Varying Cardinality in Metonymic Extensions to Nouns 
Helmut Horacek
Universität des Saarlandes
F.R. 6.2 Informatik
Postfach 151150
 D-66041 Saarbrücken, Germany
 email: horacek@cs.uni-sb.de
Abstract
Meaning shifting phenomena such as metonymy 
have recently attracted increasing interest of 
researchers. Though these phenomena have been 
addressed by plenty of computational methods, 
the impacts of cardinalities of metonymically 
related items have been widely ignored in all of 
them. Motivated by this lack of analysis, we have 
developed a method for representing expect-
ations and knowledge about the cardinalities of 
metonymically related entities and for exploiting 
this information to build logical forms express-
ing metonymic relations, the entities related, and 
their cardinalities. The representation of lexically 
motivated knowledge is realized as an enhan-
cement to Pustejovsky's Generative Lexicon, and 
the process of building logical forms takes into 
account overwriting of default information and 
mismatch of cardinality requirements. Our 
method enables a precise attachment of sentence 
complements, and it supports reference reso-
lution in the context of metonymic expressions.
1 Introduction
Meaning shifting phenomena such as metonymy 
have recently attracted increasing interest. Com-
putational approaches to these phenomena aim at 
inferring implicitly represented relations, predict-
ing meaning shifts of nouns or verbs, expressing 
restrictions on these meaning shifts in depen-
dency of context- or language-specific factors, 
and facilitating reference resolution. Measures to 
achieve these issues include representation of 
default knowledge and various sorts of inference 
methods and constructive procedures. However, 
the entities in the texts examined almost always 
appear in singular form so that issues of cardina-
lity of metonymically related items have been 
widely ignored by the approaches made so far. 
Motivated by this lack of analysis, we have 
examined metonymic expressions by varying 
cardinalities of the items appearing explicitly or 
implicitly, to analyze effects of these alternations. 
The results have inspired us to build increasingly 
explicit versions of logical forms, and to formul-
ate conditions on pronominal accessibility. The 
insights gained improve analysis methods for 
relating contextual specifications to the appropri-
ate entity, and for supporting reference reso-
lution to entities related implicitly.
This paper is organized as follows. We review 
computational approaches to metonymy. Then 
we illustrate the phenomena investigated. We 
elaborate suitable techniques to deal with these 
phenomena, that is, an enhancement to entries in 
the Generative Lexicon, and a procedure for 
building a logical form. Finally, we discuss im-
pacts of our analysis on pronominal resolution.
2 Approaches to Metonymy
Metonymy is a natural language phenomenon 
that contributes to expressing information in an 
effective and economic way. It involves what has 
been termed 'transfers of meaning' by (Nunberg 
1995), i.e., the meaning of some constituent does 
not correspond to what can be expected accord-
ing to the syntactic and semantic environment – 
the speaker is "using one entity to refer to 
another that is related to it" (Lakoff and 
Johnson 1980). For example, in the utterance 
"The ham sandwich is waiting for his check", it is 
not literally the ham sandwich, which wants to 
pay, but the person who ordered it. 
Computational approaches such as the NL 
database interface TEAM (Grosz et al. 1988) are 
concerned with inferring implicitly expressed 
metonymic relations, mostly in English; some 
analyses consider German (Horacek 1996) and 
French (Kayser 1988, Pustejovsky and Bouillon 
1995). Prominent representatives include Fass' 
program met* (1991), which makes use of 
formal definitions of several kinds of metonymic 
relations, Sowa's conceptual graphs (1992), in 
which an a priori unspecific relation is inserted  
between a concept of the type expected and the 
concept appearing on the surface, and the 
TACITUS system (Hobbs et al. 1993) which 
treats metonymy as a special case of reference 
resolution, in a uniform abduction process to 
“find the best explanation for the observables”. 
Altogether, these approaches have two charac-
teristic properties: (1) The conditions expressing 
when leaving a metonymic relation implicit or 
not is possible are too unconstrained to cover a 
larger number of examples in several languages, 
or to generate sentences with metonymic expres-
sions systematically. (2) The intended and the lit-
eral referent always appear in singular definite 
form. There are only three approaches which in 
some aspects deviate from this characterization.
