly as Grosz et. al.; e.g. lint often is
implicit in the order in which various specialized
rules or preferences are tested in the clauses of a
complex conditional. See e.g. van Lehn (1978),
Woods (1978), Allen (1987), Hurum (1988),
Moran (1988). (Note that the common
categorization of IS systems does not deny the
myriad differences of detail between systems;
indeed the functional characterization is useful
because it abstracts over these differences.)
There is an alternative to IS. In what I will
call "hybridization," different factors are
conjoined before any scope judgment is made. A
system hybridized for lexical and syntactic
factors has no lexical or syntactic specialists, but
rather a single function, call it flex-syn, whose
input is the conjunction of lexical and syntactic
factors in a sentence. Given an input with
quantifiers ql and q2 and (relevant) syntactic
features s 1, ..., Sn, such a system computes
flex-syn(ql, q2,sl ..... Sn) rather than
fint(flex(ql, q2), fsynl(Sl ) ..... fsynn(Sn)).
The advantage of this is that scope intuitions
can be recovered directly. Take the tendency for
an embedded prepositional object to scope over a
head NP. This tendency varies depending on the
quantifiers involved, among other things. In e.g.
Every man on some committee abstained, there is
a preference for the embedded NP to assume
wide scope, but in A man on many conn,nittees
abstained, the preference seems reversed. A
prepositional phrase (PP) specialist in an IS
system will not know how the preference
changes when a and many quantify the head and
the embedded object; since it is a specialist, it
does not consider lexical input. Rather, the
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system must turn to the lexical specialist, which
for its part knows e.g. that a usually takes
narrow scope, but not how the behavior of a and
many varies with specific environments, such as
embedded PP constructions. 1t is hard to see,
then, how any integration of these specialists
could prescribe a scoping of a over many in an
embedded PP context, since both prefer the
reverse scoping. (An additional ordering
specialist may prefer the correct scoping but
without ad hoc weighting, the integrated
preference will still be incorrect.) But there is no
problem in a hybrid system, because the values
flex.syn(every, some, head-embedded-PP) and
flex~syn(a, many, head-embedded-PP) are
coml~letely independent, as opposed to having a
PP specialist in common, and can be specifiext
however intuitions dictate. Scope judgments are
based on all the lexical and syntactic factors
present, rather than on each factor taken in
abstraction t¥om the others.
My case for hybridization does not rely on
counterexample, but on the flmdamentally
murky nature of IS.
Suppose there is election data showing, for any
pair of candidates and any state, the relative
vofiug preference when the candidates ran in the
state. How should we design a system to
produce a preference given two candidates and a
state? A natural approach would be to simply
retrieve the datum based on the candidate and
state input together. But on an IS approach, a
"candidate" specialist would measure a tendency
over all states of the relative performance of the
two given candidates; a "state" specialist would
measure a tendency over the relative
performances of all candidates, taken pairwise, in
the given state; then somehow the two measures
would be integrated. The problem here is that
whereas the desired datum is a simple, the
computation is barred on complex abstractions
over much data other than the desired, relevant
bit. That is the basic difficulty of an IS system,
which the PP example was meant to illustrate.
Though semantic and pragmatic factors also
influence scope, they are not central to my
current concern: the design of a "base" scoping
unit which can be ported to different domains and
adaptively extended, and which can be improved
in~,wementatly as bits of real-world knowledge are
gradually added to the system (as with Grosz et.
al. 1987, Moran 1988, and Hurum 1988).
Hence the focus on syntactic and lexical factors,
which make up most of the domain-independent
factors. I will return to this issue in section 3.
Consider an analogy.
2. ]Implementation
A hybrid scoping system has been fully
implemented as part of the PRC Adaptive
Knowledge-Ba~d Text Understanding System
(Loatman et. al. 1986). Figure 1 shows the
basic organization of the PAKTUS scoping
module (PSM). I will describe input/output, the
database, and the scoping algorithm in turn.
logical form
databaso 1
PSM
Figure 1. Organization of Scoping Module
2.1 Input/Output
Given a parse tree, PSM returns a list of the
preferred scope orders of the quantified phrases.
No degree of preference is computed. A scope
order is represented by an ordered list of the
phrases, not by a logical fbrm.
