Generating Referring Quantified Expressions 
James Shaw and Kathleen McKeown 
Dept. of Computer Science 
Columbia University 
New York, NY 10027, USA 
shaw, kathy*cs, columbia, edu 
, :, ~.*~ . 
Abstract 
In this paper, we describe how quantifiers can be 
generated in a text generation system. By taking 
advantage of discourse and ontological information, 
quantified expressions can replace entities in a text, 
making the text more fluent and concise. In ad- 
dition to avoiding ambiguities between distributive 
and collective readings in universal quantification 
generation, we will also show how different scope 
orderings between universal and existential quanti- 
tiers will result in different quantified expressions in 
our algorithm. 
1 Introduction 
To convey information concisely and fluently, text 
generation systems often perform opportunistic text 
planning (Robin, 1995; Mellish et al., 1998) and em- 
ploy advanced linguistic constructions such as ellip- 
sis (Shaw, 1998). But a system can also take ad- 
vantage of quantification and ontological informa- 
tion to generate concise references to entities at the 
discourse level. For example, a sentence such as 
"'The patient has an infusion line in each arm." is 
a more concise version of "The patient has an in- 
fusion line ir~ his left arm. The patient has an in- 
fusion line in his right arm." Quantification is an 
active research topic in logic, , and philoso- 
phy(Carpenter, 1997; de Swart. 1998). Since nat- 
ural  understanding systems need to ob- 
tain as few interpretations as possible from text, 
researchers have studied quantifier scope ambigu- 
ity extensively (Woods~ 1978;-Grosz et al., 1987; 
Hobbs and Shieber, 1987: Pereira, 1990; Moran and 
Pereira, 1992: Park, 1995). Research in quantifica- 
tion interpretation first transforms a sentence into 
predicate logic, raises tim quantifiers to the senten- 
tial level, and permutes these quantifiers {o obtain 
as many readings as possible relaled to quantifier 
scoping. Then, invalid readings are eliminated using 
various consl raints. 
Ambiguity in quantified expressions is caused by 
two main culprits. The first type of ambiguity in- 
volves the distributive reading versus the collective 
reading. In universal quantification, a referring ex- 
100 
pression refers to multiple entities. There is a po- 
tential ambiguity between whether the aggregated 
entities acted individually (distributive) or acted to- 
gether as one (collective). Under the distributive 
reading, the sentence "All the nurses inspected the 
patient." implies that each nurse individually in- 
spected the patient. Under the collective reading, 
the nurses inspected the patient together as a group. 
The other ambiguity in quantification involves mul- 
tiple quantifiers in the same sentence. The sentence 
"A nurse inspected each patient." has two possi- 
ble quantifier scope orderings. In Vpatient3nurse, 
the universal quantifier V has wide scope, outscop- 
ing the existential quantifier 3. This ordering means 
that each patient is inspected by a nurse, who might 
not be the same in each case. In the other scope 
order, 3nurseVpatient, a single, particular nurse in- 
spected every patient. In both types of ambiguities, 
a generation system should make the desired reading 
clear. 
Fortunately, the difficulties of quantifier scope dis- 
ambiguation faced by the understanding conmmnity 
do not apply to text generation. For generation, the 
problem is the reverse: given an unambiguous rep- 
resentation of a set of facts as input, how can it 
generate a quantified sentence that unambiguously 
conveys the intended meaning? In this paper, we 
propose an algorithm which selects an appropriate 
quantified expression to refer .to a set of entities us- 
ing discourse and ontological knowledge. The algo- 
rithm first identifies the entities for quantification in 
;the input :propositions. Then an- appropriate con- 
cept in the ontology is selected to refer to these en- 
tities. Using discourse and ontological information, 
the system determines if quantification is appropri- 
ate and if it is, which particular quantifier to use 
to minimize the anabiguity between distributive and 
collective readings. More importantly, when there 
are multiple quantifiers hi the same sentence, the al- 
gorithm generates different expressions for differen~ 
scope orderings. In this work, we focus on generat- 
ing referring quantified expressions for entities which 
have been mentioned before in the discourse or can 
be inferred from an ontology. There are quantified 
expressions that do not refer to particular entities 
in a domain or discourse, such as generics (i.e. "All 
whales are mammals."), or negatives (i.e., "The pa- 
tient has no allergies."). The synthesis of such quan- 
tifiers is currently performed in earlier stages.of the 
((TYPE EVENT) 
(PRED ((PRED receive) (ID idl))) 
(ARGi ((PRED patient) (ID ptl))) 
(ARG2 ((PRED aprotinin) (ID apl))) 
generation process. (MODS ((PRED after) (ID id2) 
. In the next section;we..vdll..~orapaxe ou_r~.approach ..... .:. .. tTYRE_TIME).. ............... 
