c© 2004 Association for Computational Linguistics
Centering: A Parametric Theory and Its
Instantiations
Massimo Poesio
∗
Rosemary Stevenson
†
University of Essex University of Durham
Barbara Di Eugenio
‡
Janet Hitzeman
§
University of Illinois at Chicago MITRE Corporation
Centering theory is the best-known framework for theorizing about local coherence and
salience; however, its claims are articulated in terms of notions which are only partially specified,
such as “utterance,” “realization,” or “ranking.” A great deal of research has attempted to
arrive at more detailed specifications of these parameters of the theory; as a result, the claims of
centering can be instantiated in many different ways. We investigated in a systematic fashion
the effect on the theory’s claims of these different ways of setting the parameters. Doing this
required, first of all, clarifying what the theory’s claims are (one of our conclusions being that
what has become known as “Constraint 1” is actually a central claim of the theory). Secondly,
we had to clearly identify these parametric aspects: For example, we argue that the notion of
“pronoun” used in Rule 1 should be considered a parameter. Thirdly, we had to find appropriate
methods for evaluating these claims. We found that while the theory’s main claim about salience
and pronominalization, Rule 1—a preference for pronominalizing the backward-looking center
(CB)—is verified with most instantiations, Constraint 1–a claim about (entity) coherence and
CB uniqueness—is much more instantiation-dependent: It is not verified if the parameters are
instantiated according to very mainstream views (“vanilla instantiation”), it holds only if indirect
realization is allowed, and is violated by between 20% and 25% of utterances in our corpus even
with the most favorable instantiations. We also found a trade-off between Rule 1, on the one hand,
and Constraint 1 and Rule 2, on the other: Setting the parameters to minimize the violations of
local coherence leads to increased violations of salience, and vice versa. Our results suggest that
“entity” coherence—continuous reference to the same entities—must be supplemented at least
by an account of relational coherence.
1. Motivations
Centering theory (Joshi and Weinstein 1981; Grosz, Joshi, and Weinstein 1983, 1995;
Walker, Joshi, and Prince 1998b) is the component of Grosz and Sidner’s overall theory
∗ Department of Computer Science, Wivenhoe Park, Colchester CO4 35Q, U.K. E-mail:
poesio@essex.ac.uk.
† Department of Psychology, University of Durham, U.K.
‡ Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607-7053, USA.
E-mail: bdieugen@cs.uic.edu
§ MITRE Corporation, 202 Burlington Road, Bedford, MA 01730-1428, USA. E-mail:hitze@mitre.org.
Submission received: 16 April 2002; Revised submission received: 3 September 2003; Accepted for
publication: 11 December 2003
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Computational Linguistics Volume 30, Number 3
of attention and coherence in discourse (Grosz 1977; Sidner 1979; Grosz and Sidner
1986) concerned with local coherence and salience, that is, coherence and salience
within a discourse segment. A fundamental characteristic of centering is that it is bet-
ter viewed as a linguistic theory than a computational one. By this we mean that its
primary aim is to make cross-linguistically valid claims about which discourses are
easier to process, abstracting away from specific algorithms for anaphora resolution
or anaphora generation (although many such algorithms are based on the theory).
The result is a very different theory from those one usually finds in computational
linguistics. In central papers such as Grosz, Joshi, and Weinstein (1995), no algo-
rithms are provided to compute notions such as “utterance,” “previous utterance,”
“ranking,” and “realization” that play a crucial role in the theory. The researchers
working on centering argue that while these concepts play a central role in any theory
of discourse coherence and salience, their precise characterization is best left for sub-
sequent research, indeed, that some of these concepts (e.g., ranking) might be defined
in a different way for each language (Walker, Iida, and Cote 1994). In other words,
these notions should be viewed as parameters of centering. This feature of the theory
has inspired a great deal of research attempting to specify centering’s parameters for
different languages (Kameyama 1985; Walker, Iida, and Cote 1994; Di Eugenio 1998;
Turan 1998; Strube and Hahn 1999). Competing versions of the central definitions
and claims of the theory have also been proposed: For example, different definitions
of backward-looking center (CB) can be found in Grosz, Joshi, and Weinstein (1983,
1995) and Gordon, Grosz, and Gillion (1993). As a result, a researcher wishing to test
the predictions of centering, or to use it for practical applications, is confronted with
a large number of possible instantiations of the theory.
