QUANTIFIER SCOPING 
IN THE SRI CORE LANGUAGE ENGINE 
Douglas B. Moran 
Artificial Intelligence Center 
SKI International 
333 Ravenswood Avenue 
Menlo Park, California 94025, USA 
ABSTRACT 
An algorithm for generating the possible quanti- 
fier scopings for a sentence, in order of preference, 
is outlined. The scoping assigned to a quantifier is 
determined by its interactions with other quan- 
tifiers, modals, negation, and certain syntactic- 
constituent boundaries. When a potential scoping 
is logically equivalent to another, the less preferred 
one is discarded. 
The relative scoping preferences of the individ- 
ual quantifiers are not embedded in the algorithm, 
but are specified by a set of rules. Many of the 
rules presented here have appeared in the linguis- 
tics literature and have been used in various natu- 
ral language processing systems. However, the co- 
ordination of these rules and the resulting coverage 
represents a significant contribution. Because ex- 
perimental data on human quantifier-scoping pref- 
erences are still fragmentary, we chose to design a 
system in which the set of preference rules could 
be easily modified and expanded.. 
The algorithm described has been implemented 
in Prolog as part of a larger natural language pro- 
cessing system. Extensions of this algorithm are 
in progress. 
INTRODUCTION 
One of the major sources of ambiguity in sen- 
tences results from the different scopes that can be 
assigned to the various quantified noun phrases in 
the sentence. Part of the problem in determining 
the preferred scopings of quantifiers is the number 
of factors involved. For example, consider these 
three sentences 
John visited every house on a street. (1) 
John visited every house on a square. (2) 
John visited every patient in a private room. (3) 
Each of these sentences has two quantifier scop- 
ings: in one, "every' has wider scope over "a," 
and while in the other, "a" has the wider scope. 
However, the readings that most people obtain for 
these sentences are quite different. In (1), the 
reading in which "a" has wider scope is highly 
preferred; in (3), the reading in which "everf has 
wider scope is highly preferred; in (2), the reading 
with wide-scope "everf is preferred, but wide- 
scope "a" is also acceptable. A plausible expla- 
nation for the difference between (1) and (2) is 
that, since the typical house is located on a street 
but not on a square, the default preference rep- 
resented by (2) is overridden by a conversational 
maxim of quantity--if "~ streeff has narrow scope, 
"on a street" would contribute too little informa- 
tion to justify its presence. A plausible explana- 
tion for the difference between (2) and (3) is based 
on the relationship among the components. The 
reading of (3) in which "a" is given wider scope is 
improbable because the domain of quantification 
for "every" would then be the single patient in 
the selected room--an infelicitous use of "every, ~ 
whereas there is no similar problem in (2) because 
there are normally multiple houses on a square. 
Similarly, in 
John visited a person on every committee. (4) 
John visited a house on every street. (5) 
the reading in which "a" has wider scope is reason- 
able for (4) but not for (5)--in a normal domain 
of discourse, it is conceivable that there could be 
a person who is on all of the committees, but it is 
highly improbable that the geometry of the streets 
is such that a single house could be located on all 
of them. 
In (1), (3), and (5), discourse criteria and do- 
main information seem to be the primary factors 
in determining the preferred quantifier scopings, 
whereas in (2) and (4), linguistic criteria seem to 
33 
be the determining factors. 
Our approach presumes that the determination 
of a sentence's preferred scoping can be divided 
into two phases, the first of which is the subject of 
the algorithm described here. In this initial phase, 
linguistic information is used to generate the possi- 
ble quantifier scopings in order of preference. The 
relevant linguistic information consists of surface 
position, syntactic structure, and the relationship 
among the function words (determiners, modals, 
and negation). In the second phase (future work), 
domain and discourse information is applied suc- 
cessively to these scopings, modifying the scores 
produced by the first phase. We expect that the 
modifications will be only penalties, thus making 
it possible to identify the best choice when it is en- 
countered (cutting off the processing of remaining 
scopings generated by the first phase). 