with previous work in the generation of quantified 
expressions. In Section 3, we will describe the appli- 
cation where the need for concise output motivated ))) 
our research in quantification. The algorithm for 
generating universal quantifiers is detailed in Sec- 
tion 4, including how the system handles ambiguity 
between distributive and collective readings. Sec- 
tion 5 describes how our algorithm generates sen- 
tences with multiple quantifiers. 
2 Related Work 
Because a quantified expression refers to multiple 
entities in a domain, our work can be categorized as 
referring expression generation (Dale, 1992; Reiter 
and Dale, 1992; Horacek, 1997). Previous work in 
this area did not address the generation of quantified 
expressions directly. In this paper, we are interested 
in how to systematically derive quantifiers from in- 
put propositions, discourse history, and ontological 
information. Recent work on the generation ofquan- 
tifiers (Gailly, 1988; Creaney, 1996; Creaney, 1999) 
follows the analysis viewpoint, discussing scope ana- 
biguities extensively. Though our algorithm gener- 
ates different sentences for different scope orderings, 
we do not achieve this through scoping operations as 
they did. Creaney also discussed various imprecise 
quantifiers, such as some, at least, and at most. 
In regards to generating generic quantified expres- 
sions, (Knott et al., 1997) has proposed an algorithm 
for generating defeasible, but informative descrip- 
tions for objects in nmseums. 
Other researchers (van Eijck and Alshawi, 1992; 
Copestake et al., 1999) proposed representations in a 
machine translation setting which allow underspec- 
ification in regard to quantifier scope. Our work is 
different, in that we perform quantification directly 
on the instance-based representation obtained from 
database tuples. Our input .does not have the in-.. 
formation about which entities are quantified as is 
the case in machine translation, where the quanti- 
tiers are already specified in the input from a source 
. 
3 The Application Domain 
We implemented our quantification algorithm as 
part of MAGIC (Dalai et al., 1996: McKeown et 
al., 1997). MAGIC automatically generates multi- 
media briefings to describe the post-operative sta- 
tus of a patient after undergoing Coronary Artery 
Bypass Graft, surgery. The system embodies a stan- 
. f ....... 
(ARG2 ((PRED critical-point) 
(NAME intubation) (IDcl))) 
Figure h The predicate-argument structure of 
"After intubation, a patient received aprotinin." 
dard text generation system architecture with three 
modules (Rambow and Korelsky, 1992): a content 
planner, a sentence planner, and a linguistic realizer. 
Once the bypass surgery is finished, information that 
is automatically collected during surgery such as 
blood pressure, heart rate, and medications given, 
is sent to a domain=specific medical inference mod- 
ule. Based on the medical inferences and schemas 
(McKeown, 1985), the content planner determines 
the information to convey and the order to convey 
it. 
The sentence planner takes a set of propositions 
(or predicate-argument structures) with rhetorical 
relations from the content planner and uses linguistic 
information to make decisions about how to convey 
the propositions fluently. Each proposition is repre- 
sented as a feature structure (Kaplan and Bresnan, 
1982; Kay, 1979) similar to the one shown in Fig- 
ure 1. The sentence planner's responsibilities include 
referring expression generation, clause aggregation, 
and lexical choice (Wanner and How, 1996). Then 
the aggregated predicate-argument structure is sent 
to FUF/SURGE (Elhadad and Robin, 1992), a lin- 
guistic realizer which t.ransforms the lexicalized se- 
inantic specification into a string. The quantification 
algorithm is implemented in the sentence planner. 