Pustejovsky's Generative Lexicon (1991) ad-
dresses the first aspect. He proposes a Theory of 
Qualia, with an explanation of systematic polyse-
my. Applying type coercion enables one to arri-
ve at cases of ordinary metonymy which can be 
grounded in terms of the semantics of lexemes, 
as well as at word senses which Pustejovsky has 
termed logical metonymy, like the reading of a 
book in the sentence “Mary enjoyed the book”. 
Such contexts reflect prototypical knowledge 
derived from AGENTIVE or TELIC roles of the 
lexical entry for 'book', which are prominent 
roles in the Qualia Structure of nouns. Particular-
ities of the Qualia Structure of nouns regulate the 
acceptability of leaving a metonymic relation 
implicit (Pustejovsky and Bouillon 1995).
Stallard (1993) indirectly addresses the 
second aspect by taking into account scoping re-
lations and impacts on pronominal reference. He 
introduces a distinction between referential and 
predicative metonymy, depending on whether 
the intended or the literal argument is accessible 
for subsequent pronominal reference. This dis-
tinction manifests itself in different scope rela-
tions that hold between these arguments in the 
corresponding logical forms. We will argue 
against his usage of scoping and the resulting 
strict distinction of pronominal accessibility.
Markert and Hahn (1997) address interactions 
of metonymic relation extension and anaphora 
resolution, which enables them to handle textual 
ellipsis references. They apply extensive langu-
age independent conceptual definitions with rela-
tional path classifications and preference rules. 
In their corpus, there are also cases of indefinite 
metonymic NPs, which is an indication for 
metonymic relations to several objects.
Though neither Pustejovsky's nor Stallard's 
approach address cardinalities, we show that both 
can be extended accordingly: we augment the 
Generative Lexicon by representing cardinality 
information, and techniques for building logical 
forms are enhanced to yield more precise speci-
fications of the metonymically related entities.
3 Phenomena Investigated
For a number of metonymic relations, such as 
PRODUCER for PRODUCT (“I bought a Ford”), 
ARTIST for ARTWORK (“He plays Bach”), as 
well as eventualities involved in logical meto-
nymy, cardinalities are not a problem because 
the literal referents are expressed as proper 
names. For other metonymic relations, especially 
ORGANIZATION for MEMBER and PART for 
WHOLE, several complications may arise, as the 
following examples demonstrate. Let us start with 
two contrastive sentences (1) and (2), taken from 
(Lakoff and Johnson 1980), and (Hobbs et al. 
1988), respectively (see also (Horacek 1994)):
(1) The ham sandwich is waiting for his check.
(1a) He is getting impatient.
(1b)It is 2 $.
(2) The Boston office called.
? (2a) He was angry.
(2b)It is our head quarter.
(2c) They want us to organize a meeting.
Following Stallard, (1) is interpreted as an ex-
ample of referential reading, while (2) as an ex-
ample of predicative reading: (1) can be rephras-
ed more explicitly by The manx who has eaten a 
ham sandwichy is waiting for hisx check, while 
(2) in a similar way gets expanded to The Boston 
officex represented by one of itsx employeesy call-
ed. These reformulations suggest that the man in 
(1) and the Boston office in (2) have wider scope 
in Stallards representation than the ham sand-
wich in (1) and the employee in (2), which pre-
dicts pronominal accessibility in (1a) and (2b), as 
opposed to (1b), (2a) and (2c). We challenge this 
analysis with evidence from the examples above. 
Pronominal reference in (1b) is also possible, but 
may be less common than in (1a). (2c) seems 
even more natural than (2b), only (2a) is unclear.
Further complications arise when variations of 
cardinality in sentence (1) (see sentences (3) to 
(6) and their follow-ups), and variation of cir-
cumstances in sentence (2) (see the follow-ups of 
sentences (7) and (8)) are considered. For dishes 
made of animals ('the mussels'), complications 
arise through interference between animals and 
persons as pronominal referents. Because we 
want to study the effects of cardinality variations 
per se, we avoid such examples.
(3) The pizzas are waiting for their checks.
? (3a) He/she is getting impatient. 
(3b)They are getting impatient. 
(4) The fruit dumplings is/are waiting for
 his/her/their check(s).
(4a) He/she/they is/are getting impatient.
(5) The meat plate is/are waiting for his/her/ 
their check(s).
(5a) He/she/they is/are getting impatient.
(6) Table 7 is/are waiting for his/her/their 
check(s).
(6a) He/she/they is/are getting impatient.
