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<Paper uid="W98-0614">
  <Title>The Role of Cardinality in Metonymic Extensions to Nouns</Title>
  <Section position="4" start_page="104" end_page="106" type="metho">
    <SectionTitle>
3 Phenomena Investigated
</SectionTitle>
    <Paragraph position="0"> For a number of metonymic relations, such as PRODUCER for PRODUCT ('I bought a Ford') and ARTIST for ARTWORK ('He plays Beethoven'), cardinalities are never a problem because the literal referents are expressed as proper names. Similar considerations apply to the eventualities involved in logical metonymy.</Paragraph>
    <Paragraph position="1"> For other metonymic relations, especially PART for WHOLE and ORGANIZATION for MEMBER, a number of complications may arise due to the * cardinality of the items involved in a metonymic expression, as the following examples demonstrate. Let us start with two contrastive sentences  (1) and (2), taken from (Hobbs et al. 1993), and (Lakoff and Johnson 1980), respectively (an earlier version of the subsequent analysis is available in (Horacek 1994)): (1) The ham sandwich is waiting for his check.</Paragraph>
    <Paragraph position="2"> (2) The Boston office called.</Paragraph>
    <Paragraph position="3">  Following Stallard, (1) is interpreted as an example of referential reading, while (2) as an example of predicative reading: (1) can be rephrased 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 called: These reformulations suggest that the man m (1) and the Boston office in (2) have wider scope in Stallards representation than the ham sandwich in (1) and the employee in (2), which predicts pronominal accessibility in (la) and (2b), as opposed to (lb) and (2a). We challenge this analysis in its strict sense, but we agree with it insofar as pronominal references as in (lb) or (2a) are rare, but quite common in sentences such as (la) and (2b).</Paragraph>
    <Paragraph position="4">  (1) The ham sandwich is waiting for his chec!&lt;.</Paragraph>
    <Paragraph position="5"> (1 a) He is getting impatient.</Paragraph>
    <Paragraph position="6"> (lb) It is25.</Paragraph>
    <Paragraph position="7"> * (lc) They are getting impatient.</Paragraph>
    <Paragraph position="8"> (2) The Boston office called.</Paragraph>
    <Paragraph position="9"> (2a) He was angry.</Paragraph>
    <Paragraph position="10"> (2b) It is our head quarter.</Paragraph>
    <Paragraph position="11"> (2c) They want us to organize a meeting.</Paragraph>
    <Paragraph position="12">  Apart from this difference, there do not seem to be further complications in these sentences: all referents involved are in singular form, as are the metonymic extensions. Since cardinalities of the entities involved are identical, conditions about pronominal reference depend primarily on pragmatic factors, which make references such as (la) and (2b) more common than those in (lb) and (2a). However, more complications than the analysis made so far has shown arise, when variations of cardinality in sentence (1) (see sentences (3) to (6) and their follow-ups), and variation of circumstances in sentence (2) (see the follow-ups of sentences (7) and (8)) are considered. For dishes made of animal ('the mussels'), additional complications may arise through interference between animals and persons as pronominal referents. Because we want to study the effects of cardinality variations per se, we avoid examples of this sort.</Paragraph>
    <Paragraph position="13">  (3) The pizzas are waiting for their checks. ? (3a) He/she is getting impatient.</Paragraph>
    <Paragraph position="14"> (3b) They are getting impatient.</Paragraph>
    <Paragraph position="15"> (4) The fruit dumplings want(s) to pay.</Paragraph>
    <Paragraph position="16"> (4') The fruit dumplings is waiting for his/her check.</Paragraph>
    <Paragraph position="17"> (4a) He/she is getting impatient.</Paragraph>
    <Paragraph position="18"> (4&amp;quot;) The fruit dumplings are waiting for their check(s).</Paragraph>
    <Paragraph position="19"> (4b) They are getting impatient.</Paragraph>
    <Paragraph position="20"> (4'&amp;quot;) Die Fruchtknrdel warten auf ihre Rechnung.</Paragraph>
    <Paragraph position="21"> (5) The meat plate want(s) to pay.</Paragraph>
    <Paragraph position="22"> (5') The meat plate are waiting for their check(s).</Paragraph>
    <Paragraph position="23"> (5a) They are getting impatient.</Paragraph>
    <Paragraph position="24"> (5&amp;quot;) The meat plate is waiting for his/her check.</Paragraph>
    <Paragraph position="25"> (5b) He/she is getting impatient.</Paragraph>