Though eventually there will be translation
to logical form, there is good reason for delaying
this until after the scope determination. The
.problem with systems which translate a parse tree
into an "unscoped" logical form as input to the
scoping module (e.g. Hobbs and Shieber 1987)
is that syntactic influences are not discernible to
the module, since logical structure is not
syntactic structure. For example, Every teacher
who is at some high school joined the union and
Every teacher at some high scl~ool joined the
union have the same un~oped logical form: for
Hobbs and Shieber, joined-union( <every t and
(teacher(t),at (t, <some h high-school(h)>))>). So
the different syntactic influences are invisible.
Though syntactic input can of course be added
(e.g. Hurum 1988), doing so amounts to an
admission that the translation was premature. It
is more efficient to have the input to the module
consist just of the parse, postponing the
t~mslation to logical form until after the scoping
determination. Thus, the translator (not yet
implemented) is not part of PSM.
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2.2. Database
PSM encodes a function flex s- defined for
quantifier elements,
quantificational adverbs such as always, and 49
syntactic environments.
"vertical" environments - embedded PP, reduced
and full relatives - and 46 "horizontal"
environments, where a horizontal environment is
defined by a combination of grammatical roles,
voice, and/or various ordering relations.
Defining the mapping from a conjunction of
quantifier pair and environment to a prescribed
scope order for the over 9000 mathematically and
syntactically possible conjunctions admittedly is
a daunting task. This may be the main reason to
prefer an IS approach. But while the required
research effort has been lengthy and tedious, it
has paid dividends in a body of data (150 pages,
described in the appendix of Chien 1992), which
subsumes existing consensus on lcxical and
syntactic scoping influences while going deeper
and beyond. However, the corpus is naturally
subject to continual correction and extension, and
while this upgrading can be accommodated, the
process is not modular. It seems to me that this
is the tradeoff for the hybrid's greater precision.
Database implementation was motivated by
the desire to make access to the large volume of
data as efficient as possible. There are three
levels of data objects. The first, top-level, object
has slots corresponding to pairings of
grammatical roles (subject, direct object, etc.; for
their relevance to scope, see Ioup 1975). In each
slot are pointers to several second-level objects,
called "rule groups". In these, a "conditions"
slot contains procedures which test for syntactic
properties such as voice and linear ordering, and
another slot contains pointers to third-level
objects called "rules". In these, a conditions slot
contains procedures to test for the lexical identity
of a quantifier pair, and an "actions" slot contains
procedures which effect a scope preference.
Thus the latter procedures are invoked only after
the collective syntactic and lexical properties of
the input are verified.
conditions in stages via the object hierarchy
permits large aggregates of data to be eliminated
from consideration at each stage. Data objects of
all levels total about 325, including a second top-
level object for vertical relations, el. 2.3 below.
Database organization is illustrated in Figure
2. If a direct object and adverbial in a clause are
quantified, the rule groups in the appropriate slot
of RULEGRPS are tested. If in addition the
clause is passive and the adverbial immediately
precedes the main verb, then RULEGRtY25 is
-., .vii
including 26 9
There are three
But checking the
RULEGRPS
subject-dirobject
subject-indirobject
subject-prepobject
subject-adve~
dirobject-indirobject
dirobject-prepobject
dirobjecl-adverbial
indirobject-prepobject ... l
indirobject-adverbial
prepobject-adverbial
rgl ,rg2 ....
...
...
...
...
"~.~,rg,?.5
RULEGRP25
conditions adv-preverb,volce-passive
rules .... rule112
RULE112
conditions dirobject-some,adv-decr
actions setparams
Figure 2. Database Hierarchy
activated and its rules tested. If, finally, the
direct object is quantified by some and the
adverbial is a "monotone decreasing" quantifier
such as never, seldom, or rarely (Barwise and
Cooper 1981) then RULE112 is activated and the
procedure "setparams" invoked. The effect of
this - in the context of the algorithm explained in
the next section - is to register a preference for
the object to scope over the adverbial, as e.g. in
He was seldom seen by some agent. (The
alternative scoping is awkward, better expressed
with polarity-sensitive any replacing some; for
the treatment of any, see Chien 1991.)
It should not be thought that a hybrid system
cannot exploit generalizations in the data. PSM
can and must do so, for even with a structured
database, search would be relatively slow if there
were as many actual data structures as abstract
data points (i.e. values of flex-syn). But in fact
each rule represents a cluster'of like points,
grouped together by quantifier categories - e.g.
"deer" in RULE112, or the category of universal
quantifiers - by boolean combination, or by other
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generalization, thus gaining economies in the
database. To illustrate generalization by syntactic
information alone, consider the verb objects in
He sent a firm each invoice: they appear to scope
in order regardless of how they are quantified.
