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<Paper uid="P00-1053">
  <Title>A Hierarchical Account of Referential Accessibility</Title>
  <Section position="3" start_page="2" end_page="5" type="intro">
    <SectionTitle>
2 VT and Stack-based Models
</SectionTitle>
    <Paragraph position="0"> Veins Theory claims that references from a given unit are possible only in its DRA, i.e., that discourse structure constrains the areas of the text over which references can be resolved. In previous work, we compared the potential of hierarchical and linear models of discourse--i.e., approaches that enumerate potential antecedents in an undifferentiated window of text linearly preceding the anaphor under scrutiny--to correctly establish co-referential links in texts, and hence, their potential to correctly resolve anaphors (Cristea, et al., 2000). Our results showed that by exploiting the hierarchical discourse structure of texts, one can increase the potential of natural language systems to correctly determine co-referential links, which is a requirement for correctly resolving anaphors. In general, the potential to correctly determine co-referential links was greater for VT than for linear models when one looks back 4 elementary discourse units. When looking back more than four units, the linear model was equally effective.</Paragraph>
    <Paragraph position="1"> Here, we compare VT to stack-based models of discourse structure based on Grosz and Sidner's (1986) (G&amp;S) focus spaces (e.g., Hahn and Strube, 1997; Azzam, et al., 1998). In these approaches, discourse segments are pushed on the stack as they are encountered in a linear traversal of the text. Before a dominating segment is pushed, subordinate segments that precede it are popped from the stack.</Paragraph>
    <Paragraph position="2"> Antecedents for REs appearing in the segment on the top of the stack are sought in discourse segments in the stack below it. Therefore, in cases where a subordinate segment a precedes a dominating segment b, a reference to an entity in a by an RE in b is not resolvable. Special provision could be made in order to handle such cases--e.g., subsequently pushing a on top of b--but this would violate the overall strategy of resolving REs appearing in segments currently on the top of the stack.</Paragraph>
    <Paragraph position="3"> The special status given to left satellites in VT addresses this problem. For example, one RST analysis of (1) proposed by Moser and Moore (1996) is given in Figure 3. Moser and Moore note that the relation of an RST nucleus to its satellite is analogous to the dominates relation proposed by G&amp;S (see also Marcu, 2000). As a subordinate segment preceding the segment that dominates it, the satellite is popped from the stack before the dominant segment (the nucleus) is pushed in the stack-based model, and therefore it is not included among the discourse segments that are searched to resolve co-references.</Paragraph>
    <Paragraph position="4">  Similarly, the text in (2), taken from the MUC annotated corpus (Marcu, et al., 1999), was assigned the RST structure in Figure 4, which presents the same problem for the stack-based approach: the referent for this in C2 is to the Clinton program in A2, but because it is a subordinate segment, it is no longer on the stack  when C2 is processed.</Paragraph>
    <Paragraph position="5"> (1) A1. George Bush supports big business.</Paragraph>
    <Paragraph position="6"> B1. He's sure to veto House Bill 1711.</Paragraph>
    <Paragraph position="7">  Note that Moser and Moore (1996) also propose an informational RST structure for the same text, in which a &lt;&lt; volitional-cause &gt;&gt; relation holds between the nucleus a and the satellite b, thus providing for a to be on the stack when b is processed.</Paragraph>
    <Paragraph position="8"> (2) A2. Some of the executives also signed letters on behalf of the Clinton program.</Paragraph>
    <Paragraph position="9"> B2. Nearly all of them praised the president for his efforts to pare the deficit.</Paragraph>
    <Section position="1" start_page="3" end_page="3" type="sub_section">
      <SectionTitle>
2.1 Validation
</SectionTitle>
      <Paragraph position="0"> To validate our claim, we examined 23 newspaper texts with widely varying lengths (mean length = 408 words, standard deviation 376). The texts were annotated manually for co-reference relations of identity (Hirschman and Chinchor, 1997). The co-reference relations define equivalence relations on the set of all marked references in a text. The texts were also annotated manually with discourse structures built in the style of Mann and Thompson (1988).</Paragraph>
      <Paragraph position="1"> Each analysis yielded an average of 52 elementary discourse units. Details of the annotation process are given in (Marcu et al., 1999).</Paragraph>
      <Paragraph position="2"> Six percent of all co-references in the corpus are to left satellites. If only co-references pointing outside the unit in which they appear (inter-unit references) are considered, the rate increases to 7.76%. Among these cases, two possibilities exist: either the reference is unresolvable using the stack-based method because the unit in which the referent appears has been popped from the stack, or the stack-based algorithm finds a correct referent in an earlier unit that is still on the stack. Twenty-two percent (2.38% of all co-referring expressions in the corpus) of the referents that VT finds in left satellites fall into  the first category. For example, in text fragment (3), taken from the MUC corpus, the co-referential equivalence class for the pronoun he in C3 includes Saloman Brothers analyst Jeff Canin in B3 and he in A3. The RST analysis of this fragment in Figure 5 shows that both A3 and B3 are left satellites. A stack-based approach would not find either antecedent for he in C3,  since both A3 and B3 are popped from the stack before C3 is processed.</Paragraph>
