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<Paper uid="C00-1031">
  <Title>An Empirical Investigation of the Relation Between Discourse Structure and Co-Reference</Title>
  <Section position="4" start_page="208" end_page="209" type="intro">
    <SectionTitle>
2 Background
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="208" end_page="208" type="sub_section">
      <SectionTitle>
2.1 Assumptions
</SectionTitle>
      <Paragraph position="0"> Our approach is based on the following assmnptions: I. For each anaphor in a text, an anaphora resolution system must produce an LPA that contains a referent to which 111e anaphor can be resolvcd. The size of this LPA wuies fronl system to system, depending on tile theory a system implements.</Paragraph>
      <Paragraph position="1">  2. The smaller the I,PA (while retaining a correct antecedent), the less likely that errors ill the \]7tI,TH{ :(lid PI',V,I;F, RI;,NCI ~, modules will affect the ability of a system to select the appropriate referent.</Paragraph>
      <Paragraph position="2"> 3. Theory A is better than lheory B for the task of rel null erence resolution if theory A produces IJ'As that contain more antecedents to which amtphors can be corrcclly resolved than theory B, and if the l,l~As produced by theory A arc smaller than those produccd by theory B. l;or cxaml)lc, if for a given anaphor, theory A produces an I,PA thai contains a referee to which the anaphor can be resolved, while theory B produces an IJ~A that does not contain such a re\[eree, theory A is better than theory B.</Paragraph>
      <Paragraph position="3"> Moreover, if for a given anaphor, theory A produces an Lt)A wilh two referees and theory B produces an LPA with seven rel'crees (each LPA containing a referee to which tile anal)her can be resolved), lheory A is considered better than theory 11 because it has a higher probability of solving that anaphor correctly.</Paragraph>
      <Paragraph position="4"> We consider two classes of models for determining the LPAs of anaphors ill a text: Linear-k models. This is at class of linear models in which the LPAs include all the references foulad in the discourse unit under scrutiny and the k discourse units that immediately precede it. Linear-0 models an approach that assumes that :tll anaphors can be resolved intra-unit; Linear- 1 models an approach that cor,'esponds roughly to centering (Grosz et al., 1995). Linear-k is consistent with the asslunl)tions that underlie most current anaphora resohltion systems, which look back h units in order to resolve an anaphor.</Paragraph>
      <Paragraph position="5"> l)iscourse-V1:k models. In |his class ()1'models, LPAs include all lhe refcrentM expressions fotmd in the discourse unit under scrutiny and the k discourse units that hierarchically precede it. The units that hierarchically precede a given unit are determined according to Veins Theory (VT) (Cristea et al., 1998), which is described brielly below.</Paragraph>
    </Section>
    <Section position="2" start_page="208" end_page="209" type="sub_section">
      <SectionTitle>
2.2 Veins Theory
</SectionTitle>
      <Paragraph position="0"> VT extends and formalizes the relation between discourse structure and reference proposed by Fox (1987).</Paragraph>
      <Paragraph position="1"> It identilies &amp;quot;veins&amp;quot;, i.e., chains of elementary discourse units, over discourse structure trees that are built according to the requirements put forth in Rhetorical Structure Theo,y (RST) (Mann and Thompson, 1988).</Paragraph>
      <Paragraph position="2"> One of the conjectures ()1' VT is that the vein expression of an elementary discourse unit provides a coherent &amp;quot;abstract&amp;quot; of the discourse fi'agmcnt that contains that unit. As an internally coherent discottrse fragment, most ()1' the anaphors and referentM expressions (REst in a unit must be resolved to referees that oceul&amp;quot; in the text subs:used by the units in tile vein. This conjecture is consistent with Fox's view (1987) that the units that contain referees to which anaphors can be resolved are determined by the nuclearity of the discourse units thal precede the anaphors and the overall structure of discourse. According to V'I; REs of both satellites and nuclei can access referees of hierarchically preceding nt,cleus nodes. REs of nuclei can mainly access referees of preceding nuclei nodes and of directly subordinated, preceding satellite nodes. And the interposition ()1' a nucleus after a satellite blocks tim accessibility of the satellite for all nodes that att'e lovcer in the corresponding discourse structure (see (Cristea et al., 1998) for a full delinition).</Paragraph>
      <Paragraph position="3"> Hence, the fundamental intuition unde,lying VT is that the RST-spceilie distinction between nuclei and satellites constrains the range of referents to which anaphors can 19e resolved; in other words, the nucleus-satellite distinction induces for each anaphor (and each referential expression) a Do,naita of Refcrenlial Accessibility (DRA). For each anaphor a in a discourse unit ~z, VT hypothesizes that a can be resolved by examining referential expressions that were used in a subset o1' the discourse units that precede it; this subset is called the DRA of u. For any elcntentary unit u in a text, the corresponding DRA is computed autonmtically from the rhetorical representation of that text in two steps: 1. lteads for each node are computed bottom-up over the rhetorical representation tree. Heads ()1&amp;quot; elementary discottrse traits are the traits themselves. Heads of internal nodes, i.e., discourse spans, are con&gt; pt, ted by taking the union of the heads of the immediate child nodes that :ire nuclei. For example, for the text in Figure I, whose rhetorical structure is shown in Figure 2, the head ()1' span 115,711 is unit 5 because the head ()t' the inmmdiate nucleus, the elementary unit 5, is 5. However, the head of span 116,7\] is the list (6,7) because both immediate children are nuclei of a multinuclear relation.</Paragraph>