    <Paragraph position="26"> (5&amp;quot;') Die Schlachtplatte wartet auf ihre Rechnung.</Paragraph>
    <Paragraph position="27"> (6) Table 7 want(s) to pay.</Paragraph>
    <Paragraph position="28"> (6') Table 7 are waiting for their check(s). (6a) They are getting impatient.</Paragraph>
    <Paragraph position="29"> (6&amp;quot;) Table 7 is waiting for his/her check. (6b) He/she is getting impatient.</Paragraph>
    <Paragraph position="30"> (6'&amp;quot;) Tisch 7 wartet auf seine Rechnung.  These sentences demonstrate that both intra((1) and (3)) and intersentential ((la) and (3b)) prononminal reference work fine, if the literal referents (here, various sorts of food) and the real referents (here, the persons) agree in number. Otherwise, a variety of complications arise in intrasentential reference, which also include cross-language differences, as the German sentences (4&amp;quot;') to (6'&amp;quot;) as opposed to the English sentences (4') to (6') and (4&amp;quot;) to (6&amp;quot;) demonstrate. In these sentences, a fundamental difference manifests itself in the way how metonymic expressions are syntactically embedded in these languages. In English, it is the intended referent that determines verb agreement and pronominal reference in the same sentence.</Paragraph>
    <Paragraph position="31"> That is, the singular or plural form of the verb  in (4' to (6') and (4&amp;quot;) to (6&amp;quot;) indicates the cardinality of the intended referent, which may deviate from the cardinalities of the literal referents in each of these sentences. In (5'), the cardinality of the intended referent naturally differs from the number of the literal referent, assuming the meat plate is known as a dish for more than one person. For the fruit dumplings, situations with single (4') as well as with multiple intended referents (4&amp;quot;) are possible, because the expression 'fruit dumplings' is ambiguous in the sense that it can refer to one plate of dumplings to be eaten by a single person, or to several plates, each for another person. Moreover, sentences (6') and (6&amp;quot;) illustrate a case similar to sentences (4') and (4&amp;quot;). As a tendency, a single intended referent would be the default interpretation for the metonymic use of 'fruit dumplings', while 'table' seems to be more neutral with respect to the number of persons sharing it. As with the verb agreement, also the possessive pronouns are always agreed in .gender and number with the intended referent in English. In contrast to that, the verb and possessive pronouns in German appear in strict agreement with the literal referents in the corresponding sentences (4&amp;quot;') to (6'&amp;quot;). Altogether, English sentences of this sort are more conclusive by making cardinalities and, in case of singular, also gender of the intended referent explicit, while the German sentences are ambiguous in these respects.</Paragraph>
    <Paragraph position="32"> Unlike with intrasentential reference, intersentential pronominal reference with number features deviating from the referent that is pronominally accessible intrasententially is possible also in German under a variety of circumstances. These include default expectations about the cardinality of the real referents (see (4a) and (5b) as two complementary cases), and may perhaps be considered felicitous in other cases (see (5a)), similarly to (3a). The remaining case, as exemplified by sentence (4b), is felicitous for similar reasons as the different cases (4') and (4&amp;quot;). Finally, sentences (6') to (6b) constitute further pieces of evidence that default expectations about the cardinality of metonymically related entities (here, persons as eaters of kinds of food) play a certain role as to whether pronominal reference to metonymic expressions is felicitous or not, but not in a strict sense. In addition, (6b) is probably more common than (6a) as a default, due to the pragmatics of paying and plausibilities about table sharing, especially about food sharing according to reasonably assumed food quantities, seem to influence felicity in a subtle, hardly generalizable way in these sorts of sentences. For a member of a group as in (3b) (one of the pizza eaters), the pragmatics of paying (a single person on behalf of several ones) may even license the use of the singular form as in (3a). However, a somehow chained metonymic reference to a group as in (lc) (to which the eater of the ham sandwich belongs) is certainly not possible.</Paragraph>
    <Paragraph position="33">  (7) The Boston office is represented in the business meeting.</Paragraph>
    <Paragraph position="34"> ? (Ta) He/she is an expert in marketing.</Paragraph>