The main goal of the work reported in this article was to explore the space of
parameter configurations, measuring the impact of different ways of setting the pa-
rameters of centering on the theory’s claims. This required specifying in an explicit
way what centering’s main claims are; clearly identifying the parameters, not all of
which have previously been discussed in the literature; and developing appropriate
methods (and statistical tests) to carry out this evaluation. The comparison between
instantiations was carried out by annotating a corpus of English texts from different
genres with the information needed to test a variety of centering instantiations and
using this corpus to assess the extent to which the theory’s claims are verified once the
parameters are set in a certain way. The proponents of centering have clearly stated
that the aim of the theory is to identify preferences that make discourses easier to pro-
cess; clearly, the best way to test such preferences is through behavioral experiments,
and many aspects of the theory have in fact been tested this way (Hudson, Tanen-
haus, and Dell 1986; Gordon, Grosz, and Gillion 1993; Brennan 1995). But given the
enormous number of possible ways of setting the theory’s parameters, a systematic
comparison can be made only by computational means. A corpus-based evaluation
has other advantages, as well, among which is that it is perhaps the best way to
identify the aspects of the theory that need to be further specified, and the factors
such as temporal coherence or stylistic variation that may interact with the prefer-
ences expressed by centering. (Also, knowing the extent to which real texts conform
to centering preferences is an important goal in its own right.)
In previous corpus-based studies of centering (Walker 1989; Passonneau 1993;
Byron and Stent 1998; Di Eugenio 1998; Kameyama 1998; Strube and Hahn 1999;
Tetreault 2001), only a few instantiations of centering were compared. The present
study is more systematic in that it considers a greater number of parameters, as
well as more parameter instantiations, including “crossing” instantiations in which
the parameters are set according to proposals due to different researchers. Only re-
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liable annotation techniques were used; we produced an annotation manual that
can be used to extend our analysis to other data, as well as a companion Web site
(http://cswww.essex.ac.uk/staff/poesio/cbc/) to allow readers to try out instantia-
tions not discussed in this article. (The Web site also contains the annotation manual
and a technical report with a full discussion of all results.) Last but not least, our
evaluation is arguably more neutral than in most previous studies in that, first of all,
we are not proposing a new instantiation of the theory; and secondly, all parameter
instantiations were tested on the same data.
The article is organized as follows. We first review the basic concepts of the theory,
discussing the three claims on which we focus (Constraint 1, Rule 1, and Rule 2) and the
parameters used in their formulation. We then discuss how our corpus was annotated
and how the annotation was used to compute violations of the three main claims. In
Section 4 we present our main results, which are discussed in Section 5.
2. Centering Theory and Its Parameters
It is not possible to discuss in this article the entire centering literature; we merely
summarize in this section some of this work in enough detail to allow the reader to
follow the discussion in the rest of the article. For more details, we refer the reader
to classic references such as Grosz, Johsi, and Weinstein (1995) and Walker, Joshi, and
Prince (1998b) or the discussion of centering in Poesio and Stevenson (forthcoming).
2.1 Motivations and Main Intuitions
Centering is simultaneously a theory of discourse coherence and of discourse salience.
As a theory of coherence, it attempts to characterize entity-coherent discourses: dis-
courses that are considered coherent because of the way discourse entities are intro-
duced and discussed.
1
At the same time, centering is also intended to be a theory of
salience: that is, it attempts to predict which entities will be most salient at any given
time.
The main claim about local coherence made in centering is that discourse segments
in which successive utterances keep mentioning the same discourse entities are “more
coherent” than discourse segments in which different entities are mentioned. This
hypothesis was formulated by Chafe (1976) and is backed by empirical evidence such
as Kintsch and van Dijk (1978) and Givon (1983). In centering this hypothesis is further
strenghtened by proposing that every utterance has a unique “main link” with the
previous utterance: the CB. Having a unique CB, it is claimed, considerably simplifies
the complexity of the inferences required to integrate an utterance into the discourse
(Joshi and Kuhn 1979; Joshi and Weinstein 1981).
Centering’s first contention as far as local salience is concerned is that the dis-
course entities realized by an utterance (more on realization below) are ranked: that is,
that in each utterance some discourse entities are more salient than others. This claim,
as well, is a basic tenet of much work on discourse (Sidner 1979; Prince 1981; Givon
1983; Gundel, Hedberg, and Zacharski 1993) and is supported by much psychologi-
cal evidence (Hudson, Tanenhaus, and Dell 1986; Gernsbacher and Hargreaves 1988;
Gordon, Grosz, and Gillion 1993; Stevenson, Crawley, and Kleinman 1994).