4 Quantification Algorithm 
in this:,work, weprefergenerating expressions with 
universal quantifiers over conjunction because, as- 
suming that the users and the system have tile same 
domain model, the universally quantified expres- 
sions are more concise and they represent the same 
amount of information as the expression with con- 
joined entities. In contrast,, when given a conjunc- 
tion of entities and an expression with a cardinal 
quantifier, the system, by default, would use the 
conjunction if the conjoined entities can be distin- 
guished at the surface level. This is because once 
the system generates a cardinal quantifier when the 
universal quantification does not hold, such as "three 
101 
patients", it is impossible for the hearer to recover 
the identities of these patients based on the con- 
text. The default heuristics to prefer universal quan- 
tifier over conjunction over cardinal quantifier can 
be superseded by directives fromthe contentplan- 
ner which are application specific. 
The input to our quaatifica~omalgorit;hm is a set 
of predicate-argument structures after the referring 
expression module selected the properties to identify 
the entities (Dale, 1992; Dale and Reiter, 1995), but 
without carrying out the assignment of quantifiers. 
Our quantification algorithm first identifies the set 
of distinct entities which can be quantified in the 
input propositions. A generalization of the entities 
in the ontology is selected to potentially replace the 
references to these entities. If universal quantifica- 
tion is possible, then the replacement is made and 
the system must select which particular quantifier 
to use. In our system, we have six realizations for 
universal quantifiers: each, every, all 1, both, the, 
and any, and two for existential quantifiers: the in- 
definite article, a/an, and cardinal n. 
4.1 Identify Thematic Roles with Distinct 
Entities 
Our algorithm identifies the roles containing distinct 
entities among the input propositions as candidates 
for universal and existential quantification. Suppose 
the system is given two propositions similar to the 
one in Figure 1, "After intubation, Alice received 
aprotinin" and "After start of bypass, Alice received 
aprotinin", each with four roles - PRED, ARG1, 
ARG2, and MODS-TIME. By computing similarity 
anaong entities in the same role, the system deter- 
mines that the entities in ARG1, PRED, and ARG2 
are identical in each role, and only the entities in 
MODS-TIME are different. Based on this result, 
the distinct entities in MODS-TIME, "after intuba- 
tion" and "after start of bypass", are candidates for 
quantificat ion. 
4.2 Generalization and Quantification 
We used the axioms in Figure 2 to determine if 
the distinct entities can be universally or existen- 
tially quantified. Though the axioms are similar to 
those used in Generalized Quantifier (Barwise and 
Cooper, 1981; Zwarts, 1983; de Swart, 1998). the 
semantics of set X and set D are different. In the 
previous step. the entities in set X have been iden- 
tified. To compute set D in Figure 2. we introduce 
a concept, Class-X. Class-X is a generalization of 
the distinct entities in set X. Quantification can re- 
place the distinct entities in the propositions with 
a reference to their type restricled by a quantifier. 
accessing discourse and ontological information .to 
provide a context. Our ontology is implemented in 
lali is realized as "ali the". 
102 
• both: ID - X\[ = 0 and IxI = 2, can have col- 
lective reading 
• every, all, the: ID-XI = 0 and IX\[ > 2, can 
have collective reading 
• each: I D - X\[ = 0 and IXI _> 2, only distribu- 
-- • tive reading ........ 
® any: \]D- X\] = 0, when under the scope of 
negation 
° a/an: IDnXl > 0 and Ixl = 1 
• n (cardinal): IOnXl > 0 and \[Xl = n 
Figure 2: Axioms of the quantifiers discussed in this 
paper. 
CLASSIC(Borgida et al., 1989) and is a subset of 
WordNet(Miller et alL, 1990) and an online medical 
dictionary (Cimino et al., 1994) designed to support 
multiple applications across the medical institution. 
Given the entities in set X, queries in CLASSIC de- 
termine the class of each instance and its ancestors 
in the ontology. Based on this information, the gen- 
eralization algorithm identifies Class-X by comput- 
ing the most specific class which covers all the enti- 
ties. Earlier work (Passonneau et al., 1996) provided 
a framework for balancing specificity and verbosity 
in selecting appropriate concepts for generalization. 
However, given the precision needed in medical re- 
ports, our generalization procedure selects the most 
specific class. 
Set D represents the set of instances of Class-X in 
a context. Our system currently computes set D for 
three different contexts: 
e discourse: Previous references can provide an 
appropriate context for universal quantification. 
For example, if "Alice" and "Bob" were men- 
tioned in the previous sentence, the system can 
refer t.o them as "both patients" in the current 
sentence. 