The primary study of quantifier scoping prefer- 
ences was done by VanLehn (1978). The experi- 
mental data reported therein was of limited useful- 
hess in developing the algorithm described here-- 
it was gathered and evaluated under assumptions 
arising from a different linguistic theory. 
We shall first present the rules that governed the 
structure of our design, then outline the algorithm. 
This scoping algorithm has been implemented as 
a component of a larger system that is under con- 
tinuing development. In this system, called the 
Core Language Engine or CLE (Alshawi et aL, 
1987), the semantic interpretation phase produces 
unscoped logical forms in which quantifier expres- 
sions are represented by quantifier terms (qterms). 
For example, the sentence "John saw a studenf' 
has the uuscoped logical form 1 
see'(john';qterm(a',X,student'(X))) 
Since the only permissible scope for this quanti- 
fier is the whole sentence, the qterm is raised to 
produce the scoped logical form 
quant(3,X,student'(X), see'(john',X)) 
The qterm expression can best be thought of as a 
quant expression before its scope has been estab- 
lished. In the above qterm and quant expressions, 
student'(X) is the restriction of the quantified 
variable X; that is, it specifies a set of the pos- 
sible values of X over which the quantifier ranges. 
I The logical form's syntax in the implementation is ac- 
tuaJly \[seel~ohnl,qterm(al,X,\[studentl,X\])\], but the more 
conventional notation will he ~ for perspicuity. 
In the above quant expression, see'(john',X) is re- 
ferred to as either the body or the scope of the 
quantifier. This treatment of the logical form of 
quantifiers follows that employed in many previ- 
ous systems (e.g., LUNAR (Woods, 1977), Moore 
(1981), Barwise and Cooper (1981), and Hobbs 
and Shieber (1987)). 
RULES AND PREFERENCES 
Many of the following rules have appeared in 
wrious forms in multiple places in the literature, 
and most natural language processing systems in- 
clude some mechanism for selecting a preferred 
quantifier scoping. However, the published de- 
scriptious of many of those systems' capabilities 
tend to be cursory, with the scoping rules utilized 
in the LUNAR system still among the best de- 
scribed in the NLP literature. Because of space 
limitations, it is not possible to cite much of this 
discussion, nor to compare this system to others. 
Rule 1 A quantifier A that is not in the restric. 
tion of quantifier B and that occurs within the 
scope of B cannot oeLgcope any of the quantifiers 
in the restriction of B. 
Rule 2 If a quantifier is raised past an operator, 
then any quantifier that occurs within its restric- 
tion must also be raised past that operator. 
These rules, presented by Hobbs and Shieber 
(1987), can best be explained with examples. 
A bishop visits e~er*j chapel by a ri,)er. (6) 
has an uuscoped logical form of 
visit'(qterm(a',B,bishop'(B)), 
qterm(every',C,and(chapel'(C), 
by'(C,qterm(a',R,river'(R)))))) 
The following is one of the possible permuta- 
tions of the quemtifiers, but is not a valid scop- 
ing because the restriction of "every" ("chapel by 
a river") has been fragmented: 
*quant(V,C,chapel'(C), quant(=l,B,bishop'(B), 
quant(=l, R,and(river'(R),by'(C, R)), 
visit'(B,C)))) 
Similarly, for the sentence 
John did not visit a chapel by a river. (7) 
the quantifier permutation 
34 
*quant(3,C,chapel'(C), not(quant(3,R,and(river'(R),by'(C, R)), 
visit'(john',C)))) 
is not a possible scoping of the unscoped logical 
form 
not(visit'Ciohn',qterrn(a',C,and(chapel'(C ), 
by'(C,qterm(a',R,river'(R))))))) 
Rule 3 For a set of quantijiers, which quantifier 
receives wide-scope preference can be determined 
by a pairwise comparison of the determiners. This 
comparison is based upon a combination of factors 
that include their relative strengths and surface po- 
sitions, and whether or not either has been raised. 
In many systems, determiners are assigned nu- 
merical strengths and these values are compared to 
determine what scope should be assigned to each 
quantifier. Such a ranking is implicit in our prefer- 
ence rules and can be viewed as a first approxima- 
tion of the relationships represented by our rules. 