    <Paragraph position="35"> (7b) They are experts in marketing.</Paragraph>
    <Paragraph position="36"> (7c) They always send someone to important meetings.</Paragraph>
    <Paragraph position="37"> (8) The Boston office will meet for an excursion on Friday.</Paragraph>
    <Paragraph position="38"> * (Sa) He/she likes to walk.</Paragraph>
    <Paragraph position="39"> (Sb) They will make a lunch break at 2 pm.</Paragraph>
    <Paragraph position="40"> (8c) They like to organize social events.</Paragraph>
    <Paragraph position="41">  In contrast to the examples discussed so far, sentences in the next group ((2), (7), (8), and their follow-ups) involve slightly harder restrictions. These are, however, no cross-language differences, because all references in these sentences are intersentential. The example sentences demonstrate certain complications in metonymic uses of 'office' in contrast to metonymic uses of 'sandwich', which originate from the differences in the underlying relations between food and the persons eating it, as opposed to the office and the caller who is related in a more indirect or perhaps more pronounced way to the office than persons are to the food they eat. 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). In any case, these examples indicate an additional demand on :the treatment of cardinalities and referential accessibility of metonymic expressions: a distinction is to be made between the entities referred to metonymically (here: employees of the Boston office), and those of its member 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  metonymically is the one who intends to pay.</Paragraph>
    <Paragraph position="42"> (9) Which airlines serve diet food from Boston to New York? (9a) In the first class?</Paragraph>
    <Paragraph position="44"> As a further aspect of metonymic expressions, the last set of examples demonstrates 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.</Paragraph>
    <Paragraph position="45"> 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 to the airline would decontextualize the serving process, and linking it to the persons would make the serving process independent of the context of a flight and the person's working for the airline. Therefore, it is more appropriate to elaborate the relation between the airlines and their employees to include the implicitly referred flights explicitly. These flights, of course, are the items that are first class and go from Boston to New York. Note, that linking the locality context properly is essential for setting up correct database requests, at least for requests to databases not restricted to flights only.</Paragraph>
  </Section>
  <Section position="5" start_page="106" end_page="107" type="metho">
    <SectionTitle>
4 Expressing Lexical Knowledge
</SectionTitle>
    <Paragraph position="0"> In order to capture distinctions between the varying interpretations of metonymic expressions illustrated in the previous section, 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 therein 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 exploited for scope disambiguation in (Fliegner 1988).</Paragraph>
    <Paragraph position="1"> In the extended form (see Figures 2 and 3), we introduce explicit quantifiers, and we optionally add restrictors to variables referred to by events predicates. In addition, the scoping of quantifiers allows the derivation of cardinalities - see the entries for FRUIT-DUMPLING and MEAT-PLATE, as contrasting examples. We distinguish several types of quantifiers to cover the cases elaborated in the previous section, in addition to the standard quantifiers EXIST and WH (the first two constitute default information, and the others express definitional restrictions):</Paragraph>
    <Paragraph position="3"> Figures 2 and 3 show entries in the Generative Lexicon with extended TELIC roles. In principle, the same extensions also apply to the AGENTIVE roles, but we do not elaborate these extensions because we do not make use of these roles for our current purpose. Figure 2, for example, shows that some sorts of food are associated with different expectations about how many persons typically eat them. Frt::t dumplings appear as sets (quantified by DEFMULTIPLE), to be eaten as a dish by a single person (quantified by DEFSINGLE). In contrast to the fruit dumplings, cardinality relations are inverted for the meat plate. Similar, but weaker default assumptions hold for a table in a restaurant.</Paragraph>