® domain ontology: The domain ontology pro- 
vides a closed world from which we can obtain 
't-he set D by matching all the instances of a 
concept in the knowledge base, such as "'ev- 
ery patient". In addition, certain concepts in 
the ontology have limited types. For example, 
knowing that cell savers, platelets and packed 
red blood cells are the only possible types of 
blood products in the ontology, the quantified 
expression "every blood product" can be used 
instead of referring to each entity. 
® domain knowledge: The possessor of the dis- 
tinct entities in a role might contain a maximum 
number of instances allowed for Class-X. For ex- 
ample, because a person has only two arms, the tinguishable expressions at surface level. A more 
entities "the patient's left arm" and "the pa- developed pragmatic module is needed before quan- 
tient's right arm" can be referred to as "each tifiers such as some, raps'e, at least, and few, can 
arm". be systematically generated. Indiscriminate applica- 
tion of imprecise quantification can result in- vague 
The computation of set D can also involve interac- or inappropriate text in our domain, such as "The 
tions with a referring expression m0dule(Dale aad~ ~-:patient~rec~ived.~some 61ood~produetS:"'-v.ia-our~e~P - 
Reiter, 1995). For example, instead of the expres- plication, knowing exactly what blood products are 
sion "Alice and Bob" and "both patients" covered 
by the current algorithm, by interacting with a refer- 
ring expression module, the system might determine 
that "both CABG patients operated on this morn- 
ing by Dr. Rose" is a clearer expression to refer to 
the entities. Though this is desirable, we did not 
incorporate this capability into our system. 
Although the is often used to indicate a generic 
reference (i.e., "The lion is the king of jungle."), in 
English, the can also be used as an unmarked uni- 
versal quantifier when its head noun is plural, such 
as "the patients." Like the quantifier all, the can 
be both distributive and collective. However, the 
cannot always replace all as a universal quantifier. 
the cannot be used when universal quantification is 
based on the domain ontology. For example, it is 
not obvious that the quantified expression in "John 
received the blood products." refers to "each blood 
product" in the ontology. Although unmarked uni- 
versal quantifiers can be used to refer to body parts, 
as in "The lines include an IV in the arms.", the ex- 
pression is ambiguous between the distributive and 
collective readings. Of the three contexts discussed 
above, the system occationally generates the instead 
of every and both in a discourse context, yielding 
more natural output. 
When the computed set D matches set X exactly 
(ID - X I = 0), a quantified expression with either 
each, all, every, both, the, and any, replaces the 
entities in set X. 
4.3 Selecting a Particular Quantifier 
In general, the universal quantification of a partic- 
ular type of entity, such as "every patient", refers 
to all such entities in a context. As a result, read- 
ers can recover what a universally quantified expres- 
sion refers to. In contrast, readers cannot pinpoint 
which entity has been refei'red to. in an existentially . 
quantified expression, such as "a patient." or "two 
patients". Because a universally quantified expres- 
sion preserves original semantics and is more con- 
cise than listing each entity, it is the focus of our 
quantificalion algorithm. The universal quantifiers 
hlaplemented in our system include the six possible 
realizations of V in English: every, all. each. both. 
the, and any. The only existential quantifiers im- 
plemented in our system are the singular indefinite 
quantifier, a/an. and cardinal quantifiers, n. They 
are used in sentences with multiple quantifiers and 
when the entities being referred to do not have dis- 
used is very important. To avoid generating such 
inappropriate sentences, the system only performs 
generalization on the entities which can be univer- 
sally quantified. If the distinct entities cannot be 
universally quantified, the system will realize these 
entities using coordinated conjunction. 
Once the system decides that a universally quan- 
tified expression can be used to replace the entities 
in set X, it must select which universal quantifier. 
Because our sentence planner opportunistically com- 
bines distinct entries from separate database entries 
for conciseness, it is not the case that these aggre- 
gated entities acted together (the collective read- 
ing). Given such input, the referring expression for 
aggregated entities should have only the distribu- 
tive reading 2. The universal quantifier, each, al- 
ways imposes a distributive reading when applied. 
In general, each requires a "matching" between the 
domain of the quantifier and the objects referred 
to(McCawley, 1981, pp. 37). In our algorithm, this 
matching process is exactly what happened, thus it 
is the default universal quantifier in our algorithm. 