These sentences demonstrate that both intra- ((1) 
and (3)) and intersentential ((1a) and (3b)) pro-
nonminal reference work fine, if the literal ref-
erents (here, various sorts of food) and the real 
referents (here, the persons) agree in number. 
Otherwise, a variety of complications arise in in-
trasentential reference, which also demonstrate a 
specificity of English. Whereas pronouns agree 
with the literal referent in most languages, it is 
the intended referent that determines verb agree-
ment and pronominal reference in the same 
sentence in English. For example, metonymic 
extension to the expression 'fruit dumplings' is 
ambiguous in the sense that it can refer to one 
plate of dumplings to be eaten by a single per-
son, or to several plates, each for another person 
(see the variants in (4)). Conversely, metonymic 
extension to the expression 'meat plate' can also 
be interpreted as a reference to several persons 
sharing that dish (see the variants in (5)). Finally, 
metonymic extension to the expression 'table' 
seems to be more neutral with respect to the 
number of persons sharing it (see the variants in 
(6)). Thus, the syntactic subject and the verb 
would not agree in number in English, when the 
default situation concerning these dishes is pre-
sent. Hence, English is, in principle, more infor-
mative than other languages when the cardinality 
of the intended referent differs from the number 
of the literal referent. However, those expressions  
without subject/verb agreement are unlikely to 
occur in practice, since they appear to be strange.  
Unlike with intrasentential reference, intersen-
tential pronominal reference with number feat-
ures deviating from the referent that is pronomi-
nally accessible intrasententially is possible due 
to default expectations about the cardinality of 
the real referents (compare complementary vari-
ants in (4a) and (5a)). It is more problematic in 
other cases (see (3a)). In the less precise referen-
ce by the table, all variants in (6a) are felicitous. 
(7) The Boston office is represented in the 
meeting.
? (7a) He/she is an expert in marketing.   
(7b) They are experts in marketing.   
(7c) They always send someone to meetings.
(8) The Boston office will meet for an
excursion today.
* (8a) He/she likes to walk.
(8b) They will make a lunch break at 2 pm.
(8c) They like to organize social events.
The following sentences ((2), (7), (8), and their 
follow-ups) involve slightly harder restrictions. 
Plural pronominal references as in sentences 
(7b), (7c), (8b) and (8c) are felicitous, but there 
is a difference between the sets of entities the 
plural pronouns refer to. While in (7c) and (8c), 
the pronouns refer to the entire set of employees 
of the Boston office, they more plausibly refer to 
the representatives in the meeting in (7b) and to 
the excursion participants in (8b). These examp-
les indicate an additional demand on the treat-
ment of cardinalities and referential accessibility 
of metonymic expressions: a distinction is to be 
made between the entities referred to metonymi-
cally (here: employees of the Boston office), and 
those of its members involved in the event 
expressed by the sentence (here: the meeting and 
the excursion). For the restaurant scenario, these 
sets of persons are mostly identical except to 
those cases where one person out of a group of 
persons eating together and referred to metony-
mically is the one who intends to pay.
(9) Which airlines serve food from Boston to 
New York ?
(9a) In the first class?
As a further aspect of metonymic expressions, 
the last two examples demonstrate chaining of 
metonymic relations and the relevance of each 
set of items involved for the associated analysis. 
In sentence (9), the airlines are the literal, and the 
persons the real referents. However, relating these 
two entities directly by an employment relation is 
problematic, since it is impossible to connect the 
locality information (from Boston to New York) 
and the first class restriction to either of them. 
Linking this information appropriately requires 
explicit elaboration of the relation between the 
airlines and their employees to include the 
implicitly referred flights.
The consideration exposed so far primarily 
hold for English. Apart from the partitive con-
struction, which seems to be a specificity of Eng-
lish in comparison to many other languages, the 
results can widely be transferred to other langu-
ages. However, there are a lot a language-specific 
subtleties which may influence the felicity or 
non-felicity of some of the expressions discussed 
in one particular language. In order to find out, 
to what extent other languages behave similar to 
English, we have asked native speakers of Ger-
man, French, Italian, Spanish, Russian, and Viet-
namese about the transferabillity of the English 
sentences to these languages. Though the results 
are subjective to a certain extent (only one 
speaker was available for most of these langu-
ages), some tendencies became apparent. Even 
sentence (1) was considered unacceptable in 
some languages, in which there is more emphasis 
on referring to persons explicitly. In Spanish, 
this seems to be caused syntactically, by the 
absence of personal pronouns, while the reasons 
seem to be more pragmatically or culturally 
related in French and Vietnamese, respectively. 