    <Paragraph position="4"> In contrast to the restaurant scenario, cardinality relations are less vague and associated with defaults for elementary relations in organizations. Each office, and airlines in particular, are supposed to employ a set of persons larger than one, and each person is working for one organization only, at least in his/her individual activities (hence, the quantifiers SINGLE and MULTIPLE in the lexical entries shown in Figure 3). Similarly, each flight carries some set of people, each of which participates in one flight only (at the same time).</Paragraph>
    <Paragraph position="5"> The knowledge contained in these lexicon entries can be used for building logical forms representing metonymic expressions of the kind discussed in section 3. The event predicates in the TELIC roles (and, less frequently, in the AGENTIVE roles) are exploited to infer the relation involved, which works similarly to other approaches. Moreover, the new quantification specification yields the otherwise missing source of information to build an explicit logical form with cardinality specifications from concise surface expressions in a precise manner.</Paragraph>
  </Section>
  <Section position="6" start_page="107" end_page="108" type="metho">
    <SectionTitle>
5 Building Logical Forms
</SectionTitle>
    <Paragraph position="0"> Based on entries in the Generative Lexicon and on the context given by a sentence to be interpreted, appropriate logical forms can be built that represent semantic relations involved more explicitly than this is the case with previous approaches. These logical forms take into account sorts of the entities involved and sorts of case frame slots in which these entities appear, syntactic information about number, and default expectations or semantic restrictions about the cardinality of these entities, the latter aspect being a new feature in our approach. 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 semantic cardinality specifications is achieved, which may require overwriting defaults or introducing a new set of entities as a subset of those already introduced. In concrete, logical forms are built by pursuing the procedure sketched in Figure 4, with step 2a performing metonymic extensions, and step 2c performing a final extension in case of a cardinality mismatch. In the following, we illustrate the procedure by some examples. Consider the sentence  (4) The fruit dumplings wants to pay.</Paragraph>
    <Paragraph position="2"> 1. Build an initial logical form from the surface expression.</Paragraph>
    <Paragraph position="3"> The representation is composed as an expression of the form (Qs xE Sz &lt;P&gt;), with XE being the variable whose representation is to be extended (initially equal to x, denoting the literal referent), QE being its quantifier, and SE its sort (initially equal to Q and S, which are associated with the literal referent), and &lt;P&gt; being an eventually structured representation of the sentence predicate and its modifiers. Moreover, the conflicting restrictions are stored. Let SR be the sort required within the referring case frame, and QR the quantifier representing the associated case slot restrictions.</Paragraph>
    <Paragraph position="4"> 2. Extend the meaning of noun phrases where a sortal incompatibility occurs. 2a. Build a metonymically extended expression through consultation of lexical knowledge. Merge the partial expression (QE xE SE &lt;P&gt;) with the extended representation found in the lexical entry for SE (typically under the TELIC role), which structurally yields (Q~ x~ S~ (AND &lt;P~&gt; (Q2 x2 $2 &lt;P2&gt;))) - that is, the structure taken from the lexicon, with</Paragraph>
    <Paragraph position="6"> if the referent with the same sort as xE has wider scope in the lexicon entry, or</Paragraph>
    <Paragraph position="8"> if the referent with the same sort as xz has narrower scope in the lexicon entry.</Paragraph>
    <Paragraph position="9"> &lt;P&gt; is partitioned according to sortal compatibility of its components, as follows if xl = xE then &lt;P~&gt; contains parts that refer to xE and are sortally compatible with S~, else &lt;P2&gt; contains parts that refer to xE and are sortally compatible with SE. Similarly, the remaining parts of &lt;P&gt; become &lt;P2&gt;, if xl = XE, and &lt;P~&gt; otherwise. 2b. Test the compatibility of the newly inserted sort with the restrictions to be met. If SN (SN = $2, if S~ = SE, and SN = S1 otherwise) is again incompatible with SR, then repeat step 2a with Xs, SN, QN and &lt;PN&gt; as XE, SE, QE and, &lt;P&gt;, respectively (XN, QN and &lt;PN&gt; have the same index as Ss); else QN is overwritten by QR if QN is a default quantifier compatible with QR.</Paragraph>