Of course, indiscriminate use of each can result in 
awkward sounding text. For example, tile sentence 
"Every patient is awake" sounds more natural than 
"Each patient is awake." However, since quantified 
expressions with the universal quantifiers all and 
every 3 can have collective readings (Vendler, 1967; 
McCawley, 1981), our system generates every and 
all under two conditions when the collective read- 
ing is unlikely. First if the proposition is a state, as 
opposed to an event, we assume only the distribu- 
tive reading is possible 4. The quantifier every is 
used in "Ever.q patient tmd.taehycardia.'" because 
the proposition is a state proposition and contains 
the predicate has-attribute, an attributive relation. 
..... 2For our system to generate noun-phrases.wivh ,col}eetive 
readings, the quantification process must be performed at the 
content planner level not in the clause aggregation module. 
3every is also distributive, but it stresses completeness or 
rather, exhaustiveness(Vendler, 1967). The sentence "John 
took a picture of everyone in the room." is ambiguous while 
"John took a picture os t each person in the room." is not. 
4There are cases where state propositions do have dis- 
teibuted readings (e.g., "Mountains surround the village." ). 
Sentences with collective readings are bandied earlier in the 
content planner and thus, this type of problem does not occur 
at this point in our system. Though .this observation seems to 
be true in our medical application, when implementing quan- 
tifiers in a new domain, we can limit this assumption to only 
the subset of state relations for which it holds. 
103 
Second, when the concept being universally quan- 
tified is marked as having a distributive reading in 
the lexicon, such as the concept episode, quantifiers 
every will be used instead of each. These quanti- 
tiers make the quantified sentences more natural be- 
cause they do not pick out the redundant distribu- 
tive meaning. ...... .~ . -: ....... =~:: .... ~" :~; 
The use of prepositions can also affect which quan- 
tifier to use. For example, "After all the episodes, 
the patient received dobutamine" is ambiguous in re- 
gards to whether the dobutamine is given once dur- 
ing the surgery, or given after each episode. In con- 
trast, the sentence "In all the episodes, the patient 
received dobutamine." does not have this problem. 
The current system looks at the particular preposi- 
tion (i.e., "before", "after", or "in") before selecting 
the appropriate quantifier. 
4.4 Examples of a Single Quantifier 
Given the four propositions, "After intubation, 
Mrs. Doe had tachycardia", "After skin incision, 
Mrs. Doe had tachycardia", "After start of bypass, 
Mrs. Doe had tachycardia', and "After coming off 
bypass, Mrs. Doe had tachycardia.", the algorithm 
first identifies roles with similar entities, ARG1, 
PRED, ARG2 and removes them from further quan- 
tification processing while the distinct entities in the 
role MODS-TIME, "after intubation", "after skin in- 
cision", "after start of bypass", and "after coming off 
bypass", are further processed for universal quantifi- 
cation. The role MODS-TIME is further separated 
into two smaller roles, one role with the preposi- 
tions and the other role with different critical points. 
Since the prepositions are all the same, universal 
quantification is only applied to the distinct entities 
in set X, in this case, the four critical points. Queries 
to the CLASSIC ontology indicate that the enti- 
ties in set X, "intubation", "skin-incision", "start- 
of-bypass", and "conaing-off-bypass" match all the 
possible types of the concept critical-point, sat- 
isfying the domain ontology context in Section 4.2. 
Since set D and set X match exactly, generalization 
and universal quantification can be used to replace 
the references to these entities: "After each criti- 
cal point, Mrs. Doe had tachycardia." The system 
currently does not.perfor.m generMization omeJ~tities 
which failed the univeral quantification test.. In such 
cases, a sentence with conjunction will be generated, 
i.e., "After intubation and skin incision, Mrs. Doe 
had tachycardia." 
In addition to every, the system generates both 
when the number of entities in set X is two. In 
our application, both is used as a universal quanti- 
tier under discourse context: "Alice had q)isodes of 
bradycardia b@)re inductio1~ and start of bypass, h~ 
both episodes, she received Cefazolin and Phen!lle- 
phrine. " 
When a universal quantifier is under the govern- 
104 
ment of negation, each, all, every and both are in- 
appropriate, and any should be used instead. Given 
that the patient went on bypass without compli- 
cations, the system should generate "The patient 
went on bypass without any problem." In contrast, 
"The patient went on bypass without every prob- 
/em.V=-~as-~ a,:differeut.-~meani~g; -,Our, :,system-cur=. 
rently uses any as a universal quantifier when the 
universal quantification is under the government of 
negation, such as "The patient denied any drug al- 
lergy.", or "Her hypertension was controlled without 
any medication." Currently, the generation of nega- 
tion sentences about surgery problems and allergies 
are handled in the content planner. They are not 
synthesized from multiple negation sentences: "The 
patient is not allergic to aspirin. The paitent is not 
allergic to penicillin..." 
