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<Paper uid="C00-2088">
  <Title>A Formal Semantics for Generating and Editing Plurals</Title>
  <Section position="2" start_page="0" end_page="607" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> A natural language generator typically generates a noun plnase l'rom a representation consisting of an object with one or more attributes (cf. Reiter &amp; l)ale, 2000). Usually this representation is supplemented with inl'ormation concerning the context in which the noun phrase has io be realized (e.g., the set of distractors, whether tile object is in focus, etc.). \];or instance, the lil,ICUP, l{ system (Dale, 1992) deals with reference to plural objects by having the l'ollowing three attributes on physical objects: structure, whose wflue can be either a set or individual, cardinalio, which in case of a set records the numbers of elements which the set has, and constituents which in case of a set contains the elements of the set.</Paragraph>
    <Paragraph position="1"> Our proposal is intended to extend the representations proposed in (Dale, 1992)) Most importantly, wc replace the attribute cardinalily with the more general attribute quant (for quantifier) whose value is a quantilier such as 'most', 'few', '5', '&lt; 6' (at most 6), etc. Furthermole, we introduce the new attribute parl_of which takes its a value an ob.jecl of which the object in question is a part. ~ ~Note that we are dealing with the generation of plurals from (logically) structured data as opposed lo raw data as in, e.g., Stone (1999).</Paragraph>
    <Paragraph position="2"> 2We use the mcfcologicat 'part of' relation as an alternative It} &amp;quot;subset' For details, see the next section.</Paragraph>
    <Paragraph position="3"> The object-oriented (00) forlnalism in which we implement tile al'orelnentioned attributes is an extension of standard oo formalisms. It is known as Scoped Semantic Networks (SSN; Kibble et al., 1999; Power, 1999). 3 An SSN consists of a network of objects together with a mapping o1' these objects to a set o1' logical contexts. This makes it possible to represent universal quantification, implication, negation and other logical operators. In particulal; Power (1999) shows how an SSN can be mapped into a I)iscourse Representation Structure (DRS; Kamp &amp; Reyle, 1993), lhus providing a forlnal semantic interpretation of SSNs.</Paragraph>
    <Paragraph position="4"> In tiffs paper, we provide a mapping of SSNs with plural objects to an adapted version of Discourse Represemation Theory (I)RT). The mapping is provided to obtain t%rmal truth conditions for the SSNs. Such a lnaPlfing provides us with a mathenmlically precise characterization el' the information which is represented by a SSN ill terms of its truth-condilions.</Paragraph>
    <Paragraph position="5"> This is useful if we want to automatically lnanipulale lhe information which is represented by means of an SSN. For example, we can formally define whether some piece of information is aheady implicit in some other piece of information; in other words, we can deline a notion of logical consequence. Related to this is the possibility to use the semantics in order to test the consistency of the informatiou conveyed by an SSN. For tlmt purpose, we can do so-called model checking: an SSN is consislent if we can construct a model -that is, a logically possible state of the world- in which tile SSN is true according to our truth-conditional semantics.</Paragraph>
    <Paragraph position="6"> We do not provide a direct formal semantics for SSN, but rather map it to a more convenient logical l'ormalistn, i.e., I)P,T. The main reason for tiffs approach is that phenomena which we will be modelling in this paper, i.e. (plural) reference and aScc also, e.g., Sowa (1984).</Paragraph>
    <Paragraph position="7">  anaphora, have been studied extensively within I)RT (see, e.g., Kamp &amp; Reyle, 1993; Krahmer &amp; Van Deemter, 1998; Piwek, 1997). Fnrthermore, we believe that the adaptation of DRT that we propose is of interest in its own right.</Paragraph>
    <Paragraph position="8"> The mapping which we provide from SSNs with plural objects to DRSs requires some modifications to standard DRT with plurals (Kamp &amp; Reyle, 1993: Chapter 4). For networks with only singular objects, there is a straightforward mapping of the objects in a network to the discourse referents which populate  a DRS. Things are different for networks with plural objects. Consider: (1) Susan has found most books which Bill needs.</Paragraph>
    <Paragraph position="9"> The DP, S for this sentence is: (2)</Paragraph>
    <Paragraph position="11"> Intuitively, the meaning of this condition is that: fi')r most y which satisfy the conditions to the le/'t of the diamond, it holds that they also sati,@~ the condition on the right. Note, that the representation contains no plural discourse referent corresponding to the Nt' 'most books which Bill needs'. The 'y' in this representation is a referent for singular individuals. This might make one wonder how it is possible in standard DRT to refer back to plural individuals as in: (3) Susan has found most books which Bill needs.</Paragraph>
    <Paragraph position="12"> They were on her desk.</Paragraph>
    <Paragraph position="13"> For this purpose, there is a so-called abstraction operation (Kamp &amp; Reyle, 1993:313) with which we can obtain a discourse referent for the set of books which Bill needs and Susan Jbund. In more technical terms, the set is obtained by the summation of the values which 'y' can take. Thus there is no direct way of mapping a plural object in a semantic network (which represent the interpretation of an NP) to a plural discourse referent in the corresponding DRS. For this reason we have chosen to adapt the DP, T formalism, so that plural noun phrases do directly colTelate with plural discourse referents.</Paragraph>
    <Paragraph position="14"> We now proceed as follows. In Section 2, we specify the mapping from SSNs to our version of DRT. In the next section (Section 3), we describe an application which uses the SSNs with plurals. We finish this paper with a conclusions section (Section 4).</Paragraph>
  </Section>
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