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<Paper uid="J01-4007">
  <Title>A Reformulation of Rule 2 of Centering Theory</Title>
  <Section position="2" start_page="0" end_page="585" type="abstr">
    <SectionTitle>
2. Transition Rules
</SectionTitle>
    <Paragraph position="0"> The main claims of CT are formalized in terms of Cb, the backward-looking center; Cf, a list of forward-looking centers for each utterance Un; and Cp or preferred center, the most salient candidate for subsequent utterances. Cf(Un) is a partial ordering on the entities mentioned (or &amp;quot;realized&amp;quot;) in Un, ranked by grammatical role; for example, SUBJ &gt; DIR-OBJ &gt; INDIR-OBJ &gt; COMP(S) &gt; ADJUNCT(S). Cb(Un) is defined as the highest-ranked member of Cf(Un-1) that is realized in U,. Cp(U,) is the highest-ranked member of Cf(Un), and is predicted to be Cb(Un+l).</Paragraph>
    <Paragraph position="1"> The ranking of Cf by grammatical role has been widely adopted in the literature following BFE though it is questioned by some researchers including Strube and</Paragraph>
    <Paragraph position="3"> Hahn (1999), who propose a ranking based on &amp;quot;functional information structure,&amp;quot; a combination of degrees of &amp;quot;givenness&amp;quot; and left-to-right order. They note that the BFP ranking is not appropriate for German, which they say is a free-word-order language (page 310); more accurately, relative order of NPs within a clause is not determined by grammatical role to the extent that it is in English. For the purposes of this paper, there is no need to commit to either BFP's or Strube and Hahn's rankings, or to go into the details of the latter's &amp;quot;functional centering&amp;quot; model, as both make the same predictions for the examples considered. Strube and Hahn themselves (page 334) state that the grammatical and functional analyses achieved consistent results for all examples in GJW. I adopt the ranking by grammatical role for purposes of exposition. null</Paragraph>
    <Section position="1" start_page="580" end_page="580" type="sub_section">
      <SectionTitle>
2.1 &amp;quot;Salience&amp;quot; and &amp;quot;Cohesion&amp;quot;
</SectionTitle>
      <Paragraph position="0"> Transitions are defined in terms of two tests: whether the Cb stays the same (Cb(Un) = Cb(U,~-I)), and whether the Cb is realized as the most prominent NP (grammatically or otherwise): Cb(Un) = Cp(Un). For the sake of convenience and concision, I refer to the first of these tests as cohesion and the second as salience; it is important to keep in mind that I use the terms in these defined and limited ways, and to disregard (for the time being) other uses of the terms in the literature. There are four possible combinations, which are displayed in Table 2, resulting in the named transitions Continue, Retain, Smooth Shift, and Rough Shift. The optimal case, where both salience and cohesion obtain, is Continue; the least preferred is Rough Shift. Walker, Joshi, and Prince (1998), following BFP, stipulate that Retain is preferred over Smooth Shift, which implies that cohesion is a stronger requirement than salience. However, corpus analyses reported by di Eugenio (1998, page 127), Hurewitz (1998, pages 280ff.), and Passoneau (1998, pages 338ff.) do not support this claim. In fact, all these researchers found a higher percentage of Smooth Shifts than Retains. In a spoken corpus, Passoneau found more Shifts than Continues.</Paragraph>
      <Paragraph position="1"> A preponderance of Shifts over Continues may reflect the domain and content of a text rather than the author's organizational goals. In fact, it can be seen that sequences of Smooth Shifts are rather natural in certain kinds of narrative or descriptive texts; see Example 1 (adapted from a pharmaceutical leaflet).</Paragraph>
      <Paragraph position="2">  This does not appear to be an incoherent text, but there is no way that the content could be rearranged to turn the Shifts into Continues. However, we can see that the author has maintained centering coherence as far as the content allows.</Paragraph>
      <Paragraph position="3"> We may conclude that not only does corpus evidence fail to confirm the canonical ordering, but in fact corpus analysis itself is not sufficient to evaluate the claims of CT without taking into account the underlying semantic content of a text. That is, statistics about the relative frequency of occurrences of different transition types do not in themselves tell us much about which transitions are preferred in particular situations since they do not take account of the choices available to an author. 1 A more promising approach is that of Brennan (1998), who gave subjects the controlled narrative task of providing a running commentary on a video recording of a basketball game, and used the videotape itself to construct a &amp;quot;propositional script&amp;quot; listing the sequence of events and their participants, and identifying players who were likely to continue as the center of attention over a sequence of incidents.</Paragraph>
    </Section>
    <Section position="2" start_page="580" end_page="585" type="sub_section">
      <SectionTitle>
2.2 Rule 2 Applied to Generation
</SectionTitle>
      <Paragraph position="0"> Reiter (1994) claimed that existing generation systems converged on a &amp;quot;consensus,&amp;quot; generic natural language generation (NLG) architecture consisting of the following tasks: * Content determination/text planning: deciding the content of a message and organizing the component propositions into a text tree; * Sentence planning: aggregating propositions into clausal units and choosing lexical items corresponding to concepts in the knowledge base, including referring expressions; * Linguistic realization: taking care of surface details such as agreement and orthography.</Paragraph>