Moreover, references to objects ((1b) and (2b)) 
appeared unusal in some languages, including 
Vietnamese and Italian. Also in German, a de-
monstrative pronoun seems to be preferable to a 
personal pronoun. Finally, (2) is quite weird in 
Spanish, since the alternative 'From the Boston 
office _ called'  exists (unlike in (7) and (8)). In 
constrast, precisely (2) is acceptable in Vietname-
se, because only 'calling' is considered technical.
                                                                                                                                                                                                                                                
food(x)
CONST = {ingredients, …}
FORMAL = eatable(x)
TELIC = eat(eT,y,x)
AGENTIVE = cook(e'T,z,x)
sandwich(x)
CONST = {ham, bread, …}
FORMAL = eatable(x)
TELIC = eat(eT,y,x)
AGENTIVE = prepare(e'T,z,x)
pizza(x)
CONST = {dough, tomato, …}
FORMAL = eatable(x)
TELIC = eat(eT,y,x)
AGENTIVE = bake(e'T,z,x)
                                                                                                                                                                                                                                                   
Fig. 1. Some 'standard' examples of Qualia Structures, for 'food', 'sandwich', and 'pizza'
4 Expressing Lexical Knowledge
In order to capture distinctions between the 
varying interpretations of metonymic expres-
sions, knowledge about the lexical items involved 
plays a crucial role. For adequately expressing 
this knowledge, we make use of entries in the 
Generative Lexicon (see Figure 1). Since the 
information represented there is insufficient for 
reasoning about cardinalities, we extend the 
entries in the Generative Lexicon, prominently 
the TELIC role, by quantifier specifications. In 
the original form, the entities involved (typically, 
the lexical item itself and some related entity) are 
implicitly quantified, and a typed event variable 
is used (an event may be a state (S), a process 
(P), or a transition (T)). A similar exploitation of 
taxonomic knowledge in terms of cardinality 
restrictions has been undertaken for scope dis-
ambiguation in (Fliegner, 1988).
In the extended form, we introduce explicit 
quantifiers and scoping, and we optionally add 
sort restrictors to variables referred to by event 
predicates. We introduce new quantifiers to cover 
the cases elaborated in the previous section, in 
addition to the usual NL quantifiers EXIST and 
WH: SINGLE and MULTIPLE for a single resp. 
multiple objects without defaults, DEFSINGLE 
and DEFMULTIPLE for the same with defaults.
Figures 2 and 3 show entries in the Generative 
Lexicon with extended TELIC roles. The same 
extensions also apply to the AGENTIVE roles, but 
we do not elaborate this aspect here. Figure 2, for 
example, shows some sorts of food associated 
with different expectations about how many per-
sons typically eat them. Fruit dumplings appear 
as sets (quantified by DEFMULTIPLE), to be eaten 
as a dish by a single person (quantified by DEF-
SINGLE). For the meat plate, cardinality relations 
are inverted. For a table in a restaurant, relations 
to food eaten at that table are not specified.   
Unlike in the restaurant scenario, cardinality 
relations are less vague for some relations in 
organizations. Each office and each airline are 
supposed to employ several persons, and each 
person is working for one organization only, at 
least in his/her individual activities (this is ex-
pressed by the quantifiers SINGLE and MULTIPLE 
in the lexical entries in Figure 3). Each flight 
carries some set of people, each of which parti-
cipates in one flight only (at the same time). 
These extensions allow us to derive cardina-
lities for the referents involved in a metonymic 
expression – compare the entries for FRUIT-
DUMPLING and MEAT-PLATE, as contrasting 
examples. To achieve this goal, the knowledge 
represented in the lexicon entries is used for 
building logical forms in which metonymic 
relations are made entirely explicit. The event 
predicates in the TELIC (or AGENTIVE) roles are 
exploited to infer the relation involved. More-
over, the new quantification specification yields 
crucial information to build an explicit logical 
form with cardinality specifications from concise 
surface expressions in a precise manner.