1 Entity-based theories of coherence are so-called by contrast with relation-centered theories of
coherence, such as those developed in Hobbs (1979) and Mann and Thompson (1988) and used in Fox
(1987) and Lascarides and Asher (1993). The earliest detailed entity-based theory of coherence we are
aware of is by Kintsch and van Dijk (1978), who also explicitly mention the need to supplement such
theories with a theory of relational coherence (more on this in Section 5)
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These claims about coherence and salience are linked by two further hypotheses:
that the identity of the CB is crucially determined by the entities’ ranking and that the
CB is most likely to be realized as a pronoun. This assumption that a “main entity” or
“topic” or “focus” is the preferred interpretation of pronouns is commonly found in
theories in the psychological (e.g., Sanford and Garrod 1981), computational (Sidner
1979) and linguistic (Gundel, Hedberg, and Zacharski 1993) literature and is motivated
by evidence such as the contrast between examples (1) and (2):
(1) a. Something must be wrong with John.
b. He has been acting quite odd. (He = John)
c. He called up Mike yesterday.
d. John wanted to meet him quite urgently.
(2) a. Something must be wrong with John.
b. He has been acting quite odd. (He = John)
c. He called up Mike yesterday.
d. He wanted to meet him quite urgently.
Discourses (1) and (2) differ only only in their (d) sentences, but according to
Grosz et al., (1d) is not as felicitous as (2d). The reason, they argue, is that after the
(c) utterances, the discourse entity John is more highly ranked than Mike, so it will be
the CB of the next utterance provided that it is realized in it; and given the preference
for pronominalizing the CB, John should be pronominalized if anything else is.
This link between pronominalization and the identity of the CB has been used
by Grosz et al. to support the claim discussed above that utterances have a unique
CB (contra, e.g., Sidner [1979] whose theory assumed two foci). Grosz et al. note
the contrast between continuations (3c)–(3f) of the discourse initiated by utterances
(3a)–(3b):
(3) a. Susan gave Betsy a pet hamster.
b. She reminded her that such hamsters were quite shy.
c. She asked Betsy whether she liked the gift.
d. Betsy told her that she really liked the gift.
e. Susan asked her whether she liked the gift.
f. She told Susan that she really liked the gift.
Grosz et al. argue that continuations (3c)–(3f) are less and less acceptable, whereas if
Susan and Betsy were equally ranked after (3b), all variants should be equally accept-
able.
2.2 Terminology and Definitions
2.2.1 Local Focus, Forward-Looking Centers, and Utterances. A fundamental assump-
tion underlying centering is that processing a discourse involves continuous updates
to the local attentional state, or local focus. The local focus includes a set of forward-
looking centers (CFs), which correspond to Sidner’s (1979) “potential discourse foci”
and can be viewed as mentions of discourse entities (Karttunen 1976; Webber 1978;
Heim 1982; Kamp and Reyle 1993). The local focus also contains information about the
relative prominence or rank of these CFs. The local focus gets updated after every ut-
terance: In this update, the current CFs are replaced by new ones, and the CB changes,
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as well (see below).
2
The set of CFs introduced in the local focus by utterance U
i
in
a discourse segment (DS) is indicated by CF(U
i
,DS), generally abbreviated to CF(U
i
).
Brennan, Friedman, and Pollard (1987) formalized the relationship between utterances
and CFs by means of one of their so-called constraints:
3
Constraint 2: Every element of CF(U,DS) must be realized in U.
2.2.2 Ranking, Preferred Centers, and Backward-Looking Centers. We already men-
tioned two important claims of the theory: that forward-looking centers are ranked,
and that because of this ranking, some CFs acquire particular prominence. The ranking
function is only required to be partial, but the most highly ranked CF realized by an
utterance (when one exists) is called the Preferred Center (CP). Ranking is also used
to characterize one of the CFs as the CB. The CB is the closest concept in centering
to the traditional notion of “topic” (Sgall 1967; Chafe 1976; Sanford and Garrod 1981;
Givon 1983; Vallduvi 1990; Gundel, Hedberg, and Zacharski 1993) and plays a cen-
tral role in the theory’s claims about both coherence and salience. Although in Grosz,
Joshi, and Weinstein (1983), the CB was characterized only in intuitive terms, most
subsequent work has been based on the definition below (Grosz, Joshi, and Weinstein
1995), referred to as “Constraint 3” by Brennan, Friedman, and Pollard (1987):
Constraint 3 CB(U
i
), the backward-looking center of utterance U
i
, is the highest-
ranked element of CF(U
i−1
) that is realized in U
i
.
Notice that according to this definition, the computation of the CB depends exclusively
on ranking and “previous utterance,” making these parameters crucially important for
the framework.