      <Paragraph position="1"> I have argued elsewhere (Kibble 1999) that if CT is to be implemented in an NLG system, the principles I call &amp;quot;salience&amp;quot; and &amp;quot;cohesion&amp;quot; belong to different tasks within this scheme: &amp;quot;salience&amp;quot; is a matter for sentence planning, choosing a verb form or some other construction that makes the Cb prominent within a clause or sentence, while &amp;quot;cohesion&amp;quot;---ordering propositions in a text to maintain referential continuity-is a matter for text planning. So there may be no single point in the generation process where the system has a choice between Retain and Shift, for instance: rather, the terms retain and shift describe the composite results of choices made at different stages of the generation task. This point is discussed in more detail in the cited paper. Referential continuity as determined by CT is only one of a number of factors determining the fluency and acceptability of generated text; see Kibble and Power (2000) for further  Kibble Rule 2 of Centering Theory 3. The &amp;quot;Cheapness&amp;quot; Principle  The Cp or preferred center has a dual role in CT: in optimal transitions, where Cp = Cb, it highlights the center of attention of the current utterance, and it is also intended to signal the center of attention of the following utterance: The preferred center represents a prediction about the Cb of the following utterance. (Walker, Joshi, and Prince 1998, page 3) It turns out that this informally stated aspect of the Cp is not actually made explicit in the rules and constraints of CT: transitions /Un, U~+I) are defined in terms of the Cp of U~+I and the Cbs of Un and Un+l, but no definition mentions the Cp of U~. Strube and Hahn's &amp;quot;cheapness&amp;quot; principle can be seen as the &amp;quot;missing link&amp;quot; of CT, making explicit the prediction represented by the Cp. They question the canonical ordering of transitions, partly on the grounds that this ordering fails to predict the Retain-Shift pattern that has been claimed by some researchers to signal the introduction of a new &amp;quot;discourse topic.&amp;quot; The principle of &amp;quot;cheapness&amp;quot; is intended to capture the intuition that a Retain is naturally followed by a Smooth Shift and is defined as follows: A transition pair is cheap if the backward-looking center of the current utterance is correctly predicted by the preferred center of the immediately preceding utterance, i.e., Cb(Ui) = Cp(Ui_l)... (Strube and Hahn 1999, page 332) Cheapness is claimed to minimize the inferential costs of processing sequences of utterances, and is proposed as a constraint on pairs of successive transitions as a replacement for the canonical orderings in Rule 2, which is restated as follows: Rule 2 ~ Cheap transition pairs are preferred over expensive ones. (Strube and Hahn 1999, page 334) This claim is supported by analysis of a variety of German texts. It turns out that although cheapness appears to be a sensible principle, it does not neatly partition the types of transition pairs; in particular, this principle does not necessarily hold of all Retain-Smooth Shift sequences. Strube and Hahn propose to rectify this by redefining the transitions, with an additional test Cp(Ui) = Cp(Ui-1) to subdivide Continue and Smooth Shift, resulting in new &amp;quot;expensive&amp;quot; transitions Exp-Continue and Exp-Smooth Shift. Strube and Hahn (1999, page 333) provide a table (not reproduced here) of 36 transition pairs, labeled as &amp;quot;cheap,&amp;quot; &amp;quot;expensive,&amp;quot; or &amp;quot;-&amp;quot; (not occurring). In fact, it seems that the way this principle is presented is unnecessarily complicated, and on closer examination it appears to be rather weak. First, if cheapness is the only criterion considered, CT would have nothing to say about texts such as Example 1 that have no cheap transition pairs. So it appears unwise to simply abandon the canonical ordering altogether. Second, the constraint on transition pairs can be stated more economically in terms of triples of utterances. If it is the preferred case that for every transition pair in a discourse IIUn_l, Unl, IUn, Unq-lll, Cb(Un+l) = Cp(U,z), then this equation also holds for each triple IUn_l, Un, U~+I/and vice versa. Note also that if Cp(Un) is mentioned at all in Un+l, it is by definition the Cb of Un+l; so the requirement can be stated more simply as Cp(Un) E Cf(Un+l). I propose that the cheapness principle should supplement rather than replace the principles of salience and cohesion.  Computational Linguistics Volume 27, Number 4 A consequence of this is that the choice of Cp for an utterance Un has to look backward to/-/,,_1 (to identify the current Cb) and forward to Un+l. In general, the question of which principles take precedence in cases of conflict cannot be settled in this short paper, but I adopt the following working hypothesis: the optimal case will be the one where both cheapness and salience obtain; the normal case will be the one where at least one of them is satisfied, which may be at the expense of cohesion between the current and the subsequent utterance. If the Cp is part of a &amp;quot;cheap&amp;quot; sequence, correctly predicting the upcoming Cb, but does not identify the current Cb, this will normally be signaled by a nonanaphoric nominal form.</Paragraph>
      <Paragraph position="2"> Example 2 (adapted from GJW, page 217) illustrates the Retain-Shift pattern, though it does not provide unambiguous support for the proposal sketched above.</Paragraph>
