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<Paper uid="W00-1416">
  <Title>On Identifying Sets</Title>
  <Section position="3" start_page="121" end_page="121" type="metho">
    <SectionTitle>
(16) E---- (L,r,R,x,P(L;R, Dx),P(L;Dr,Dx))
</SectionTitle>
    <Paragraph position="0"> The state represents: (17)a a description L; b a tuple r of distinguished free variables in the description for which we must identify specific intended values; c a tuple R of sets describing the value Ri which we intend for the corresponding -variable ri; .... . * d the remaining free variables of the description x; in Cithat are-not c-consistent_ e a constraint network P(L; R, Dx) describing the values for all the free variables in the description, on the assumption that the distinguished variables take on the values we intend; and f a constraint network p(L; Dr, Dx) describing the values for all the free variables in the description, on the assumption that the distinguished variables may, like other variables, take on any values from the context set.</Paragraph>
    <Paragraph position="1"> The distinction between the variables whose intended reference is fixed and those for which it is derived as a byproduct of the search process is due to Horacek (Horacek, 1995; Horacek, 1996); the distinction derives increased importance when relating one collection to another as the choice of collections need not give rise to explicit branching in search. The initial state involves an empty description and so has the form given in (18).</Paragraph>
    <Paragraph position="2"> (18) Y~= ((r),r,R, 0,P(Q;R),P(Q;Dr)) A state such as (16) represents a final state that successfully resolves the generation task when each variable x from r and x is associated with the same set Cx in both P(L;R,Dx) and P(L;Dr,Dx). This simply means that the hearer's interpretation of the referring expression matches the speaker's intended interpretation.</Paragraph>
    <Paragraph position="3"> At any state Z, the grammar defines a set of constraints of the form (~) L(rx; y) that could potentially be added to the description to obtain L~--L is some domain relation, r and x name the old variables from L while y names fresh variables. Of course, we want to restrict our attention to constraints that are compatible with our intended interpretation. To achieve this restriction, we begin by computing the new constraint network C ~ = P(L~;R;Dxy). We check, whenever R assigns a value to x, that Rx C C' x. If this test admits .the_new constraint, the newstate obtained from state E is computed as in (19).</Paragraph>
    <Paragraph position="4"> (19) (L', r, R, xy, P(L'; R, Dxy), P(L'; Dr, Dxy)}</Paragraph>
    <Section position="1" start_page="121" end_page="121" type="sub_section">
      <SectionTitle>
4.3 An Example
</SectionTitle>
      <Paragraph position="0"> I return to (1) to provide an illustration of the final scheme; the goal is to identify the segments in (20f), R, from among those in (20a). I use figures and references to figures, .in .place-of=.eonstraint, networks; the description uses the variable r. The states proceed, perhaps, thus:</Paragraph>
      <Paragraph position="2"/>
    </Section>
  </Section>
  <Section position="4" start_page="121" end_page="122" type="metho">
    <SectionTitle>
5 Closing thoughts
</SectionTitle>
    <Paragraph position="0"> Descriptions of sets obviously have much in common with expressions that describe a single entity from the shared context* In particular, adopting the standard view of NLG as goal-directed activity (Appelt, 1985; Dale, 1992; Moore, 1994; Moore and Paris, 1993), singular and plural descriptions agree both in the kinds of intentions that they can achieve and the stages of generation at which they can be formulated. We cannot expect a single process to be responsible for set descriptions across all intentions or stages of NLG.</Paragraph>
    <Paragraph position="1"> For example, as with a singular description, a description of a set may appeal to properties that play a role in the argument the speaker is trying to make, and may therefore address goals above and beyond simple identification of discourse entities.</Paragraph>
    <Paragraph position="2"> (Se e .(Donellan, ..! 966;: Kx~0nfeld, 1986) on the dis- .tinction.) (Green et al., 1998a; Green et al., 1998b) show how such descriptions may be represented and formulated in NLG at a high-level process of content or rhetorical planning. At the same time, plurals and singulars are alike in offering resources for reference--such as pronouns, one-anaphora or aggregated expressions--that bypass explicit description altogether* The use of these resources may be .... ~quite-closety dependent onthe surface 'form being generated and so could reflect a relatively late decision in the generation process (Dale and Haddock,  1991; Reiter, 1994; Dalianis, 1996).</Paragraph>
    <Paragraph position="3"> These complexities notwithstanding, we can expect many descriptions of sets, like descriptions of individuals, to be formulated from scratch to achieve purely referential goals during the SEN-TENCE PLANNING. plaase: of .NLG, io:.he:tween ~gon=. tent planning and surface realization (Rainbow and Korelsky, 1992; Reiter, 1994). I have shown that using covers to abstract collective and distributive readings--and using sets of assignments to represent plural references--yields a search space for this problem which largely mirrors that for singulars, and which avoids computation and search over sets of collections. Although sets proliferate explosively, it is no surprise that the search space for plurals set up by (19) is, like that for singulars, ultimately defined by the sequences of elements that make up descriptions. NLG involves search to use words effectively--choices of words should be the only decisions a referring expression generation system has to make.</Paragraph>
  </Section>
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