Our algorithm permits a set of properties to be 
associated with determiners and for these to be 
used in ascertaining which determiner has wide- 
scope preference. The properties currently em- 
ployed are surface position (the integer index of 
the determiner) and a Boolean value indicating 
when a quantifier has already been raised. 
Preference 3.1 There is a strong preference for 
%ach" to outscope other determiners. 
That "each" is the strongest determiner is a 
common feature of most quantifier-scoping treat- 
ments. However, the evidence for the relative 
strengths of the remaining quantifiers is much less 
clear---our current ranking of them is an ad hoc 
blending of those in TEAM (Grosz ef al., 1987) 
and VanLehn (1978). 
Preference 3.2 There is a strong preference for 
WH.terms to outscope all determiners ezcepf 
"each," which outscopes WH-terms. 
In the unscoped logical forms currently pro- 
duced, WH-words ("which," "who," "what") and 
phrases are represented as qterms. Our scoping- 
preference rules assign wide scope to "each" in 
Which ezams did each student pass? (8) 
There is a reported dialect in which sentences of 
the above form are judged to be malformed, but 
that dialect was not found among our informants. 
The design of our algorithm makes it easy to re- 
place the current preferences with these. 
The definite determiner "the" is currently 
treated as a very strong quantifier, but this ap- 
proach is not entirely satisfactory. Consider 
Every student passed the ezam. (9) 
The student in every race celebrated. (1O) 
The student in each race celebrated. (11) 
Every student in the race celebrated. (12) 
Each student in the race celebrated. (13) 
In (9)-(12), the preferred scopings are as predicted 
by the rules. However in (13), the preferred read- 
ing selected is the one with wide-scope "each." Al- 
though both scopings of this sentence are logically 
equivalent (as are those for (9) and (12)), wide- 
scope "the" seems to he the preferred reading. 
Our algorithm does not distinguish between spe- 
cific and nonspecific use of indefinite articles. It is 
debatable whether this belongs in quantifier scolP 
ing or in another part of the system. 
Preference 3.3 A logically weaker interpretation 
is preferred. This preference is strong when it 
maintains surface order, weak when it inverts sur- 
face order. 2 
The quantifier order V'~ is weaker than ~/, ac- 
counting for the preferences in 
A man loves every woman. (14) 
Every man loves a woman. (15) 
In both sentences, the reading with wide-scope 
"eeerf is the preferred one; the reading with 
wide-scope "a" is possible for (14), but is very 
strained for (15). 
Rule 4 Raising a quantifier out of certain syntac- 
tic constituents changes the strength of its deter- 
miner. 
VanLehn presents an "embedding hierarchy" of 
the probability of a quantifier in the modifier of 
an NP being raised to have wider scope than the 
quantifier in the NP's head 
2Vanl.mhn proposes a more general form of this 
preference--that, when comparing two quantifiers within 
the same ge~neral group, the "more numerous" one will have 
a preference for wider scope. For example, "many" would 
take wider scope over "few." However, for everything ex- 
cept "ever~'/"a," such preferences appear to he very slight. 
35 
PP > Reduced Relative Clause > Relative Clause 
A method frequently proposed to account for this 
distinction is to use, as a measure of the cost of 
raising, a count of the number of nodes in the syn- 
tactic structure over which the quantifier is raised. 
However, such accounts are acknowledged to have 
various deficiencies and to be overly sensitive to 
the syntactic representation used. We have cho- 
sen to permit rules to associate a cost for raising a 
quantifier with certain types of nodes (other nodes 
can be viewed as having zero costs). This capabil- 
ity of the system is currently invoked only on an 
all-or-nothing basis. 
Preference 4.1 A quantifier cannot be raised 
across more than one major clause boundary. 
A common rule in the quantifier-scoping litera- 
ture is "quantification is generally clause bound." 
While it is possible to generate sentences with 
acceptable readings when a quantifier has wider 
scope than the clause in which it occurs, we have 
been unable to find any examples showing that it 
can be raised out of two clauses. 