      <Paragraph position="3"> (3) A3. Although the results were a little lighter than the 49 cents a share he hoped for, B3. Salomon Brothers analyst Jeff Canin said C3. he was pleased with Sun's gross margins for the quarter.</Paragraph>
      <Paragraph position="4">  In cases where stack-based approaches find a co-referent (although not the most recent antecedent) elsewhere in the stack, it makes sense to compare the effort required by the two models to establish correct co-referential links. That is, we assume that from a computational perspective (and, presumably a psycholinguistic one as well), the closer an antecedent is to the referential expression to be resolved, the better. We have shown elsewhere (Cristea et al., 2000) that VT, compared to linear models, requires significantly less effort for DRAs of any size. We use a similar strategy here to compute the effort required by VT and stack-based models.</Paragraph>
      <Paragraph position="5"> DRAs for both models are treated as ordered lists. For example, text fragment (4) reflects the set of units on the stack at a given point in processing one of the MUC texts; units D4 and E4, in brackets, are left satellites and therefore not available using the stack-based model, but visible using VT. To determine the correct antecedent of Mr. Clinton in F4 using the stack-based model, it is necessary to search back through 3 units (C4, B4, A4) to find the referent President Clinton. In contrast, using VT, we search back only 1 unit to D4.</Paragraph>
      <Paragraph position="6">  (4) A4. A group of top corporate executives urged Congress to pass President Clinton's deficitreduction plan, B4. declaring that it is superior to the only apparent alternative: more gridlock.</Paragraph>
      <Paragraph position="7"> C4. Some of the executives who attended  yesterday's session weren't a surprise.</Paragraph>
      <Paragraph position="8"> [ D4. Tenneco Inc. Chairman Michael Walsh, for instance, is a staunch Democrat who provided an early endorsement for Mr.</Paragraph>
      <Paragraph position="9"> Clinton during the presidential campaign.</Paragraph>
      <Paragraph position="10"> E4. Xerox Corp.'s Chairman Paul Allaire was one of the few top corporate chief executive officers who contributed money to the Clinton campaign. ] F4. And others, such as Atlantic Richfield Co. Chairman Lodwrick M. Cook and Zenith Electronics Corp. Chairman Jerry Pearlman, have also previously voiced their approval of Mr. Clinton's economic strategy.</Paragraph>
      <Paragraph position="11"> We compute the effort e(M,a,DRA k ) of a model M to determine correct co-referential links with respect to a referential expression a in unit u, given a DRA of size k (DRA k (u)) is given by the number of units between u and the first unit in</Paragraph>
      <Paragraph position="13"> that contains a co-referential expression of a. The effort e(M,C,k) of a model M to determine correct co-referential links for all referential expressions in a corpus of texts C using DRAs of size k is computed as the sum of the efforts</Paragraph>
      <Paragraph position="15"> ) of all referential expressions a where VT finds the co-reference of a in a left satellite. Since co-referents found in units that are not left satellites will be identical for both VT and stack-based models, the difference in effort between the two models depends only on co-referents found in left satellites.</Paragraph>
      <Paragraph position="16"> Figure 6 shows the VT and stack-based efforts computed over referential expressions resolved by VT in left satellites and k = 1 to 12.</Paragraph>
      <Paragraph position="17"> Obviously, for a given k and a given referent a, that no co-reference exists in the units of the</Paragraph>
      <Paragraph position="19"> the effort to be equal to k. As a result, for small k the effort required to establish co-referential links is similar for both models, because both can establish only a limited number of links.</Paragraph>
      <Paragraph position="20"> However, as k increases, the effort computed over the entire corpus diverges, with VT performing consistently better than the stack- null Note that in some cases, the stack-based model performs better than VT, in particular for small k. This occurs when VT searches back through n adjacent left satellites, where n &gt; 1, to find a coreference, but a co-referent is found using the stack-based method by searching back m nonleft satellite units, where m &lt; n. This would be the case, if for instance, VT first found a co-referent for Mr. Clinton In text (4) in D4 (2 units away), but the stack-based model found a co-referent in C4 (1 unit away since the left satellites are not on the stack).</Paragraph>
      <Paragraph position="21"> In our corpus, 15% of the co-references found in left satellites by VT required less effort using the stack-based method, whereas VT out-performed the stack-based method 23% of the time. In the majority of cases (62%), the two models required the same level of effort. However, all of the cases in which the stack-based model performed better are for small k (k&lt;4), and the average difference in distance (in units) is 1.25. In contrast, VT out-performs the stack-based model for cases ranging over all values of k in our experiment (1 to 12), and the average difference in distance is 3.8 units. At k=4, VT can determine all the co-referents in our corpus, whereas the stack-based model requires DRAs of up to 12 units to resolve them all. This accounts for the marked divergence in effort shown in Figure 6 as k increases. So, despite the minor difference in the percentage of cases where VT out-performs the stack-based model, VT has the potential to significantly reduce the search space for co-referential links.</Paragraph>
