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<Paper uid="P97-1014">
  <Title>Centering in-the-Large: Computing Referential Discourse Segments</Title>
  <Section position="3" start_page="0" end_page="105" type="metho">
    <SectionTitle>
2 Global Discourse Structure
</SectionTitle>
    <Paragraph position="0"> There have been only few attempts at dealing with the recognition and incorporation of discourse structure beyond the level of immediately adjacent utterances within the centering framework. Two recent studies deal with this topic in order to relate attentional and intentional structures on a larger scale of global discourse coherence. Passonneau (1996) proposes an algorithm for the generation of referring expressions and Walker (1996a) integrates centering into a cache model of attentional state. Both studies, among other things, deal with the supposition whether a correlation exists between particular centering transitions (which were first introduced by Brennan et al. (1987); cf. Table 1) and intention-based discourse segments. In particular, the role of SHIFT-type transitions is examined from the perspective of whether they not only indicate a shift of the topic between two immediately successive utterances but also signal (intention-based) segment boundaries. The data in both studies reveal that only a weak correlation between the SHIFT transitions and segment boundaries can be observed. This finding precludes a reliable prediction of segment boundaries based on the occurrence of  SHIFTS and vice versa. In order to accommodate to these empirical results divergent solutions are proposed. Passonneau suggests that the centering data structures need to be modified appropriately, while Walker concludes that the local centering data should be left as they are and further be complemented by a cache mechanism.</Paragraph>
    <Paragraph position="1"> She thus intends to extend the scope of centering in accordance with cognitively plausible limits of the attentional span. Walker, finally, claims that the content of the cache, rather than the intentional discourse segment structure, determines the accessibility of discourse entities for anaphora resolution.</Paragraph>
    <Paragraph position="3"> As a working hypothesis, for the purposes of anaphora resolution we subscribe to Walker's model, in particular to that part which casts doubt on the hypothesized dependency of the attentional from the intentional structure of discourse (Grosz &amp; Sidner, 1986, p. 180). We diverge from Walker (1996a), however, in that we propose an alternative to the caching mechanism, which we consider to be methodologically more parsimonious and, at least, to be equally effective (for an elaboration of this claim, cf. Section 6).</Paragraph>
    <Paragraph position="4"> The proposed extension of the centering model builds on the methodological framework of functional centering (Strube &amp; Hahn, 1996). This is an approach to centering in which issues such as thematicity or topicality are already inherent. Its linguistic foundations relate the ranking of the forward-looking centers and the functional information structure of the utterances, a notion originally developed by Dane~ (1974). Strube &amp; Hahn (1996) use the centering data structures to redefine Dane~'s trichotomy between given information, theme and rheme in terms of the centering model. The Cb(Un), the most highly ranked element of C! (Un-1) realized in Un, corresponds to the element which represents the given information. The theme of Un is represented by the preferred center Cp (Un), the most highly ranked element of C! ( Un ). The theme/rheme hierarchy of Un corresponds to the ranking in the C! s. As a consequence, utterances without any anaphoric expression do not have any given elements and, therefore, no Cb. But independent of the use of anaphoric expressions, each utterance must have a theme and a C! as well.</Paragraph>
    <Paragraph position="5"> The identification of the preferred center with the theme implies that it is of major relevance for determining the thematic progression of a text. This is reflected in our reformulation of the two types of thematic progression (TP) which can be directly derived from centering data (the third one requires to refer to conceptual generalization hierarchies and is therefore beyond the scope of this paper, cf. Dane~ (1974) for the original statement):  1. TP with a constant theme: Successive utterances continuously share the same Cp.</Paragraph>
    <Paragraph position="6"> 2. TP with linear thematization of rhemes: An element  of the C! (Ui- 1 ) which is not the Cp (Ui- 1 ) appears in Ui and becomes the Cp(Ui) after the processing of this utterance.</Paragraph>