4
2.2.3 Transitions. The hypothesis that discourses are easier to process when successive
utterances are perceived as being “about” a unique discourse entity is formalized in
centering in terms of a classification of utterances according to the type of transition
(update) they induce in the local focus. Many such classifications of transitions have
been proposed; Grosz, Joshi, and Weinstein (1995) distinguish among three types of
transitions, depending on whether the backward-looking center of U
i−1
is maintained
or not in U
i
and on whether CB(U
i
) is also the most highly ranked entity (CP) of U
i
:
Center Continuation (CON): CB(U
i
) = CB(U
i−1
), and CB(U
i
) is the most highly
ranked CF (CP) of U
i
(i.e., CP(U
i
) = CB(U
i
))
Center Retaining (RET): CB(U
i
) = CB(U
i−1
), but CP(U
i
) negationslash= CB(U
i
)
Center Shifting (SHIFT): CB(U
i−1
) negationslash= CB(U
i
)
We will consider a few alternative classification schemes below, after discussing how
these classifications are used to formulate one of the core claims of centering, Rule 2.
2 The hypothesis that discourse processing involves continuous updates to the discourse model also lies
at the heart of so-called “dynamic” theories of discourse semantics (Heim 1982; Kamp and Reyle 1993).
3 The order of presentation of constraints and rules followed here differs from that more familiar in the
centering literature. This is because we want to distinguish between definitions and claims, and the
three constraints proposed by Brennan et al. do not all have the same status: While Constraint 2 can be
seen as a “filter” ruling out certain values of CF(U
i
), Constraint 3 is a definition, and Constraint 1 an
empirical claim.
4 Other ways of defining the CB have been proposed. We refer the interested reader to the longer report
and to the companion Web site.
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2.3 Main Claims
In the words of Grosz et al., the most fundamental claim of centering is that “to the
extent that discourse adheres to centering constraints, its coherence will increase and
the inference load placed upon the hearer will decrease” (Grosz, Joshi, and Wein-
stein 1995, page 210). Grosz et al. list seven such “costraints,” three of which can be
directly evaluated. Even though we are not following here the distinction between
“constraints” and “rules” introduced in Brennan, Friedman, and Pollard (1987), we
will use for these three claims the names Brennan et al. gave them, by which they are
now best known:
Constraint 1 (Strong): All utterances of a segment except for the first have exactly
one CB.
Rule 1 (GJW95): If any CF is pronominalized, the CB is.
Rule 2 (GJW95): (Sequences of) continuations are preferred over (sequences of)
retains, which are preferred over (sequences of) shifts.
2.3.1 Constraint 1, Topic Uniqueness, and Entity Coherence. If we view the CB as
a formalization of the idea of “topic” (Vallduvi 1990; Gundel 1998; Hurewitz 1988;
Miltsakaki 1999; Beaver 2004), Constraint 1 expresses, first and foremost, the original
claim from Joshi and Kuhn (1979) and Joshi and Weinstein (1981) that discourses with
exactly one (or no more than one) “topic” at each point are easier to process. This view
contrasts both with Sidner’s (1979) hypothesis that utterances may have two “topics”
and with theories such as Givon (1983), Alshawi (1987), Lappin and Leass (1994) and
Arnold (1998), which view “topichood” as a matter of degree and therefore allow for
an arbitrary number of topics.
In the strong form just presented, Constraint 1 is also a claim about local coher-
ence. It expresses a preference for discourses to be entity coherent: to continue talking
about the same entities. Each utterance in a segment should realize at least one of the
discourse entities realized in the previous utterance. A weaker form of Constraint 1
has also been suggested (e.g., Walker, Joshi, and Prince 1998a, footnote 2, page 3); the
preference for a unique CB is preserved, but not the preference for entity coherence.
Constraint 1 (Weak): All utterances of a segment except for the first have at most
one CB.
2.3.2 Rule 1 and Pronominalization. Rule 1 is the main claim of centering about
pronominalization. In the version presented above, it states a preference for pronomi-
nalizing the CB, if anything is pronominalized at all. We also examined two alternative
formulations. The original form of the claim in Grosz, Joshi, and Weinstein (1983) was
as follows:
Rule 1 (GJW83): If the CB of the current utterance is the same as the CB of the
previous utterance, a pronoun should be used.
Gordon, Grosz, and Gillion (1993) proposed a much stronger form of the claim. They
found that entities realized in certain positions in the sentence were read more slowly
unless pronominalized (repeated-name penalty [RNP]).
5
This evidence led them to
5 Gordon et al. observed increased reading times when proper names were used instead of pronouns to
realize an entity in subject position referring to an entity realized in first-mentioned or subject position.
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Poesio et al. Centering: A Parametric Theory
propose a more restrictive definition of CB (briefly, that the CB is the entity subject to
the RNP—for discussion, see the longer version of this article available on the Web
site) and a stronger form of Rule 1, requiring the CB (defined in this more restrictive
way) to be always pronominalized:
Rule 1 (Gordon et al.): The CB should be pronominalized.
Although we will refer to this version as “Gordon et al.’s” for brevity, readers should
keep in mind that because the definition of CB proposed by Gordon et al. is more
restrictive, their version of Rule 1 is properly evaluated only using that definition.