      <Paragraph position="4"> 2. Using the results of step 1, Vein expressions are eOmlmted top-down lbr each node in the tree. The vein of the root is its head. Veins of child nodes  i. \[Michael D. Casey,\[a top Johnson&amp;Johnson ...... get, moved teCGe~ Therapy In~, a small biotechnology concern here, 2. to become_~_t&gt;president and chieC operating officer. \[ 3. \[Mr. Casey, 46 years old,\] was\[ president of J&amp;J's McNeil Pharmaceutical subsidiary,\] *t. which was merged with another J&amp;J unit, Ortho Pharmaceutical Corp., this year in a cost-cutting move.</Paragraph>
      <Paragraph position="5"> 5. I,Ir. Casev\[ succeeds M. James Barrett, 50, as\[president of ~,~netic Ther-ap~.</Paragraph>
      <Paragraph position="6"> 6. Mr. Barrett remains chief executive officer 7. and becomes chainaan.</Paragraph>
      <Paragraph position="7"> 8. \[Mr-\] Mr. Casey\] said 9. ~made the move te {\]{e smaller compan~ i0. because~saw health care moving toward technologies like products.</Paragraph>
      <Paragraph position="8"> ll. Ubelieve that the field is emerging and i~ prepared to break loose,  The |'eferential expressions surrounded by boxes and ellipses correspond to two distinct co-referential equivalence classes. Referential expressions surrounded by boxes refer to Mr: Casey; those surrounded by ellipses refer to Genetic Thercq~y Inc.</Paragraph>
      <Paragraph position="9"> are computed recursively according to tile rules described by Cristea et al.(1998). The DRA ot&amp;quot; a unit u is given by the units that precede u in 1t~e vein.</Paragraph>
      <Paragraph position="10"> For example, for the text and RST tree in Figures 1 and 2, the vein expression of unit 3, which contains units 1 and 3, suggests that anaphors from unit 3 should be resolved only to referential expressions in units 1 and 3. Because unit 2 is a satellite to unit 1, it is considered to be &amp;quot;blocked&amp;quot; to referential links fi'om trait 3. In contrast, tile DRA of unit 9, consisting o1' units 1, 8, and 9, reflects the intuition that anaphors lY=om unit 9 can be resolved only to referential ext)ressions fi'om unit 1, which is the most important trait in span \[1,7\], and to unit 8, a satellite that immediately precedes unit 9. Figure 2 shows the heads and veins of all internal nodes in the rhetorical representation.</Paragraph>
    </Section>
    <Section position="3" start_page="209" end_page="209" type="sub_section">
      <SectionTitle>
2.3 Comparing models
</SectionTitle>
      <Paragraph position="0"> The premise underlying out&amp;quot; experiment is that there are potentially significant differences in the size of the search space rcquired to resolve referential cxpressions when using Linear models vs. Discou|'se-VT models. For example, for text and tile RST tree in Figures 1 and 2, the Discourse-VT model narrows tlle search space required to resolve the a|mphor the smaller company in unit 9.</Paragraph>
      <Paragraph position="1"> According to VT, we look lbr potential antecede|Us for the smaller company in the DRA of unit 9, which lists units I, 8, and 9. The antecedent Genetic Therapy Inc.</Paragraph>
      <Paragraph position="2"> appears in unit 1 ; therefore, using VT we search back 2 units (units 8 and 1) to lind a correct antecedent. In contrast, to resolve the same reference using a linear model, four units (units 8, 7, 6, and 5) must he examined before Genetic The;zq?y is found. Assuming that referential links are established as tile text is processed, Genetic Therapy would be linked back to pronottn its in unit 2, which would in turn be linked to the first occurrence of the antecedent,Genetic Therapy Inc., in unit 1, tile antecedent determined directly by using V'E In general, when hierarchical adjacency is considered, an anaphor may be resolved to a referent that is not the closest in a linear interpretation of a text. Simihu'ly, a referential expression can be linked to a referee that is not the closest in a linear interpretation of a text. However, this does not create problems because we are focusing here only on co-referential relations of identity (see section 3). Since these relations induce equivalence classes over tile set of referential expressions in a text, it is suf\[icient that an anaphor or referential expression is resolved to any of the members of the relevant equiw|lence class.</Paragraph>
      <Paragraph position="3"> For example, according to V'I, the referential expression MI: Casey in unit 5 in Figm'e 1 can be linked directly only to the referee Mr Casey in unit 1, because the DRA o1' unit 5 is { 1,5}. By considering the co-referential links of the REs in the other units, tile full equivalence class can be determined. This is consistent with tile distinction between &amp;quot;direct&amp;quot; and &amp;quot;indirect&amp;quot; references discussed by Cristea, et al.(1998).</Paragraph>
    </Section>
  </Section>
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