    <Paragraph position="8"> Cf(Ui-1): \[el ..... cj ..... cs\] l&lt;j&lt;s Cf(Vd: \[el ..... ek ..... e~l  terns. In our example (cf. Table 8 in Section 4), U1 to Ua illustrate the constant theme, while U7 to U10 illustrate the linear thematization of rhemes. In the latter case, the theme changes in each utterance, from &amp;quot;Handbuch&amp;quot; (manual) via &amp;quot;Inhaltsverzeichnis&amp;quot; (table of contents) to &amp;quot;Kapitel&amp;quot; (chapter) etc. Each of the new themes are introduced in the immediately preceding utterance so that local coherence between these utterances is established. Daneg (1974) also allows for the combination and recursion of these basic patterns; this way the global thematic coherence of a text can be described by recurrence to these structural patterns. These principles allow for a major extension of the original centering algorithm.</Paragraph>
    <Paragraph position="9"> Given a reformulation of the TP constraints in centering terms, it is possible to determine referential segment boundaries and to arrange these segments in a nested, i.e., hierarchical manner on the basis of which reachability constraints for antecedents can be formulated. According to the segmentation strategy of our approach, the Cp of the end point (i.e., the last utterance) of a discourse segment provides the major theme of the whole segment, one which is particularly salient for anaphoric reference relations. Whenever a relevant new theme is established, however, it should reside in its own discourse segment, either embedded or in parallel to another one. Anaphora resolution can then be performed (a) with the forward-looking centers of the linearly immediately preceding utterance, (b) with the forward-looking centers of the end point of the hierarchically immediately reachable discourse segment, and (c) with the preferred center of the end point of any hierarchically reachable discourse segment (for a formalization of this constraint, cf. Table 4).</Paragraph>
  </Section>
  <Section position="4" start_page="105" end_page="105" type="metho">
    <SectionTitle>
3 Computing Global Discourse Structure
</SectionTitle>
    <Paragraph position="0"> Prior to a discussion of the algorithmic procedure for hypothesizing discourse segments based on evidence from local centering data, we will introduce its basic building blocks. Let x denote the anaphoric expression under consideration, which occurs in utterance Ui associated with segment level s. The function Resolved(x, s, Us) (cf. Table 3) is evaluated in order to determine the proper antecedent ante for x. It consists of the evaluation of a teachability predicate for the antecedent on which we will concentrate here, and of the evaluation of the predicate lsAnaphorFor which contains the linguistic and conceptual constraints imposed on a (pro)nominal anaphor (viz. agreement, binding, and sortal constraints) or a textual ellipsis (Hahn et al., 1996), not an issue in this paper. The predicate lsReachable (cf. Table 4) requires ante to be reachable from the utterance Us associated with the segment level s. 2 Reachability is thus made dependent on the segment structure DS of the discourse as built up by the segmentation algorithm which is specified in Table 6. In Table 4, the symbol &amp;quot;=str&amp;quot; denotes string equality, N the natural numbers. We also introduce as a notational convention that a discourse segment is identified by its index s and its opening and closing utterance, viz. DS\[s.beg\] and DS\[s.end\], respectively. Hence, we may either identify an utterance Ui by its linear text index, i, or, if it is accessible, with respect to its hierarchical discourse segment index, s (e.g., cf. Table 8 where</Paragraph>
    <Paragraph position="2"> segment index is always identical to the currently valid segment level, since the algorithm in Table 6 implements a stack behavior. Note also that we attach the discourse segment index s to center expressions, e.g., Cb(s, Us).</Paragraph>
    <Paragraph position="3">  Finally, the function Lift(s, i) (cf. Table 5) determines the appropriate discourse segment level, s, of an utter- null assume that they are accessed in the total order given. ance Ui (selected by its linear text index, i). Lift only applies to structural configurations in the centering lists in which themes continuously shift at three different consecutive segment levels and associated preferred centers at least (cf. Table 2, lower box, for the basic pattern).</Paragraph>
    <Paragraph position="5"/>
  </Section>
  <Section position="5" start_page="105" end_page="106" type="metho">
    <SectionTitle>
8 else
</SectionTitle>
    <Paragraph position="0"> Whenever a discourse segment is created, its starting and closing utterances are initialized to the current position in the discourse. Its end point gets continuously incremented as the analysis proceeds until this discourse segment DS is ultimately closed, i.e., whenever another segment DS' exists at the same or a hierarchically higher level of embedding such that the end point of DS' exceeds that of the end point of DS. Closed segments are inaccessible for the antecedent search. In Table 8, e.g., the first two discourse segments at level 3 (ranging from U5 to U5 and Us to Ull ) are closed, while those at level 1 (ranging from U1 to U3), level 2 (ranging from U4 to UT) and level 3 (ranging from U12 to U13) are open.</Paragraph>