    </Section>
    <Section position="2" start_page="3" end_page="5" type="sub_section">
      <SectionTitle>
2.2 Exceptions
</SectionTitle>
      <Paragraph position="0"> We have also examined the exceptions, i.e., co-referential links that VT and stack-based models cannot determine correctly. Because of the equivalence of the stack contents for leftbalanced discourse trees, there is no case in which the stack-based model finds a referent where VT does not. There is, however, a number of referring expressions for which neither VT nor the stack-based model finds a co-referent. In the corpus of MUC texts we consider, 12.3% of inter-unit references fall into this category, or 9.3% of the references in the corpus if we include intra-unit references.</Paragraph>
      <Paragraph position="1"> Table 1 provides a summary of the types of referring expressions for which co-referents are not found in our corpus--i.e., no antecedent exists, or the antecedent appears outside the DRA.</Paragraph>
      <Paragraph position="2">  We show the percentage of REs in our corpus for which VT (and the stack-based model as well, since all units in the DRA computed according to VT are in the DRA computed using the stack-based model) fails to find an antecedent, and the percentage of REs for which VT finds a co-referent (in a left satellite) but the stack-based model does not.</Paragraph>
      <Paragraph position="3">  Our calculations are made based on the RST analysis of the MUC data, in which we detected a small number of structural errors. Therefore, the values given here are not absolute but rather provide an indication of the relative distribution of RE types.  We consider four types of REs:  (1) Pragmatic references, which refer to entities that can be assumed part of general knowledge, such as the Senate, the key in the phrase lock them up and throw away the key, or our in the phrase our streets.</Paragraph>
      <Paragraph position="4"> (2) Proper nouns, such as Mr. Gerstner or Senator Biden.</Paragraph>
      <Paragraph position="5"> (3) Common nouns, such as the steelmaker, the proceeds, or the top job.</Paragraph>
      <Paragraph position="6"> (4) Pronouns  Following (Gundel, et al., 1993), we consider that the evoking power of each of these types of REs decreases as we move down the list. That is, pragmatic references are easily understood without an antecedent; proper nouns and noun phrases less so, and are typically resolved by inference over the context. On the other hand, pronouns have very poor evoking power, and therefore a message emitter employs them only when s/he is certain that the structure of the discourse allows for easy recuperation of the antecedent in the message receiver's memory.  Except for the cases where a pronoun can be understood without an antecedent (e.g., our in our streets), it is virtually impossible to use a pronoun to refer to an antecedent that is outside the DRA.</Paragraph>
      <Paragraph position="7">  The alignment of the evoking power of referential expressions with the percentage of exceptions for both models shows that the predictions made by VT relative to DRAs are fundamentally correct--that is, their prevalence corresponds directly to their respective evoking  Ideally, a psycho-linguistic study of reading times to verify the claim that referees outside the DRA are more difficult to process would be in order. powers. On the other hand, the almost equal distribution of exceptions over RE types for the stack-based model shows that it is less reliable for determining DRAs.</Paragraph>
      <Paragraph position="8"> Note that in all VT exceptions for pronouns, the RST attribution relation is involved. Text fragment (5) and the corresponding RST tree (Figure 7) shows the typical case:  (5) A5. A spokesman for the company said, B5. Mr. Bartlett's promotion reflects the current  emphasis at Mary Kay on international expansion.</Paragraph>
      <Paragraph position="9"> C5. Mr. Bartlett will be involved in developing the international expansion strategy, D5. he said The antecedent for he in D5 is a spokesman for the company in A5, which, due to the nuclear-satellite relations, is inaccessible on the vein. Our results suggest that annotation of attributive relations needs to be refined, possibly by treating</Paragraph>
    </Section>
    <Section position="3" start_page="5" end_page="5" type="sub_section">
      <SectionTitle>
2.3 Summary
</SectionTitle>
      <Paragraph position="0"> In sum, VT provides a more natural account of referential accessibility than the stack-based model. In cases where the discourse structure is not left-polarized, at least one satellite precedes its nucleus in the discourse and is therefore its left sibling in the binary discourse tree. The vein definition formalizes the intuition that in a sequence of units a b c, where a and c are satellites of b, b can refer to entities in a (its left satellite), but the subsequent right satellite, c, cannot refer to a due to the interposition of nuclear unit b--or, if such a reference exists, it is  harder to process. In stack-based approaches to referentiality, such configurations pose problems: because b dominates a, in order to resolve potential references from b to a, b must appear below a on the stack even though it is processed after a. Even if the processing difficulties are overcome, this situation leads to the postulation of cataphoric references when a satellite precedes its nucleus, which is counterintuitive. null</Paragraph>
    </Section>
  </Section>
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