Preference 4.2 A quantifier cannot be raised out 
of a relative clause. 
This is a common restriction in many quantifier- 
scoping algorithms. In our system, this is not a 
special rule, but one of the preferences. Conse- 
quently, this could easily be modified from vever 
being permitted to being "highly unpreferred." 
Rule 5 In unscoped logical form, quantifiers can 
occur within the scope of an opaque operator. 
Whether or not to raise such a quantifier outside 
that operator is determined by a pairwise compar- 
ison between the operator and the determiner in 
the quantifier, as well as by their relative surface 
position. 
Preference 5.1 There is a strong preference for 
"some" to outscope negation. 
Preference 5.2 There is a preference for nega- 
tion to outscope %very." This preference is strong 
when it maintains surface order, weak when it 
doesn't. 
Different scopings of "some" and "every" under 
negation produce equivalent readings (3"~ is equiv- 
alent to --V). The preferred scopings for the two 
sentences 
John did not see someone. (16) 
John did not see everyone. (17) 
have equivalent logical forms 
quant(3,P, person'(P),not(see'(john',P))) 
not(quant(V,e, person'(e),see'(john',e))) 
Similarly, the preferred scopings of sentences 
Someone did not see John. (18) 
Everyone did not see John. (19) 
have equivalent logical forms 
quant(3,P, person'(P),not(see'(P, john'))) 
not(quant(V,e.person'(P),see'(e, john'))) 
The reading of (16), which would assign nar- 
row scope to "some" is produced by substituting 
"an~ 's for "some" : 
John did not see anyone. (20) 
This has the following logical form (no other scop- 
ings exist): 
not(q ua nt(3, P, person'(P),see'(joh n', P))) , 
which is logically equivalent to 
quant(V,e, per$on '(e),not(see'(john' ,e))) , 
which corresponds to the strongly "unpreferred" 
readings of (16) and (17). Similarly, the sentence 
No one saw John. (21) 
which has a scoped logical form of 
quant(V,P, person'(P),not(see' (p,john'))) 
corresponds to the "unpreferred" scoping for (18) 
and (19). 
One of LUNAR's scoping rules was that in 
the antecedent of "if-then" statements, quantifiers 
"some" and "anf should be assigned wide scope, 
and that "a" and "every" should be given nar- 
row scope. If such antecedents were treated as a 
negative environment (or equivalent thereto), the 
foregoing preferences could produce this effect. 
SThe CLE system does not currently provide a treat- 
merit of ",n~." However, within the qu~ati~er-scoping 
compon~t, "4n~" is treated ~ ~ potenti~dly am- 
biguotm between the usual universal quantifier, free- 
choice "any," and a ~cond form, polarity-sensitive "anlt," 
which occurs in conjunction with negative-polarlty items. 
Polarity-~mitive "anlh" is treated as & narrow.cope exis- 
telxtied quantifier (Ladtmaw, 1980). 
36 
Preference 5.3 There is a strong preference for 
free-choice "any" to have wider scope than modals. 
There is a strong preference for all other determin- 
ers that occur within the scope of a modal to have 
narrower scope than that modal. 
Did some student take every testf (22) 
Does some student take every test? (23) 
Some student took every test. (24) 
Some student takes every test. (25) 
Some student is taking every test. (26) 
For sentences (23), (25), and (26), there are two 
acceptable quantifier scopings. However, for (22) 
and (24), the scoping in which "every" is assigned 
narrower scope seems to be strongly preferred. We 
ascribe this to the presence in the logical form 
of a modal operator corresponding to the past 
tense. This effect is accentuated in (27), which ex- 
hibits an ambiguity resulting from whether "some 
teacher" is scoped inside or outside the modal, cor- 
responding to (28) and (29), respectively: 
Some teacher took every course. (27) 
Last summer, some teacher took every coarse(28) 
As a student, some teacher took every course~29) 
The scoping in which "every" outscopes "some ~ 
is possible, although unpreferred, for the reading 
• (28); but it is not a possible scoping for (29) in 
any dialect that we have encountered. 