(The results with this instantiation are discussed in the longer version of the article
availabel on the Web site.)
2.3.3 Rule 2 and the Classification of Transitions. Rule 2 is a claim about coherence, as
well: It states a preference for preserving the CB over changing it and for realizing it as
the most salient entity over changing its relative ranking. This aspect of the theory has
received a lot of attention; several variants of this constraint have been proposed, as
well as many ways of classifying transitions. We studied many alternative proposals.
The version of Rule 2 presented in Grosz, Joshi, and Weinstein (1995) expresses
preferences among sequences of transitions (e.g., CON-CON over SHIFT-SHIFT) rather
than preferences for particular transitions. This form of the constraint is in part mo-
tivated by empirical results. Di Eugenio (1998), for example, found that the relative
distribution of null and explicit pronouns in Italian depends on the previous transition
as well: in Center Continuations that follow a CON or a SHIFT, it is much more likely
that a null pronoun will be used, whereas in Center Continuations that follow a RET
transition, both null and explicit pronouns are equally likely. Turan (1998) obtained
similar results for null and explicit pronouns in Turkish.
Other researchers argue instead that the inferential load is evaluated utterance by
utterance (Brennan, Friedman, and Pollard 1987; Walker, Iida, and Cote 1994; Walker,
Joshi, and Prince 1998a). The version of Rule 2 proposed by Brennan et al. is as follows:
Rule 2 (Single Transitions): Transition states are ordered. The CON transition is
preferred to the RET transition, which is preferred to the Smooth Shift
transition, which is preferred to the Rough Shift transition.
This formulation of Rule 2 depends on a further distinction between two types of
SHIFT: Smooth Shift (SSH), when CB(U
n
) = CP(U
n
), and Rough-Shift (RSH), when
CB(U
n
) negationslash= CP(U
n
). Transitions can then be classified along two dimensions, as in the
following table:
CB(U
n
) = CB(U
n−1
) or CB(U
n−1
) = NIL CB(U
n
) negationslash= CB(U
n−1
)
CB(U
n
) = CP(U
n
) Continue Smooth Shift
CB(U
n
) negationslash= CP(U
n
) Retain Rough Shift
Further refinements of these classification schemes have been proposed. Kameyama
(1986) proposed a fourth transition type, Center Establishment (EST), for utterances
E.g., in Bruno was the bully of the neighborhood. Bruno / He often taunted Tommy, the second sentence would
be read more slowly when Bruno was used than when He was used.
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Computational Linguistics Volume 30, Number 3
that establish a CB after an utterance without one, such as the first utterance of a seg-
ment. Walker, Iida, and Cote (1994) argued that these utterances should be classified
as Center Continuations, the idea being that even the first utterance of a segment does
have a CB, but this CB is initially underspecified and is determined only when the sec-
ond utterance is processed. Notice that according to the strong version of Constraint
1, the first utterance of a discourse segment is the only utterance allowed not to have a
CB in a coherent discourse; hence, none of these classification schemes for transitions
includes classes either for the inverse of Center Establishment, that we might call Ze-
roing (ZERO) transition (a CB less utterance following one which does have a CB) or
for CB-less utterances following other CB-less ones (the NULL transition).
Strube and Hahn (1999), like Grosz, Joshi, and Weinstein (1995), claim that infer-
ential load is evaluated across sequences (pairs, in fact) of transitions but argue for
a different way of evaluating the inferential load of utterances. In their view, classi-
fications of transitions such as those above do not reflect what should be one of the
crucial claims of the theory: that the CP of one utterance predicts the CB of the next.
In order to formalize their view, they propose a different classification scheme, based
on the distinction between cheap and expensive transitions (Strube and Hahn 1999,
page 332):
• A transition pair is cheap if the CB of the current utterance is correctly
predicted by the CP of the previous utterance, that is, if CB(U
n
)=
CP(U
n−1
).
• A transition pair is expensive if CB(U
n
) negationslash= CP(U
n−1
).
Strube and Hahn then propose a new version of Rule 2 based on this distinction:
Rule 2 (Strube and Hahn): Cheap transition pairs are preferred to expensive ones.
6
2.4 The Parameters of Centering
Although Grosz et al. discussed possible definitions for the concepts used in the claims
above–“utterance,” “previous utterance,” “ranking,” and “realization”—they didn’t
settle on a specific definition, even for English. Similarly undefined is the notion of
“pronominalization” governed by Rule 1. But without further specification of these
concepts it is impossible to evaluate the claims above, just as it is not possible to
evaluate the predictions of, say, “government and binding theory” without providing
an explicit definition of “command” or “argument”. As a result, a considerable amount
of research has been concerned with establishing the best specification for what are,
essentially, parameters of the theory. We briefly review some of these proposals in this
section.