5 Building Logical Forms
Based on entries in the Generative Lexicon and 
on the context given by a sentence to be inter-
preted, logical forms can be built that represent 
the semantic relations involved more explicitly  
than this is the case with previous approaches. In 
a nutshell, metonymic extensions are tried 
according to specifications found in the lexicon, 
as long as the sort of an NP and the sort of the 
referring case role are incompatible. In addition, 
agreement between syntactic number and seman-
                                                                                                                                                                                                                                                 
fruit-dumpling(x)
CONST = {dough, fruit, …}
FORMAL = eatable(x)
TELIC = (DEFSINGLE y
(DEFMULTIPLE x
(eat(eT,y,x))))
AGENTIVE = cook(e'T,z,x)
meat-plate(x)
CONST = {pork, beef, …} 
FORMAL = eatable(x)
TELIC = (DEFSINGLE x
(DEFMULTIPLE y
(eat(eT,y,x))))
AGENTIVE = prepare(e'T,z,x)
table(x)
CONST = {legs, plate, …}
FORMAL = physobj(x)
TELIC = (DEFSINGLE x
(DEFMULTIPLE y
(sit-at(eS,y,x))))
AGENTIVE = build(e'T,z,x)
                                                                                                                                                                                                                                                 
Fig. 2. Some 'extended' examples of Qualia Structures, for special food sorts and 'table'
                                                                                                                                                                                                                                                 
office(x)
CONST = {employees, ...}
FORMAL = organization(x)
TELIC = (SINGLE x
(MULTIPLE y
PERSON                         
(work(eP,y,x))))
AGENTIVE = establish(e'T,z,x)
airline(x)
CONST = {planes, office, ...}
FORMAL = organization(x)
TELIC = (SINGLE x
(MULTIPLE y
FLIGHT
(organize
(eT,y,x))))
AGENTIVE = found(e'T,z,x)
flight(x)
 CONST = {place, source, ...}
 FORMAL = loc-change(x)
 TELIC = (SINGLE x
(DEFMULTIPLE y
 PERSON
 (carry(eT,y,x))))
AGENTIVE = organize(e'T,z,x)
                                                                                                                                                                                                                                                 
Fig. 3. Some 'extended' examples of Qualia Structures, for 'office', 'airline', and 'flight'
tic cardinality specifications is achieved, which 
may require overwriting defaults or introducing 
a new set of entities as a subset of a known set. In 
concrete, logical forms are built by pursuing the 
procedure in Figure 4. Logical forms appear as 
(Q x S <P>), where Q is a quantifier, x and S its 
associated variable and sortal restrictor, and <P> 
the predication related. In step 2a, metonymic 
extensions are carried out, which can potentially 
be chained, and in step 2c a final extension is 
performed in case of a cardinality mismatch. In 
the following, we illustrate the procedure by 
some examples. For sentence (4), “The fruit 
dumplings wants to pay”, the initial logical form   
(MULTIPLE x FRUIT-DUMPLING (WANT-PAY x))
contains a sortal incompatibility. Using the lexi-
cal entry for 'fruit dumplings' and expanding the 
expression according to the TELIC role yields
(SINGLE y PERSON
(MULTIPLE x FRUIT-DUMPLING
(AND (EAT y x) (WANT-PAY y))))
where the sortal incompatibility is removed. 
Note, that the cardinality of PERSON is singular, 
due to the inflection of the predicate 'wants'. In 
German, the quantifier is unspecific concerning 
the cardinality, because the sentence predicate 
would not give the same indication as this is the 
case in English. For another predicate, such an 
ambiguity may not be present, as in the example
(SINGLE x OFFICE (AND (BOSTONIAN x)
           (CALL x)))
Making use of the TELIC role in the lexical entry 
of 'office', as exposed in Figure 3, yields
(SINGLE x OFFICE (AND (BOSTONIAN x)
(MULTIPLE y PERSON (AND (WORK y x) 
 (CALL y)))))
                                                                                                                                                                                                                                                 
1. Build an initial logical form out of the surface expression.
The representation is composed as an expression of the form (QE xE SE <P>):
xE being the variable whose representation is to be extended (initially x, the literal referent),
QE being its quantifier, and SE its sort (initially Q and S, associated with the literal referent), and
<P> being a structured representation of the sentence predicate and its modifiers.
SR is the sort required in the referring case frame, and QR the quantifier of its case slot restrictions.
2. Extend the meaning of noun phrases which are involved in a sortal incompatibility.
2a. Build a metonymically extended expression by consulting lexical knowledge.