Rule 6 If polarity-sensitive "any" occurs within a 
clause in which its trigger does not occur, it must 
be raised out of that clause. 
De Dicto/De Re The mechanism described here 
can provide an account for the de dicto/de re dis- 
tinction. 
Another ambiguity associated with quantifier 
terms is whether or not the referent is required 
to exist. In PTQ (Montagne, 1973), the sentence 
John seeks a unicorn. (30) 
is assigned a de dicto reading (which does not re- 
quire that any unicorns exist), 
seek'(~john ',%~(P,q uant(3,X,u nlcorn '(X),'P(X)))) 
and a de re reading (which requires the existence 
of some unicorn) 
quant(3,X,unicorn'(X),seek'Cjohn',^A(P,'P(X)))) 
In PTQ, this distinction is produced by syntactic 
rules. Cooper (1975, 1983) demonstrated that a 
mechanism using a store could produce both read- 
ings from a single logical form. 
Our mechanism obtains similar results. Starting 
from the unscoped logical form 
seek'Cjohn','A(P,:P(qterm(a',X,unicorn'(X))))) 
with the intension operator " treated as being op- 
tionally opaque, both readings are produced by 
the quantifier-scoping algorithm described here. 
Additional (unwarranted) scopings are not pro- 
duced because these are the only two sites at which 
quantifiers can be pulled from the store. 
Nonrule There is a strong preference for a noun 
phrase in a prepositional phrase complement to 
outscope the head noun. 
This criterion is used in many quantifier scoping 
mechanisms. It is a good heuristic, but it is not a 
reliable rule. In 
John visited every house on a street. (31) 
John visited every house with a dog. (32) 
the heuristic correctly predicts the preferred stop- 
ing for (31), but fails for (32). 4 This heuristic is 
not part of our scoping algorithm; we believe that 
its effects are part of the processing consigned by 
us to the second phase of quantifier scoping (future work). 
BASIC ALGORITHM 
The first level of our scoping algorithm gener- 
ates the possible scopings, as described by Hobbs 
and Shieber (1987). However, we implemented ~ 
this with a different algorithm, partly for reasons 
of effÉciency and partly because it could be easier 
expanded to include additional capabilities. The 
performance of the Hobbs and Shieber algorithm 
deteriorates as the number of quantifiers in the 
sentence increases---our analysis is that it spends 
a significant amount of time repeatedly travers- 
ing the logical form and doing structure copying 
(their goal was to produce a provably correct algo- 
rithm, not a highly efficient one). Our algorithm 
traverses the unscoped logical form, collecting the 
qterms (quantifier terms) into a store; then as the 
scoping for each qterm is determined, it is pulled 
out of the store, producing a scoped logical form. 
4This was brought to my attention by Richard Crouch. 
37 
For a sentence with four qusatifiers, our algorithm 
is typically an order of magnitude faster than that 
presented by Hobbs sad Shieber. 
A simple example of the use of the store is pro- 
vided by the sentence "John saw a student," which 
has an unscoped logical form of 
see'(john',qterm(a',X,student'(X))) 
After quantifier scoping has placed the qterm in 
the store, the logical form is 
see'(john',X) 
sad the store is 
\[ \[ qterm(a',X,student'(X)) \] \] 
The scope for this quantifier is the whole sentence, 
so the qterm is puned out of the store to produce 
the scoped logical form 
quant(3,X,studeet'(X), see'~iohn',X)) 
The sentence "Few students pass most ezamg' has 
the unscoped logical form 
pass'(qterm(few',X,student'(X)), qterm(most'.V.exam'(V))) 
After the qterms have been extracted, the remain- 
ing logical form sad the store are 
p ss'(x,v) \[ \[ qterm(few',X,stud ent'(X)) \], 
\[ qterm(rhost',Y,exam'(Y))) \] \] 
A qterm can have other qterms in its restric- 
tion sad our quantifier store is a structured col- 
lection (unlike the stores of Cooper sad LUNAR). 