7
6 Kibble (2001) proposed a version of Rule 2 that further develops the “decompositional” view of Rule 2
introduced by Brennan et al., while simultaneously incorporating Strube and Hahn’s intuition that
“cheap” transitions should be preferred. Kibble formulates his version of Rule 2 as a series of
preferences: for transitions that preserve the CB—that is, those such that CB(U
n
) = CB(U
n−1
) (he calls
these transitions cohesive), that identify CB(U
n
) with CP(U
n
), and/or that are cheap. Code to test an
earlier version of Kibble’s form of Rule 2 (Kibble 2000) has been incorporated in the scripts discussed
later in the article, and the results can be seen in the longer technical report accompanying this article,
or from the companion Web site. We will, however, omit a discussion of this version here, in part for
reasons of space, in part because the final version of the rule in Kibble (2001) differs substantially from
the original version that we evaluated.
7 For more details, and for a discussion of the motivations behind these proposals, see the extended
version of this article and Poesio and Stevenson (forthcoming).
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Poesio et al. Centering: A Parametric Theory
2.4.1 Utterance and Previous Utterance. In the early centering papers, utterances were
implicitly identified with sentences. Kameyama (1998), however, argued that such
identification makes the number of potential antecedents of anaphoric expressions
much greater than if they were resolved clause by clause. Furthermore, she noted
that this identification leads to problems with multiclausal sentences: for example,
grammatical function ranking becomes difficult to compute, as a sentence may have
more than one subject. Kameyama proposed that the local focus be updated after every
tensed clause, not after every sentence, and classified tensed clauses into (1) utterances
that constitute a “permanent” update of the local focus, such as coordinated clauses
and adjuncts, and (2) embedded utterances that result in temporary updates that are
then “popped”, much as the information introduced into discourse by subordinated
discourse segments is popped according to Grosz and Sidner (1986). According to
Kameyama, only a few types of clauses, such as the complements of certain verbs,
are embedded. For example, Kameyama proposes to break up (4) into utterances as
follows, and to treat each of these utterances, including subordinate clauses such as
(U2) or (U5), as an update:
(4) (u1) Her entrance in Scene 2 Act 1 brought some disconcerting applause
(u2) even before she had sung a note. (u3) Thereafter the audience
waxed applause happy (u4) but discriminating operagoers reserved
judgment (u5) as her singing showed signs of strain.
Experiments by Pearson, Stevenson, and Poesio (2000) confirmed that CFs introduced
in main clauses are significantly more likely to be subsequently mentioned than CFs
introduced in complement clauses. However, a semicontrolled study by Suri and Mc-
Coy (1994) suggested that other types of clauses—specifically, adjunct clauses headed
by after and before–are also “embedded,” not “permanent updates” as suggested by
Kameyama; these results were subsequently confirmed by Cooreman and Sanford
(1996). The status of other types of clauses is less clear. Kameyama (1998) also pro-
posed a tentative analysis of relative clauses, according to which they are temporarily
treated as utterances and update the local focus but are then merged with the embed-
ding clause; she didn’t, however provide empirical support for this hypothesis. Other
types of subordinate clauses and parentheticals are not discussed in this literature.
Strube (1998) and Miltsakaki (1999) question Kameyama’s identification of utter-
ances with (tensed) clauses. Miltsakaki (1999) argues, on the basis of data from English
and Greek, that the local focus is updated only after every sentence and that only the
CFs in the main clause are considered when establishing the CB.
2.4.2 Realization. Grosz, Joshi, and Weinstein (1995) simply say that what it means for
utterance U to realize center C depends on the particular semantic theory one adopts.
They consider two ways in which a discourse entity may be “realized” in an utterance
as required by Constraint 2. Direct realization is when a noun phrase in the utterance
refers to that discourse entity. Indirect realization is when one of the noun phrases
in the utterance is an associative reference to that discourse entity in the sense of
Hawkins (1978),
8
that is, an anaphoric expression that refers to an object which wasn’t
mentioned before but is somehow related to an object that already has. For example,
in the following discourse:
(5) (u1) John walked toward the house. (u2) The door was open.
8 Associative references are one type of bridging reference (Clark 1997).
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John, the house and the door are directly realized in the respective utterances; in addition,
the house can be thought as being indirectly realized in (u2) by virtue of being referred
to by the associative reference the door (see, e.g., the discussion in Grosz, Joshi, and
Weinstein [1995] and Walker, Joshi, and Prince [1998b]). Clearly, the computation of
the CB is affected by which entities are considered to be “realized” in an utterance: In
(5), for example, (u2) has a CB (the house) only if the house is considered to be realized
in (u2) by virtue of its being associated with the door. To our knowledge, the effect of
these alternative notions of realization on the predictions of the theory has not been
previously studied, even though theories of focusing such as Sidner’s (1979) do allow
the (discourse) focus to be realized in an utterance in these cases, and the issue is often
mentioned in discussions of centering.