Merge the partial expression (QE xE SE <P>) with the extended lexicon representation for SE:
(Q1 x1 S1 (AND <P1> (Q2 x2 S2 <P2>))) – 
from the lexicon, <Q1,x1,S1> = <QE,xE,SE> and <Q2,x2,S2> = <QN,xN,SN> 
if the referent with the same sort as xE has wider scope in the lexicon, or with inverted equalities.
<P> is partitioned according to sortal compatibility of its components:
if x1 = xE then <P1> contains parts that refer to xE, sortally compatible with SE, otherwise <P2>.           
The remaining parts of <P> become <P2>, if x1 = xE, and <P1> otherwise.
2b.Test the compatibility of the newly inserted sort with the restrictions to be met.
If SN (SN = S2, if S1 = SE, and SN = S1 otherwise) is incompatible with SR, 
then repeat step 2a with xN, SN, QN and <PN> as xE, SE, QE and, <P>, respectively;
else QR overwrites QN if QN is a default quantifier compatible with QR.
2c. Test the cardinality compatibility of the new sort with the restrictions to be met.
If SN is compatible with SR, but QN is incompatible with QR, insert MEMBER between xE and xN.
If not the whole set of entities bound to xE participates in the eventuality, insert SUBSET instead.                                                                                                                                                                                                                                                 
Fig. 4. The procedure for building logical forms with extended metonymic relations
which still contains a cardinality incompatibility. 
Further expanding this form by performing step 
2c in the procedure leads to the insertion of a 
MEMBER relation, yielding
(SINGLE x OFFICE (AND (BOSTONIAN x)
(MULTIPLE y PERSON (AND (WORK y x) 
(SINGLE z PERSON (AND (MEMBER z y) 
(CALL z))))))) 
in which all incompatibilities are resolved. Pro-
ceeding in the same manner, the analysis of the 
sentence “The Boston office makes an excur-
sion” yields a similar result, with only two minor 
deviations, partially grounded in the semantic 
difference between 'calling' and 'excursion 
making': (1) The variable z is quantified by 
MULTIPLE instead of SINGLE, and (2) the 
expression (SUBSET z y) replaces (MEMBER z y). 
However, obtaining precisely this representation, 
that is, performing the insertion of the SUBSET 
relation, additionally requires some sort of prag-
matic knowledge: typically not all members of 
an organization participate in events such as 
excursions. Nevertheless, suitable ways to repre-
sent such domain-dependent pieces of knowl-
edge adequately are delicate. 
Finally, sentence (9), “Which airlines serve 
food from New York to Boston?”, shows how 
chained metonymic extensions are handled:
(WH x AIRLINE (AND (SERVE x FOOD)
(SOURCE x NEW YORK) (GOAL x BOSTON)))
The first metonymic extension, based on the 
lexicon entry for 'airline' (see Figure 3), tenta-
tively inserts 'flights' linked to 'airline' via an 
ORGANIZE relation, and yields
(WH x AIRLINE (MULTIPLE y FLIGHT
(AND (ORGANIZE x y) (SERVE y FOOD)
  (SOURCE y NEW YORK) (GOAL y BOSTON))))
and the final operation based on the lexicon 
entry for 'flight' (see Figure 3) leads to a similar 
extension, inserting 'person' related to 'flight' via 
a CARRY relation:
(WH x AIRLINE
(MULTIPLE y FLIGHT (AND (ORGANIZE x y)
(SOURCE y NEW YORK) (GOAL y BOSTON)
(MULTIPLE z PERSON
(AND (CARRY y z) (SERVE z FOOD))))))
Note the distinguished treatment of the predi-
cations containing the variable which represents 
the phrase to be extended, as opposed to the 
previous examples. In all cases discussed so far, 
appearances of this variable are replaced by the 
new variable introduced in the course of an 
extension. Here, replacing y by z in the second 
extension step is only carried out in (SERVE y 
FOOD), while y remains unchanged in (SOURCE y 
NEW YORK) and (GOAL y BOSTON). This is 
because SOURCE and GOAL can be established as 
properties of flights, while CARRY needs a 
further extension to 'person' to be connected 
appropriately. Building explicit logical forms in 
this way demonstrates a number of achievements 
over other methods:
• Scoping of variables reflects their depen-
dencies in the event they are involved in.
• More referents than just the real and the literal 
referent may be introduced, through chained 
metonymic extensions or through member-
ship/subset insertions.
• An additional referent may provide a proper 
place to relate sentence complements.