    <Paragraph position="1"> The main algorithm (see Table 6) consists of three major logical blocks (s and Ui denote the current discourse  segment level and utterance, respectively).</Paragraph>
    <Paragraph position="2"> 1. Continue Current Segment. The Cp(s, Ui-1) is  taken over for Ui. If Ui-1 and Ui indicate the end of a sequence in which a series of thematizations of rhemes have occurred, all embedded segments are lifted by the function Lift to a higher level s'. As a result of lifting, the entire sequence (including the final two utterances) forms a single segment. This is trivially true for cases of a constant theme.</Paragraph>
    <Paragraph position="3">  2. Close Embedded Segment(s).</Paragraph>
    <Paragraph position="4"> (a) Close the embedded segment(s) and continue another, already existing segment: If Ui does not include any anaphoric expression which is an element of the Cf (s, Ui-O, then match the antecedent in the hierarchically reachable segments. Only the Cp of the utterance at the end point of any of these segments is considered a potential antecedent. Note that, as a side effect, hierarchically lower segments are ultimately closed when a match at higher segment levels succeeds.</Paragraph>
    <Paragraph position="5"> (b) Close the embedded segment and open a new, parallel one: If none of the anaphoric expressions under consideration co-specify the  Cp(8 - 1, U\[8_l.end\]), then the entire C! at this segment level is checked for the given utterance. If an antecedent matches, the segment which contains Ui- 1 is ultimately closed, since Ui opens a parallel segment at the same level of embedding. Subsequent anaphora checks exclude any of the preceding parallel segments from the search for a valid antecedent and just visit the currently open one.</Paragraph>
    <Paragraph position="6">  (c) Open new, embedded segment: If there is no matching antecedent in hierarchically reachable segments, then for utterance Ui a new, embedded segment is opened.</Paragraph>
    <Paragraph position="7"> 3. Open New, Embedded Segment. If none of the  above cases applies, then for utterance Ui a new, embedded segment is opened. In the course of processing the following utterances, this decision may be retracted by the function Lift. It serves as a kind of &amp;quot;garbage collector&amp;quot; for globally insignificant discourse segments which, nevertheless, were reasonable from a local perspective for reference resolution purposes. Hence, the centered discourse segmentation procedure works in an incremental way and revises only locally relevant, yet globally irrelevant segmentation decisions on the fly.</Paragraph>
    <Paragraph position="9"/>
  </Section>
  <Section position="6" start_page="106" end_page="107" type="metho">
    <SectionTitle>
4 A Sample Text Segmentation
</SectionTitle>
    <Paragraph position="0"> The text with respect to which we demonstrate the working of the algorithm (see Table 7) is taken from a German computer magazine (c't, 1995, No.4, p.209). For ease of presentation the text is somewhat shortened. Since the method for computing levels of discourse segments depends heavily on different kinds of anaphoric expressions, (pro)nominal anaphors and textual ellipses are marked by italics, and the (pro)nominal anaphors are underlined, in addition. In order to convey the influence of the German word order we provide a rough phrase-to-phrase translation of the entire text.</Paragraph>
    <Paragraph position="1"> The centered segmentation analysis of the sample text is given in Table 8. The first column shows the linear text index of each utterance. The second column contains the centering data as computed by functional centering (Strube &amp; Hahn, 1996). The first element of the C I, the preferred center, Cp, is marked by bold font. The third column lists the centering transitions which are derived from the Cb/C! data of immediately successive utterances (cf. Table 1 for the definitions). The fourth column depicts the levels of discourse segments which are computed by the algorithm in Table 6. Horizontal lines indicate the beginning of a segment (in the algorithm, this corresponds to a value assignment to DS\[s.beg\]). Vertical lines show the extension of a segment (its end is fixed by an assignment to DS\[s.end\]). The fifth column indicates which block of the algorithm applies to the current utterance (cf. the right margin in Table 6).</Paragraph>