The structure of qterms in the store corresponds 
to their relative positions in the unscoped logical 
form. For example, the unscoped logical form for 
"every student in a college attends the lecture' is 
atten d'(qterrn(every' ,X,and(student'(X), 
in'(X,qterm(a',Y,college'(Y))))), 
qterm(the',Z,lecture'(Z))) 
When such qterms are placed in the store, this re- 
lationship is maintained by representing the col- 
lected qterms as trees (called qtrees), with the 
outer qterm as the root and those in its restric- 
tion as daughters: 
\[\[ qterm(every',X,and(student'(X),in'(X,Y))), 
qterm(a' ,Y,college'(Y)) \], 
\[ qterm(the',Z,lecture'(Z)) \] \] 
Consequently, the store is a forest of such qtrees, 
and the qterms occurring in the restriction of a 
qterm are themselves a forest of qtrees and are 
treated as if they were a store. 
As qterms are collected, they are inserted into 
the store in inverse order of preferencc c.g., the 
qterm that has narrowest-scope preference appears 
at the front of the list representing the forest. In 
implementing this algorithm in Prolog, we found 
that it was considerably easier to generate the 
scopings by working from the narrowest to the 
widest scope, rather than rice versa. As the vari- 
ous permutations of the quantifiers are generated, 
equivalent scopings are detected, and all but the 
most preferred one are then filtered out. In the 
following, both scopings of each sentence are logi- 
tally equivalent: 
Every student takes every test. 
Every student takes each test. 
A student takes a test. 
Some student takes a tes~. 
Each student takes the test. 
Eeery student takes the test. 
The student takes every test. 
(33) 
(34) 
(35) 
(36) 
(37) 
(38) 
(39) 
In (33), (35), (37), sad (39), the preferred order is 
the same as the surface order, while in (34), (36), 
sad (38), the stronger quantifier occurs second in 
surface order, sad the scoping that corresponds 
to surface order is discarded. Filtering of equiva- 
lent permutations is achieved simply by compar- 
ing the qtree currently being pulled from the store 
with the preceding one; if the qusatifiers in their 
head qterms are logically equivalent, this quantifier 
scoping is discarded unless the qtree being pulled 
has wide-scope preference over its predecessor (in 
which case the other logically equivalent ordering 
will be discarded). 
Logically equivalent scopings can also be pro- 
duced when a quantifier is raised out of the restric- 
tion of another. However, the quantifier permuta- 
tions that produce equivalent scopings by raising 
are a subset of those produced by permuting sib- 
lings: 
Every student in every race celebrated. (40) 
A student in a race celebrated. (41) 
Some student in a race celebrated. (42) 
38 
Each student in the race celebrated. (43) 
Every student in the race celebrated. (44) 
The student in every race celebrated. (45) 
Note that the scopings for (40) and (45) are not 
logically equivalent. The scopings in the others 
axe logically equivalent, but in (41) and (43), the 
preferred scoping is the one corresponding to con- 
stituent structure, whereas in (42) and (44), the 
preferred scoping has the NP from the PP raised 
to have wider scope over the head noun. 
When a qtree is pulled from the store, the algo- 
rithm tries to produce additional permutations by 
raising subsets of qterrns (actually of qtrees) out of 
that qtree's restriction. When a qtree is raised, it 
is put back into the store---since qtrees are being 
assigned scope from narrowest to widest, this en- 
sures that a raised qtree will receive wider scope 
than the qtree out of which it was raised. 
Because a raised qtrse may have its strength re- 
duced when it is placed back in the store (an op- 
tion in our system), a set of logically equivalent 
scopings could have all instances filtered out by 
a naive implementation. The problem arises in 
the following manner. Before the qtree is raised, 
the algorithm determines that the unraised scop- 
ing is logically equivalent to a raised one and that 
the latter is preferred, so it discards the former. 
When the qtree is raised and its strength reduced, 
it becomes weaker than the qtree out of which 
it was raised. The algorithm detects that the 
raised scoping is logically equivalent to an unralsed 
one, and determines--on the" basis of the current 
strengths--that the unraised scoping is preferred, 
so it now discards the raised one. This problem is 
avoided by doing some additional bookkeeping. 