5 Generation of Multiple Quantifiers 
When there are two distinct roles across the proposi- 
tions, the algorithm tries to use a universal quantifier 
for one role and an existential quantifier for another. 
To generate sentences with 33, both entities being 
referred to must have no proper names; this triggers 
the use of existential quantifiers. We intentionally 
ignore the cases where two universal quantifiers are 
generated in the same sentence. The likelihood for 
input specifying sentences with W to a text genera- 
tion system is slim. 
When generating multiple quantifiers in the same 
sentence, we differentiate between cases where there 
is or isn't a dependency between the two distinct 
roles. Two roles are independent of each other when 
one is not a modifier of the other. For example, 
the roles ARG1 and ARG2 in a proposition are in- 
dependent. In "Each patient is given a high sever- 
ity rating", performing universal quantification on 
the patients (ARG3) is a separate decision from 
the existential quantification of the severity ratings 
(ARG2). Similarly, in "An abnormal lab result was 
seen in each patient with hypertension after bypass". 
the quantification operations on the abnormal lab 
results and the patients can be performed indepen- 
dently. 
.... When there isa dependency 'between theroles be- 
ing quantified, the quantification process of each role 
might interact because modifiers restrict the range 
of the entities being modified. We found that when 
universal quantification occurs in the MODS role, 
the quantification of PRED and MODS can be per- 
formed independently, just as in the cases withou! 
dependency. Given the input propositions "Alice has 
II<I in Alice's left arm. Alice has IV-2 in Alice's 
right arm. ", the distinct roles are ARG2 "IV-i" and 
"IV-T', and ARG2-MODS "in Alice's left arm" and 
"in Alice's right arm". The ARG2-MODS is uni- 
versally quantified based on domain knowledge that 
® Roles without dependency, V Role-l,3 Role-2 
Each patient is given a high severity rating. 
® Roles without dependency, 3 Role-l, 'v' Role-2 
An abnormal lab result was seen in each patient 
geon's name is likely to be known, and the in- 
put is likely to be "Dr. Rose operated on Alice", 
"Dr~ Rose operated on Bob", and "Dr. Rose oper- 
ated on Chris". Given these three propositions, the 
entities in ARG1 and PRED are identical, and only 
with hypertension after bypass, the distinct entities in ARG2, "Alice", "Bob" and 
*Roles with depend~flcy, V PRED,-3 MODS ............. Ghns:,~-~ d.~be:;~qua,atffied.... ~Wilih-,-am:a;ppropriate context, the sentence "Dr. Rose operated on each 
Every patient with a balloon pump had hyper- 
tension. 
• Roles with dependency, 3 PRED, V MODS 
Alice has an IV in each arm,. 
Figure 3: Sentences with two quantifiers 
a patient is a human and a human has a left arm 
and a right arm. In this example, "an IV in each 
arm", the decision to generate universal and exis- 
tential quantified expressions are independent. But 
in "Every patient with a balloon pump had hyperten- 
sion", the existentially quantified expression "with a 
balloon pump" is a restrictive modifier of its head. In 
this case, the set D does not include all the patients, 
but only the patients "with a balloon pump". When 
computing set D for universal quantification, the al- 
gorithm takes this extra restriction into account by 
eliminating all patients without such a restriction. 
Once a role is universally quantified and the other is 
existentially quantified, our algorithm replaces both 
roles with the corresponding quantified expressions. 
Figure 3 shows the sentences with multiple quanti- 
tiers generated by applying our algorithm. 
5.1 Ambiguity Revisited 
In Section 4.3, we described how to minimize the 
ambiguity between distributive and collective read- 
ings when generating universal quantitiers. What 
about the scope ambiguity when there are muhiple 
quantifiers in the same sentence? If we look at the 
roles which are being universally and existentially 
quantified in our examples in Figure 3, it is inter- 
esting to note that the universal quantifiers always 
have wider scope than the existential quantifiers. In 
the first, example, ,the.scope: order is Vpatient~high- 
severity-rating, the second example is Vpatient31ab- 
result, the third is Vpatient3balloon-pump, and the 
fourth is Varm3IV. The scope orderings are all V3. 