    <Paragraph position="2"> The computation starts at U1, the headline. The C1(Ux ) is set to &amp;quot;1260&amp;quot; which is meant as an abbreviation of &amp;quot;Brother HL-1260&amp;quot;. Upon initialization, the beginning as well as the ending of the initial discourse segment are both set to &amp;quot;1&amp;quot;. U2 and Ua simply continue this segment (block (1) of the algorithm), so Lift does not apply. The C v is set to &amp;quot;1260&amp;quot; in all utterances of this segment. Since U4 does neither contain any anaphoric expression which co-specifies the Cv(1 , Ua) (block (1)) nor any other element of the 67/( 1, U3) (block (2a)), and as there is no hierarchically preceding segment, block (2c) applies. The segment counter s is incremented and a new segment at level 2 is opened, setting the beginning and the ending to &amp;quot;4&amp;quot;. The phrase &amp;quot;das diinne Handbiichlein&amp;quot; (the thin leaflet) in U5 does not co-specify the C v (2, U4) but co-specifies an element of the C! (2, U4) instead (viz. &amp;quot;Handbuch&amp;quot; (manual)).</Paragraph>
    <Paragraph position="3"> Hence, block (3) of the algorithm applies, leading to the creation of a new segment at level 3. The anaphor &amp;quot;Handbuch&amp;quot; (manual) in U6 co-specifies the Cv(3 , Us). Hence block (1) applies (the occurrence of &amp;quot;1260&amp;quot; in CI(U5 ) is due to the assumptions specified by Strube &amp; Hahn (1996)). Given this configuration, the function Lift lifts the embedded segment one level, so the  One particular - is already noticed - in the first approach to - the big Brother.</Paragraph>
    <Paragraph position="4"> Im Betrieb macht e._gr durch ein kr~iftiges Arbeitsger~usch auf sich aufmerksam, das auch im Stand-by-Modus noch gut vemehmbar ist.</Paragraph>
    <Paragraph position="5"> In operation - draws - it - with a heavy noise level attention to itself- which - also - in the stand-by mode is still well audible.</Paragraph>
    <Paragraph position="6"> F~r Standard-InstaUationen kommt man gut ohne Handbuch aus.</Paragraph>
    <Paragraph position="7"> As far as standard installations are concerned- gets - one - well - by - without any manual.</Paragraph>
    <Paragraph position="8"> Zwar ed~iutert das dSnne Handbiichlein die Bedienung der Hardware anschaulich und gut illustriert.</Paragraph>
    <Paragraph position="9"> Admittedly, gives - the thin leaflet- the operation of the hardware- a clear description of - and - well illustrated.</Paragraph>
    <Paragraph position="10"> Die Software-Seite wurde im Handbuch dagegen stiefmSttedich behandelt: The software part - was - in the manual- however - like a stepmother- treated: bis auf eine karge Seite mit einem Inhaltsverzeichnis zum HP-Modus sucht man vergebens weitere Informationen.</Paragraph>
    <Paragraph position="11"> except for one meagre page- containing the table of contents for the HP mode - seeks- one- in vain- for further information.</Paragraph>
    <Paragraph position="12"> (8) Kein Wander: unter dem lnhaltsverzeichnis steht der lapidare Hinweis, man m6ge sich die Seiten dieses Kapitels doch bitte yon Diskette ausdrucken- Frechheit.</Paragraph>
    <Paragraph position="13"> No wonder: beneath the table of contents - one finds the terse instruction, one should - oneself- the pages of this section - please - from disk - print out - - impertinence. (9) Ohne diesen Ausdruck sucht man vergebens nach einem Hinweis darauf, warum die Auto-Continue-Funktion in der PostScript-Emulation nicht wirkt.</Paragraph>
    <Paragraph position="14"> Without this print-out, looks - one - in vain - for a hint why - the auto-continue-function - in the PostScript emulation - does not work.</Paragraph>
    <Paragraph position="15"> (10) Nach dem Einschalten zeigt das LC-Display an, dab diese praktische Hilfsfunktion nicht aktiv ist; After switching on - depicts - the LC display - that - this practical help function - not active - is; (11) si__.ge tiberwacht den Dateientransfer vom Computer. it monitors the file transfer from the computer.</Paragraph>
    <Paragraph position="16"> (12) Viele der kleinen Macken verzeiht man dem HL-1260 wenn man erste Ausdrucke in H~inden h~ilt.</Paragraph>
    <Paragraph position="17"> Many of the minor defects - pardons - one - the HL-1260, when - one - the first print outs - holds in  \[one' s\] hands.</Paragraph>
    <Paragraph position="18"> (13) Gerasterte Grauflftchen erzeugt der Brother sehr homogen Raster-mode grey-scale areas - generates - the Brothervery homogeneously...</Paragraph>
    <Paragraph position="19">  segment which ended with U4 is now continued up to U6 at level 2. As a consequence, the centering data of U5 are excluded from further consideration as far as the co-specification by any subsequent anaphoric expression is concerned. Uz simply continues the same segment, since the textual ellipsis &amp;quot;Seite&amp;quot; (page) refers to &amp;quot;Handbuch&amp;quot; (manual). The utterances U8 to U10 exhibit a typical thematization-of-the-rhemes pattern which is quite common for the detailed description of objects. (Note the sequence of SHIFT transitions.) Hence, block (3) of the algorithm applies to each of the utterances and, correspondingly, new segments at the levels 3 to 5 are created. This behavior breaks down at the occurrence of the anaphoric expression &amp;quot;sie&amp;quot; (it) in Uxl which co-specifies the Cp ( 5, Ul o ), viz. &amp;quot;auto-continue function&amp;quot;, denoted by