      <Paragraph position="3"> The sequence (c-d-e) seems preferable to (c-d'-e') even though the latter apparently scores better according to the canonical ranking. In both sequences, cheapness is satisfied wherever it is applicable, but the apparently less preferred sequence scores higher on salience and cohesion.</Paragraph>
      <Paragraph position="4">  From an interpretation perspective, we can address this apparent discrepancy by looking again at the interaction between Rule 1 and Rule 2. Rule 1 states that if anything is pronominalized, the Cb will be; so in (d), for example, Mike cannot be interpreted as the Cb because the sentence contains a pronoun in addition. So in fact the Retain transition (c-d) is maximally coherent given the options available to the reader: salience is not tested for because the Cp is not a pronoun, but both cohesion and cheapness obtain. This choice means that Mike is predicted to be the new Cb of (e) so cohesion will be unavailable for (d-e). In general, it appears that cheapness is most likely to be an available option--the expectation that the current Cp will be the next Cb is generally plausible--but salience and cohesion are not always available. Thus, if we take account of the options available to a reader at each stage, both versions of the discourse conform as far as possible to the principles of cohesion, salience, and cheapness.</Paragraph>
      <Paragraph position="5"> From a production perspective the question remains, Why has the author chosen the &amp;quot;lumpy&amp;quot; sequence (c-d-e) rather than a &amp;quot;smooth&amp;quot; sequence of Continues? Some possible answers are these: the preferred sequence uses simple, canonical active verb forms, which may be easier to process; the sequence of clause-initial pronouns He... He..., and so on, in the variant sequence makes it appear &amp;quot;flat&amp;quot; and uninteresting;  a. John has had trouble arranging his vacation. -- -- Y b. He cannot find anyone to take over his responsibilities. Y Y Y c. He called up Mike yesterday to work out a plan. Y Y Y d. Mike has annoyed him a lot recently. Y N Y e. He called John at 5 A.M. on Friday last week. N Y -d'. He has been pretty annoyed with Mike recently. Y Y Y  e'. He got a call from him at 5 A.M. on Friday last week. Y y m the author is realizing a communicative goal to say something about John in (a-b-c) and something about Mike in (d-e). The bottom line is that from a generation point of view, centering is not enough. Maximizing coherent transitions will not in itself produce optimally fluent and readable text; instead, a number of other factors have to be taken into consideration in order to minimize the inferential load on the reader, hold the reader's interest, and reflect communicative intentions.</Paragraph>
      <Paragraph position="6"> Both versions of the text are preferable to one where the last two sentences have different subjects: for example, (d) followed by (e&amp;quot;)John .... The intuition is that once the topic has changed, the discourse must stay with the new topic rather than &amp;quot;flipflop&amp;quot; between two entities. This intuition can be sharpened by noting that (d-e) form an identifiable embedded discourse segment, whose subject matter is not directly related to the main issue of John's vacation plans. I conjecture that absence of salience is not penalized in segment-initial utterances as long as cheapness holds.</Paragraph>
      <Paragraph position="7"> The following restatement of Rule 2 is intended to bring out the Janus-like nature of CT, simultaneously looking backward and forward:  1. In case of conflicts, the following ordering is hypothesized: (cheapness \]salience} &gt; cohesion 2. If U, is segment-initial, salience is not required  if cheapness holds.</Paragraph>
      <Paragraph position="8"> Table 3 illustrates an analysis of Example 2 in terms of the interacting constraints. Note that the absence of salience against (d) is not penalized for reasons explained above.</Paragraph>
      <Paragraph position="9">  Computational Linguistics Volume 27, Number 4 This example suggests a need for optimization over sequences of more than two utterances. In a sequence Continue-Retain-Smooth Shift, the Shift is predicted in its local context but the Retain is not; although Retain is a cheap transition following Continue, another Continue would be cheap as well. The Retain is motivated as it allows a new topic to be introduced with a &amp;quot;cheap&amp;quot; Smooth Shift, and so we need to evaluate the whole sequence Continue-Retain-Smooth Shift. This illustrates that while a sequence that conforms to the cheapness principle may reduce the cognitive load on the hearer, it can actually increase the load on the speaker owing to the need to plan ahead beyond the current utterance. In fact, the proposals outlined here do not entail that speakers must plan the entire content and structure of sentences so far in advance. Rather, they entail that a speaker knows when uttering Un that he or she intends to express a particular fact about a particular entity E in utterance U,,+2; and it entails that the speaker would do well to prepare the hearer for this by making E prominent in utterance Un+l. The hypothesis is that speakers will make a degree of effort to help hearers to process their utterances smoothly, rather than opportunistically planning and realizing sentences one by one, but not to the extent of planning all the transitions in a discourse segment in advance of uttering anything.</Paragraph>
    </Section>
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