\Vhat happens if a sentence contains an existen- 
tial quantifier which has a wider scope than a uni- 
versal quantifier? In "A suryeon operated on each 
patient.", tile normal reading is Vpatienl3surgeon. 
13ut~ if the existentially quantified noun phrase 
"'a surgeon" refers to tile same surgeon, as in 
3surgeonVpatient. tlle system would generate "(A 
particular/The same) surgeon operated on each pa- 
tient." In an applied generation system, the sur- 
patient" will be generated. If the name of the sur- 
geon is not available but the identifiers for the sur- 
geon entities across the propositions are the same, 
the system will generate "The same surgeon oper- 
ated on each patient." As this example indicates, 
when 3 has a wider scope than V, the first step in 
our algorithm (described in Section 4.1), identify- 
ing roles with distinct entities, would eliminate the 
roles with identical entities from further quantifica- 
tion processing. Based on our algorithm, the sen- 
tences with 3V readings are taken care of by the first 
step, identifying roles with distinct entities, while V3 
cases are handled by quantification operations for 
multiple roles, as described in Section 5. 
In Section 4.3, we mentioned that it is important 
to know exactly what blood products are used in 
our application. As a result, the system would not 
generate the sentence "Each patient received a blood 
product." when the input propositions are "Alice re- 
ceived packed red blood cells. Bob received platelets. 
Chris received platelets." Even though tim conjoined 
entities can be generalized to "blood product", this 
quantification operation would violate our precondi- 
tion for using existential quantifiers: the descriptions 
for each of the conjoined entities must be indistin- 
guishable. Here, one is "red blood cells" and tile oth- 
ers are "platelets". Given these three propositions, 
the system would generate "Alice received packed 
red blood cells, and Bob and Chris, platelets." based 
on the algorithm described in (Shaw. 1998). If in 
our domain the input propositions could be "'Al- 
ice received blood-product-1. Bob received blood- 
product-2. Chris received blood-product-2.", where 
each instance of blood-product-n could be realized 
as "blood product", then the system would generate 
"Each patient received a blood product." since the 
description of conj0ined entities are not dist~inguish - 
able at the surface level. 
6 Conclusion 
We have described the quantification operators that 
can make the text more concise while preserving the 
original semantics in the input propositions. Though 
we would like to incorporate imprecise quantifiers 
such as few. many, some into our system because 
they have potential to drastically reduce the text. 
further, these quantifiers do not, have the desired 
property ill which the readers can recover the exact. 
entities in the input propositions. The property of 
105 
preserving the original semantics is very important 
since it guarantees that even though the surface ex- 
pressions are modified, the information is preserved. 
This property allows the operators to be domain in- 
dependent and reusable in different natural  
Norman Creaney. 1999. Generating quantified logi: 
cal forms from raw data. In Proe. of the ESSLLI- 
99 Workshop on the Generation of Nominal Ex- 
pressions. 
M. Dalal~ S. Feiner, K. McKeown, D. Jordan, 
generation systems. B. Allen, and Y. alSafadi. 1996. MAGIC: An 
We have described: an. algo_r.itlma :which.sy.stemati .............. e:~cpertimeeataL:aystem..for: genetattiag~ .multimedia 
cally derives quantifiers from input propositions, dis- 
course history and ontological information. We iden- 
tified three types of information from the discourse 
and ontology to determine if a universal quantifier 
can be applied. We also minimnized the ambiguity 
between distributive and collective readings by se- 
lecting an appropriate universal quantifier. Most 
importantly, for multiple quantifiers in the same sen- 
tence, we have shown how our algorithm generates 
different quantifed expressions for different scope or- 
derings. 
7 Acknowledgement 
We would like to thank anonymous reviewers for 
valuable comments. The research is supported in 
part by the National Library of Medicine under 
grant LM06593-02 and the Columbia University 
Center for Advanced Technology in High Perfor- 
mance Computing and Communications in Health- 
care (funded by the New York State Science and 
Technology Foundation). Any opinions, findings, or 
recommendations expressed in this paper are those 
of the authors and do not necessarily reflect the 
views of the above agencies. 

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