To capture this phenomenon, the relevant rule
registers a preference without checking for the
lexical identity of the quantifiers. Note that this
strategy subsumes cases which in an IS system
would be handled by an overriding specialist, i.e.
a specialist fo such that fiat fro(X), "") = fo(x) •
In such cases IS is not problematic, but
hybridizatiou is equally straightforward.
A generalization can also be based on
syntactic information together with partial lexical
infomlation, i.e. one quantifier only. It appears
e.g. that sometimes in preverbal position always
scopes over a direct object, as in She sometimes
polishes each trophy, regardless of how the
object is quantified. To implement this, the rule
group that looks for this configuration
adverbial and direct object has in its rules slot a
rule whose condition for firing is only that the
adverbial is sometimes. Here is a generalization
over the data points flex_syn(sometimes,x,e), for
all NP quantifiers x, where e is this syntactic
configuration. Note that the organization of the
database precludes an overriding determination
based on lexical information alone, since syntax
must always be checked first.
unaware of any lexical preferences which are
exceptionless across syntactic environments.
The number of rules is farther reduced by
the use of a default preference: PSM initially
assumes scope order to match linear ("natural")
order. This enables the elimination of rules
prescribing natural order, unless the preference is
very strong in that it cannot be undone by any
conflicting preference in a sentence with more
than two quantifiers. This is explained below.
of
But I am
2.3. Scoping Algorithm
PSM determines the scope order only of
quantificrs all of which arc horizontally related, or
all of which arc vertically related (as in Epstein
1988). So, for Every athlete who took some
steroids won a race the system scopes every
athlete and some steroids, likewise every athlete
and a race; then the scoping of some steroids and
a race is treatext as already indirectly determined.
The top-level scoping procedure calls the
horizontal scoping procedure (H-SCOPE) for the
top-level clause of the parsed input. It then
substitutes, for each top-level NP in each of the
resulting scope orders, an order returned by the
vertical scoping procedure (V-SCOPE) for that
NP. V-SCOPE simply returns its argunmnt NP
unless it has an embedded NP. The recognized
vertical relations are embedded PP, relative
clause, and reduced relative (or any combination).
Van Lehn's "embedding hierarchy" (van Lehn
1978) - in which these relations induce inverse
scope order, natural order, and ambiguity,
respectively = is subsumed by the preferences in
the database, which capture the variation of
hierarchy preferences as quantifiers vary.
For sentences with two quantifiers, H-
SCOPE basically just does a lookup. But for
more than two, it is non-trivial to determine an
overall order from a set of pairwise orders. H-
SCOPE first assumes the default natural order and
initializes a "record of imposed orders" (RIO).
This is a list of quantifier pairs, registering the
prescriptions which have been followed to date in
a given order; it insures that they will not be later
undone. RIO is initialized with strong natural
orders, i.e. naturally ordered pairs which must
stay that way. The main body of H-SCOPE is a
loop through the applicable rule groups, then a
loop through a group's rules. If a rule fires, it
sets one quantifier to L(eft), the other to R(ight).
How this prescription is realized depends on the
overall order under consideration, and on RIO. If
e.g. L does not already precede R, R may be
postposed to L or L may be preposed to R, non-
equiv',dent options if L and R are not contiguous
in the order, an option is not pursued if it undoes a
pairwise order in RIO. Resultant new overall
orders either replace or supplement the original,
the former if the rule prefers the inverse pairwise
order to the natural, the latter if the preferences are
equal. The results are then each operated on by
the next applicable rule.
For A person in each house on both streets
saw several men who were robbing some bank.v,
PSM returns [both each a several some] in .7
seconds (Macintosh llx Common Lisp 2.0,
scoping time only). Rarely did a park supervisor
serving several districts in two counties assign
everyone many trees with no large branches on
some limb which might fall on a passerby gets 4
scopings, all with rarely widest and a passerby
narrowest, in 1.283 seconds.
3. Conclusions
As noted, semantic and pragmatic factors
have deliberately been unaddressed.
words are in order on their eventual incorporation.
There are of a number of issues that always
arise where semantic processing is concerned:
compositionality, knowledge representation, etc.
But what I want to address is an issue peculiar to
But a few
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the current system: namely, should semantic
(read: semantic/pragmatic) factors be incorporated
by hybridization or integration? That is, should
leX.sy n be replaced by flex-syn-sem-prag, i.e. a
nctaon mat consiaers all relevant tactors before
making any scope judgment? Or should flex-syn
be integrated with semantic specialists? There are
problems with either alternative.
