A HYBRID SYSTEM FOR QUANTIFIER SCOPING 
1. Introduction 
A prominent source of ambiguity 
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: e.g. 
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" 
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 
ACRES DE COL1NG-92, NANTES, 23-28 AOt'rr 1992 8 6 0 PROC. OI: COLING-92, NANIES, AUG. 23-28. 1992 
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. Consider an analogy. 
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. 
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. 
ACrEs DE COLING-92, NANTES, 23-28 Ao(;r 1992 S 6 1 Plt~)(!. oF COIJNG-92, NANrES, AUG. 23-28, 1992 
2.2. Database 
PSM encodes a function flex s- defined for -., .vii 
26 quantifier elements, including 9 
quantificational adverbs such as always, and 49 
syntactic environments. There are three 
"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. But checking the 
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 
RULEGRPS 
subject-dirobject rgl ,rg2 .... 
subject-indirobject ... 
subject-prepobject ... 
subject-adve~ ... 
dirobject-indirobject ... 
dirobject-prepobject 
dirobjecl-adverbial "~.~,rg,?.5 
indirobject-prepobject ... l indirobject-adverbial 
prepobject-adverbial 
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 
AcrEs DE COLING-92, NANTES, 23-28 aotrr 1992 8 6 2 PROC. OF COLING-92, NANTEs, AUG. 23-28, 1992 
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 of 
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. But I am 
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. 
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. But a few 
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 
ACRES DE COIANG-92, NANIES, 23-28 AO~rI 1992 8 6 3 PRO(:. oV COLING-92, NANTES. AUG. 23-28, 1992 
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) lnat is, flex s-n sere • - . . .~y - 
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 
ultimately may be incompatible - not because 
minds are too imprecise (e.g. Glymour 1987), but 
because they are too precise. 
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