Note, that there is a scoping difference between 
“one and the same person eating several fruit 
dumplings” and “several persons sharing a meat 
plate”, which contrasts Stallard's approach.
Finally, we have to admit that this procedure 
is overgenerating, as it does not take into account 
the restrictions imposed on the use of metonymic 
expressions discussed in Section 3. The proce-
dure is cooperative in the sense that it attempts to 
interpret a given metonymic expression, but it is 
not strong enough to distinguish felicity or infe-
licity of a metonymic expression, which may be 
due to various lexical and pragmatic factors.  
6 Impacts on Reference Resolution
Empirically supported by the considerable 
number of examples discussed in section 3, our 
approach is able to explain more pronominal 
references to metonymic expressions than others:
• Reference to literal and intended referents is 
possible in an increasing number of cases.
• Pronominal reference in plural form may ha-
ve as antecedents distinguished sets of entities.
• Cross-language differences in the treatment of 
intersentential pronominal reference exist.
In order to express scoping relations among sets 
properly, the logical forms representing meto-
nymic expressions with entities of cardinality 
greater than one must deviate from Stallard's 
methods. According to Stallard, pronominal 
reference to literal and real referents is regulated 
by their scope, which distinguishes referential 
from predicative kinds of metonymy. Unfortu-
nately, this realization of metonymic extension is 
incompatible with the common use of scoping. 
However, we believe that Stallards distinction is in 
some sense artificial, because the felicity of pro-
nominal reference seems to be more complex 
and influenced by other factors than scoping. 
For example, the sentence “the ham sandwich is 
waiting for his check” can be followed by some 
information useful to a novice waiter: “It costs 
2$.” Moreover, the message “The Boston office 
called” can be followed by the remark “He spo-
ke angrily” in some plausible contexts. Hence, it 
does not seem to be referential inaccessibility 
which makes many similar examples sound odd, 
but the rare occurrence and the low coherence in 
neutral contexts. For example, it is usually of 
minor interest whether the person calling on 
behalf of the Boston office is angry himself; it is 
the attitude of the responsible representatives at 
the office that is usually more interesting.
Given these pieces of evidence, reference 
resolution is supported by the explicit logical 
form built through our techniques, and it is addi-
tionally guided as follows:
Intrasentential reference
Possessive pronouns always relate to the intended 
referent. Since possessive pronouns in the same 
sentence agree with the real referent in English, 
while they agree with the literal referent in most 
other languages, only English sentences contain 
information about cardinality and gender of the 
intended referent. For example, the sentence 'the 
fruit dumplings is waiting for his check' carries 
the additional implication that there is one male 
person who wants to pay.
Intersentential reference
Reference through personal pronouns is possible 
to the literal and to the real referent, and to refer-
ents of the same sort but with possibly different 
cardinality as the real referent. Thus, all entities 
involved in a metonymic expression in its ap-
pearance in the explicit logical form are potential 
antecedents, except to internal elements of a 
metonymic chain. For example, following the 
sentence “The Boston office called”, pronomi-
nal reference is possible to the office (the literal 
referent), to the caller (the real referent), and to 
the people at the office (differing from the caller 
by number only). However, 'the flights' appear-
ing in the logical form representing the sentence 
“Which airlines serve diet food from New York 
to Boston?” are not pronominally accessible.
7 Conclusion
In this paper, we have presented an approach to 
deal with cardinality aspects of metonymic ex-
tensions to nouns. We have discussed a variety of 
constellations with pronominal references to im-
plicitly related items, sometimes associated with 
subtle conditions, focusing on English, also in-
cluding some language specificities. In order to 
build explicit logical forms with cardinality 
specifications, we have extended entries in Pustej-
ovsky's Generative Lexicon by default quantifier 
specifications. Through exploiting these entries, 
metonymic extensions are introduced on the 
basis of events represented in the roles of the 
Qualia structure, and member or subset relations 
are introduced on the basis of the associated 
quantifier specification. Our method for building 
explicit logical forms challenges Stallard's 
distinction of predicative and referential readings 
of metonymic expressions: it produces scopings 
that reflect proper quantifier dominance relations 
rather than pronominal accessibility conditions, 
and it allows for additional cases of pronominal 
reference. In addition, our method enables a 
more precise attachment of contextual specifi-
cations to related entities, and it supports refer-
ence resolution to metonymically related entities. 

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