The problem with full hybridization is that the
database would have to be remade from scratch,
since the value flex.s~nosemy~prag(blah) is not a
function of flex syn(btah)
• -
prag(blah) is not the result of combmmg flex-
syn(blah) with other judgments based on blah: that
would be a mixed IS/hybrid model, the second
alternative. As noted in 2.2, new syntactic or
lexical factors cannot be added to PSM in a
controlled way. The same is true for any new
factors. My goal in this paper has been to show
that syntactic and lexical factors are well-behaved
enough that non-modularity restricted to these
factors is a burden which however is bearable,
and worth bearing. But if all factors including
infinite complex meanings are hybridized, the
problems become intractable. It would be perhaps
impossible to determhae even a large portion of the
function flex-syn-sem-prag. And even if it were
troy excrnciatmg out not impossible, the effort
would have to be largely duplicated whenever the
data was extended. It's not for nothing that
modularity is a hallmark of good design. (Note
also, incidentally, that scoping would have to
entirely follow translation, unlike Figure I.)
As a working hypothesis I have adopted the
second alternative. Yet the argument of section I,
extended to semantic factors, suggests that if the
system is to capture the complex and subtle
variations in human scope judgments, these
factors should be not integrated but hybridized.
To back away from this because it makes the
engineering too hard may be understandable, but
we should not forget the joke about the guy
looking for lost keys where he knows they aren't
because the light is better there. Modularity may
be imperative for approaching complex problems,
but there is no a priori reason why the mind must
be modular. Indeed Fodor (1983) has speculated
that much of it may not be, and hence he is
pessimistic about cognitive science.
Obviously this is a deep issue, and I do not
claim to have resolved it (for more, see Chien
1992). Nor am I saying either that in
computational linguistics we should model human
minds or that we should just design practical
systems. I am suggesting that these goals
lnat is, flex s-n sere
. . .~y -
ultimately may be incompatible - not because
minds are too imprecise (e.g. Glymour 1987), but
because they are too precise.
R e f e r e n c e s
Allen,
Understanding. Benjamin-Cummings, Menlo
Park, California.
Barwise, J. and R. Cooper. 1981 Generalized
Quantifiers and Natural Language. Linguistics
and Philosophy 4(2): 150-219.
Chien, A. 1991 How to Scope and Translate
Any. Georgetown Journal of Languages and
Linguistics 2(3-4): 223-233.
Chien, A. 1992 Modularity and Quantifier
Scoping. Manuscript.
Epstein, S. 1988 Principle-Based Interpretation
of Natural Language Quantifiers. Proceedings of
the Seventh National Conference on Artificial
Intelligence: 718-723.
Fodor, J. 1983 The Modularity of Mind. MIT
Press, Cambridge, Massachusetts.
Glymour, C. 1987 Android Epistemology and
the Frame Problem. In Pylyshyn, Z., ed., The
Robot's Dilemma.
Ablex, Norwood, New
Jersey, 65-75.
Grosz, B., D. Appelt,
Pereira. 1987 TEAM: An Experiment in the
Design of Transportable Natural-Language
Interfaces. Artificial Intelligence 32(2): 173-243.
Hobbs, J., and S. Shieber. 1985 An Algorithm
for Generating Quantifier
Computational Linguistics 13(1-2): 47-63.
Hurnm, S. 1988 Handling Scope Ambiguities
in English. In Proceedings of the Second
Conference on Applied Natural Language
Processing: 58-65.
Ioup, G. 1975 Some Universals Concerning
Quantifier Scope. In J. Kimball, ed., Syntax and
Semantics, Vol. 4. Academic Press, New York.
Loatman, B., J. Hermansen, S. Post, and C.
Yang. 1986 PAKTUS Version 1 User's
Guide. Report SD-RD-86-2, PRC Inc.,
McLean, Virginia.
Moran, D. 1988 Quantifier Scoping in the SRI
Core Language Engine. In Proceedings of the
26th Annual Meeting of the Association for
Computational Linguistics: 33-40.
Van Lehn, K. 1978 Determining the Scope of
English Quantifiers. Report AI-TR-483, AI Lab,
MIT, Cambridge, Massachusetts.
Woods, W. 1978 Semantics and Quantification
in Natural Language Question Answering. In M.
Yovits, ed., Advances in Computers, Vol 17.
Academic Press, New York, 2-64.
J. 1987
Natural Language
P. Martin, and F.
Scopings.
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