A related issue is whether empty realizations, or traces, should count as realiza-
tions of an entity. Many theories of grammar hypothesize that morphologically null
elements occur in the syntactic structure underlying a variety of constructions, includ-
ing control constructions as in (6a), reduced relatives as in (6b), and even coordinated
verb phrases (VP) as in (6c):
(6) a. John wanted (∅ to buy a house).
b. John bought a house (∅ abandoned by its previous occupiers).
c. John bought a house and (∅ promptly demolished it).
If, for example, the coordinated VP in (6c) is considered a separate utterance, whether
or not it contains a realization of John is going to determine whether or not it has a
CB. To our knowledge, morphologically null elements have been considered in the
centering literature only for languages other than English.
An issue that has been raised in the centering literature (e.g., Walker 1993; Di
Eugenio 1998; Byron and Stent 1998) is whether the CF list contains only entities
realized as third-person noun phrases (NPs), or also the entities realized as first- and
second-person NPs. Walker (1993) suggests that deictic entities are beyond the purview
of centering; however, in example (7), neither utterance (u2) nor utterance (u3) would
have a CB if second-person pronoun you is not counted as introducing an entity in
the CF list.
9
(7) (u1) You should not use PRODUCT-Z
(u2) if you are pregnant of breast-feeding.
(u3) Whilst you are receiving PRODUCT-Z ...
2.4.3 Ranking. Perhaps the most discussed parameter of centering, at least in the
versions of the theory that accept the definition of CB specified by Constraint 3, is
the ranking function. Most researchers working on centering, including Grosz et al.,
assume that several factors play a role in determining the relative ranking of forward-
looking centers; in fact, Walker, Iida, and Cote (1994) and Walker, Joshi, and Prince
(1998a) claim that the factors affecting ranking may not be the same in all languages.
9 According to Walker, Joshi, and Prince (1998a), in the original version of Grosz, Joshi, and Weinstein
(1995), which appeared in 1986, Grosz et al. provided a more explicit definition of realization:
An utterance U realizes a center c if c is an element of the situation described by U, or c is
the semantic interpretation of some subpart of U.
With this definition, all of the cases considered above—the anchors of associative references, traces, and
the entities realized as first- and second-person pronouns—would be considered as realized by an
utterance.
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Poesio et al. Centering: A Parametric Theory
Nevertheless, most versions of the theory developed since Kameyama (1985, 1986) and
Grosz, Joshi, and Weinstein (1986) have assumed that grammatical function plays the
main role in determining the order among forward-looking centers, at least for English.
Specifically, Grosz, Joshi, and Weinstein (1995) claim that subjects are ranked more
highly than objects, which are ranked more highly than other grammatical positions:
SUBJ ≺ OBJ ≺ OTHERS (see also Kameyama 1986; Hudson, Tanenhaus, and Dell 1986).
Slightly different ranking functions based on grammatical function were proposed by
Brennan, Friedman, and Pollard (1987) (who made a further distinction between objects
and indirect objects), by Walker, Iida, Cote (1994) for Japanese, and by Turan (1998)
for Turkish. There is quite a lot of psychological support for at least the part of this
claim stating that entities realized as subjects are more salient than entities realized in
other grammatical functions (Hudson, Tanenhaus, and Dell 1986; Gordon, Grosz, and
Gillion 1993; Brennan 1995; Hudson-D’Zmura and Tanenhaus 1998).
Other factors affecting ranking have been considered as well. Rambow (1993)
proposed that a number of facts about scrambling in German could be explained if
ranking in German were to be determined by surface order of realization. The idea
that order of mention affects salience is well supported by psychological evidence;
for example, the results of probe experiments by Gernsbacher and Hargreaves (1998)
suggest that the first-mentioned discourse entity in a sentence is the most salient. The
interaction of order of mention with grammatical function has also been studied. As
mentioned above, Gordon, Grosz and Gillion (1993) observed a repeated name penalty
for CFs in subject position coreferring with an entity previously introduced. This effect
was observed both when the antecedent was in subject position and when it was the
first-mentioned entity in a nonsubject position (as in In Lisa’s opinion, he shouldn’t have
done that), suggesting that first-mentioned CFs are as highly ranked as subjects.
Strube and Hahn (1999) argue that in German, the rank of discourse entities is
determined by the position they hold in Prince’s (1981, 1992) givenness hierarchy.