    <Paragraph position="10"> 2c. Test the cardinality compatibility of the newly inserted sort with the restrictions to be met. If SN is compatible with SR, but Qr~ is incompatible with QR, then the expression is expanded as under 2a, by a MEMBER relation between xe and xN. If not the whole set of entities bound to xz participates in the eventuality, then an expansion is performed with a SUBSET relation instead of a MEMBER relation.  The initial logical form directly built from the surface expression simply is</Paragraph>
  </Section>
  <Section position="7" start_page="108" end_page="109" type="metho">
    <SectionTitle>
(MULTIPLE x FRUIT-DUMPLING
(WANT-PAY x))
</SectionTitle>
    <Paragraph position="0"> which contains a sortal incompatibility.</Paragraph>
    <Paragraph position="1"> Making use of the lexical entry for 'fruit dumplings' and expanding the expression according to the TELIC role (see Figure 2)  * More referents than just the real and the literal referent may be introduced, either through chained metonymic extensions or through membership/subset insertions.</Paragraph>
    <Paragraph position="2"> * An additional inserted referent may provide a proper place to relate sentence complements (e.g., locality information to flights rather than to airlines or to persons). Note, that there is a scoping difference in the expressions underlying the phrases 'one and the same person eating several fruit dumplings' and 'several persons sharing a meat plate' (the default interpretations), which is in contrast to the approach by (Stallard 1993), Moreover, the additional referents may not only improve the basis for complement attachment, but also for pronoun resolution. Both aspects are briefly discussed in the next section.</Paragraph>
  </Section>
  <Section position="8" start_page="109" end_page="111" type="metho">
    <SectionTitle>
6 Impacts on Reference Resolution
</SectionTitle>
    <Paragraph position="0"> 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. This achievement is based on the following factors we have examined: * Reference to literal and intended referents is possible in an increasing number of cases.</Paragraph>
    <Paragraph position="1"> * Pronominal reference in plural form may have as antecedents distinguished sets of entities that are associated with a metonymic expression.</Paragraph>
    <Paragraph position="2"> * There are cross-language differences between German and English in the treatment of intersentential pronominal reference.</Paragraph>
    <Paragraph position="3"> In order to express scoping relations among sets properly, the logical forms representing metonymic expressions with entities of cardinality greater than one must deviate from Stallard's methods. According to (Stallard 1993), pronominal reference to literal and real referents is regulated by their scope, which distinguishes referential from predicative kinds of metonymy. Unfortunately, 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 pronominal 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 25.' Moreover, the message 'The Boston office called' can be followed by the remark 'He spoke 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 eventual 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, since this is usually considered an influential factor regarding the content of the message.</Paragraph>
    <Paragraph position="4"> Given these pieces of evidence, reference resolution is essentially supported by the explicit logical form built through our techniques, and it is additionally guided as follows: lntrasentential reference Possessive pronouns always relate to the intended referent, which is accessible through the logical form. Since possessive pronouns in the same sentence agree in gender and number with the real referent in English, while they agree with the literal referent in German, only English sentences contain additional 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.</Paragraph>
    <Paragraph position="5"> Intersentential reference Reference through personal pronouns is possible to the literal and to the real referent, and to referents of the same sort but with possibly different cardinality as the real referent. Thus, all entities involved in a metonymic expression in its appearance in the explicit logical form are potential antecedents, except to some internal elements of a metonymic chain, so that a dialog memory should be maintained accordingly, For example, following the sentence 'The Boston office called', pronominal 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' appearing in the extended logical form representing the sentence 'Which airlines serve diet food from New York to Boston?' are not pronominally accessible.</Paragraph>
  </Section>
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