another anaphoric expression, namely &amp;quot;Hilfsfunktion&amp;quot; (help function) in U10. Hence, block (1) applies. The evaluation of Lift succeeds with respect to two levels of embedding. As a result, the whole sequence is lifted up to level 3 and continues this segment which started at the discourse element &amp;quot;lnhaltsverzeichhis&amp;quot; (list of contents). As a result of applying Lift, the whole sequence is captured in one segment. U12 does not contain any anaphoric expression which co-specifies an element of the C! (3, U11), hence block (2) of the algorithm applies. The anaphor &amp;quot;HL-1260&amp;quot; does not co-specify the Cp of the utterance which represents the end of the hierarchically preceding discourse segment (UT), but it co-specifies an element of the C! (2, UT). The immediately preceding segment is ultimately closed and a parallel segment is opened at UI~ (cf. block (2b)). Note also that the algorithm does not check the C! (3, U10) despite the fact that it contains the antecedent of &amp;quot;1260&amp;quot;. However, the occurrences of &amp;quot;1260&amp;quot; in the Cfs of U9 and Ux0 are mediated by textual ellipses. If these utterances contained the expression &amp;quot;1260&amp;quot; itself, the algorithm would have built a different discourse structure and, therefore, &amp;quot;1260&amp;quot; in U10 were reachable for the anaphor in Ulz. Segment 3, finally, is continued by Ulz.</Paragraph>
  </Section>
  <Section position="7" start_page="107" end_page="109" type="metho">
    <SectionTitle>
5 Empirical Evaluation
</SectionTitle>
    <Paragraph position="0"> In this section, we present some empirical data concerning the centered segmentation algorithm. Our study was based on the analysis of twelve texts from the information technology domain (IT), of one text from a Ger- null man news magazine (Spiegel) 3, and of two literary texts 4 (Lit). Table 9 summarizes the total numbers of anaphors, textual ellipses, utterances, and words in the test set.</Paragraph>
    <Paragraph position="1">  neither specified for anaphoric antecedents in Ui, not an issue here, nor for anaphoric antecedents beyond Ui-1. In the test set, 139 anaphors (28%) and 116 textual ellipses (48,3%) fall out of the (intersentential) scope of Lit those common algorithms. So, the problem we consider is not a marginal one.</Paragraph>
    <Paragraph position="2">  and the linear distance they have to their corresponding antecedents. Note that common centering algorithms (e.g., the one by Brennan et al. (1987)) are specified only for the resolution of anaphors in Ui-1. They are  centered segmentation algorithm for anaphors and textual ellipses, respectively. The numbers in these tables indicate at which segment level anaphors and textual ellipses were correctly resolved. The category of errors  covers erroneous analyses the algorithm produces, while the one for false positives concerns those resolution results where a referential expression was resolved with the hierarchically most recent antecedent but not with the linearly most recent (obviously, the targeted) one (both of them denote the same discourse entity). The categories Cy(s, Ui-1) in Tables 12 and 13 contain more elements than the categories Ui-1 in Tables 10 and 11, respectively, due to the mediating property of textual ellipses in functional centering (Strube &amp; Hahn, 1996).</Paragraph>
    <Paragraph position="3">  The centered segmentation algorithm reveals a pretty good performance. This is to some extent implied by the structural patterns we find in expository texts, viz. their single-theme property (e.g., &amp;quot;1260&amp;quot; in the sample text). In contrast, the literary texts in the test exhibited a much more difficult internal structure which resembled the multiple thread structure of dialogues discussed by Ros6 et al. (1995). The good news is that the segmentation procedure we propose is capable of dealing even with these more complicated structures. While only one antecedent of a pronoun was not reachable given the superimposed text structure, the remaining eight errors are characterized by full definite noun phrases or proper names. The vast majority of these phenomena can be considered informationally redundant utterances in the terminology of Walker (1996b) for which we currently have no solution at all. It seems to us that these kinds of phrases may override text-grammatical structures as evidenced by referential discourse segments and, rather, trigger other kinds of search strategies.</Paragraph>
    <Paragraph position="4"> Though we fed the centered segmentation algorithm with rather long texts (up to 84 utterances), the antecedents of only two anaphoric expressions had to bridge a hierarchical distance of more than 3 levels. This coincides with our supposition that the overall structure computed by the algorithm should be rather fiat. We could not find an embedding of more than seven levels.</Paragraph>
  </Section>
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