The current implementation of the above rules 
is very coarse-grained. The "score" indicating 
whether or not a quantifier should be assigned 
wide scope over another quantifier, logical form 
operator (e.g., a modal, negation), or syntactic 
constituent is one of four values: always (narrow 
scope is impossible), never (wide scope is impos- 
sible), pref (wide scope is preferred, but narrow 
scope is acceptable), and unpref (narrow scope 
is preferred). In the current implementation of 
the above preferences, a strong preference to take 
wider scope is treated as an instance of always, 
and a weak preference is treated as pref. For ex- 
ample, Preferences (3.1)-(3.3) are given by the fol- 
lowing rules, in which Pref is the preference of a 
determiner Detl to take wider scope over another 
determiner Det2: 
if Detl and Det2 are both "each": 
- if Detl precedes Det2 in surface order, 
Pref = pref, 
- otherwise, Pref = unpre.f. 
otherwise, if Detl is "each" (and Det2 is 
not), Pref = always 
otherwise, if Detl is an interrogative 
determiner, Pref-- always 
otherwise, if the logical forms for Detl and 
Det2 are V and 3, respectively: 
- if Detl precedes Det2 in surface order, 
Pref = always 
- otherwise, Pref = pref. 
Overshoot The method described here results in 
.some quantifiers' being assigned scopes that are 
wider than appropriate, relative to other predicates 
(but not quantifiers) in the logical form. 
The sentence "John visited every person on a 
committee" has an uuscoped logical form of 
visit'(john',qterm(every',P, and(person'(P), 
on'(P, qterm(a',C,committee'(C)))))) 
and its preferred scoping is 
quant(V,P, quant(3,C,committee'(C), 
and(person'(P),on'(P,C))), 
visit'Cjohn'.P)) 
Note that person'(P) is independent of C; thus it 
can be outside the scope of the quantifier for C 
quant(V,P, and(person'(P), 
quant(q,C,committee'(C),on'(P,C))), 
visit'~iohn', P)) 
Such transformations can have a significant im- 
pact on the performance of the system, substan- 
tially reducing the processing time of queries for 
even a modest database. Rather than pass ad- 
ditional information so that quantifiers could be 
pulled at the correct point in the traversal of the 
logical form, we chose to let the scoping algorithm 
"overshoot" its mark and then lower the quanti- 
tiers to the correct position. This was considerably 
easier to implement, and it does not seem to have 
any performance penalty in our system. 
CONCLUSION 
For lack of a reasonable corpus of human quan- 
tifier scoping preferences, the testing of'this sys- 
tem has been limited to checking conformance to 
39 
the stated rules, s The semantic component of the 
CLE does not produce logical forms with mass or 
count NPs or collective readings, but that capa- 
bility is currently being developed. The foregoing 
description of qterms is a slight simplification; an 
extended form is now being used to support gen- 
eralized quantifiers in the new semantic rules. 
Examples offered by VanLehn (1978) indicate 
that dative movement affects quantifier scoping, 
but the cause may actually be domain or discourse 
information. Our examples show that passiviza- 
tion affects quantifier scoping, but we have not yet 
found a means of determining whether the effect 
is due solely to the cost of raising out of the PP. 
The algorithm does not handle "donkey sen- 
tences," nor is it intended to. A scheme for han- 
dling such sentences is being explored as part of 
the continuing development of the CLE (Fernando 
Pereira, personal communication). This would be 
a separate mechanism, rather than an extension 
of quantifier scoping. 
ACKNOWLEDGMENTS 
The research on which this paper is based was 
supported by the Natural Language Processing 
Club (NATTIE) of the Alvey Directorate program 
in Intelligent Knowledge-Based Systems (Project 
No. ALV/PRJ/IKBS/105). Most of it was per- 
formed while I was a member of SRI's Cambridge 
Computer Science Research Centre. This work 
benefited from extensive discussion with and sug- 
gestions from Robert C. Moore and Hiyan AN 
shawi. 
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