Specifically, Strube and Hahn argue that hearer-old entities rank higher than mediated
entities, which and in turn rank higher than hearer-new entities: HEARER-OLD ≺
MEDIATED ≺ HEARER-NEW.
10
Order of mention also plays a role in their ranking:
Within each category, the entities realized earlier in the sentence are ranked more
highly.
Finally, Sidner’s original (1979) claim that ranking depended on thematic roles,
abandoned in the early versions of centering, was revisited by Cote (1998). This view is
supported by psychological work on “implicit causality” verbs (Caramazza et al. 1997)
as well as work by Stevenson, Crawley, and Kleinman (1994), and Pearson, Stevenson,
and Poesio (2001). In particular, there is evidence that with certain verbs, the normal
preference for subjects to rank higher than their objects is reversed, although these
preferences are modified by other factors such as order of mention, type of connective,
and animacy (Stevenson, Crawley, and Kleinman 1994; Stevenson et al. 2000; Pearson,
Stevenson, and Poesio 2001).
2.4.4 R1-Pronouns. Rule 1 states that if any CF is pronominalized, the CB is, but
the theory does not explicitly specify which types of “pronouns” are covered by this
rule. It seems clear that realization as a third-person singular pronoun does count;
that is, if the choice is between using a third-person singular pronoun to realize a
10 Strube and Hahn’s hearer-old entities include Prince’s evoked (= discourse old) and unused entities,
which are entities such as Margaret Thatcher that are supposed to be part of shared knowledge.
Mediated entities are the entities falling in Prince’s categories inferrable, containing inferrable, and
anchored brand-new.
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CB or another CF, the CB should be chosen. We also saw that in languages such as
Italian, Japanese, and Turkish, the preferred realizations of CBs are morphologically
null elements (Kameyama 1986; Walker, Iida, Cote 1994; Turan 1998; Di Eugenio 1998).
But should an utterance in English count as verifying the rule if a CF is realized as a
third-person pronoun, and the CB as a trace? Or if the CB is realized with a full NP,
but a second CF is realized with a demonstrative pronoun? And what about first- and
second-person pronouns? The precise characterization of the (sub)class of pronouns
subject to Rule 1, which we will call R1-pronouns, is clearly an essential aspect of the
theory, yet to the best of our knowledge, no proposals in this regard can be found in
the centering literature.
2.5 Empirical Support for, and Applications of, Centering
Centering has served as the theoretical foundation for a lot of work in linguistics,
natural language processing (NLP), and psychology. This includes annotation stud-
ies testing the claims of the theory for languages including English, German, Hindi,
Italian, Japanese, and Turkish (e.g., Kameyama 1985; Passonneau 1993; Walker, Iida,
and Cote 1994; Di Eugenio 1998; Turan 1998) and several papers in (Walker, Joshi,
and Prince (1998b). The claims about pronominalization made in centering have been
applied to develop algorithms both for anaphora resolution (Brennan, Friedman, and
Pollard 1987; Strube and Hahn 1999; Tetreault 2001) and for sentence planning (Dale
1992; Henschel, Cheng, and Poesio 2000); this work can be viewed as providing an
evaluation of claims such as Rule 1. Ideas from centering, and in particular Rule 2, are
increasingly found useful in text planning (McKeown 1985; Kibble and Power 2000;
Knott et al. 2001; Karamanis 2003).
We have already seen that some predictions of the theory have also been tested
with psychological techniques. In many of these experiments, differences in process-
ing pronominal references in a sentence in a sentence to entities with different ranks
(according to a particular instantiation of the theory) were observed: Hudson, for ex-
ample, observed that pronominal references to entities introduced in subject position
in the previous sentence are interpreted more quickly than nonpronominal references
or references to nonsubjects (Hudson, Tanenhaus, and Dell 1986; Hudson-D’Zmura
and Tanenhaus 1998). And we already mentioned that Gordon, Grosz, and Gillion
(1993) identified a processing time slowdown, the RNP, when NPs in subject position
referring to entities introduced in subject or first-mentioned position in the previous
sentence are not pronominalized.
However, the discussion in this section should have made it clear just how many
parameters the theory has and in how many different ways they can be instantiated.
To our knowledge, no previous study has attempted to analyze in a systematic way
how varying the instantiation of more than one of these parameters affects the claims
of the theory, especially for combinations of parameter settings not considered in the
original papers. This analysis is the goal of the work discussed here.
3. A Corpus-Based Comparison of Centering’s Instantiations
Given the many ways in which the parameters of centering can be set, the only feasible
way to make a systematic comparison between the theory’s “instantiations” is by
computational means. That is, running computer simulations of the process of local
focus update using an annotated corpus and comparing the results obtained under
different instantiations. The evaluation principle we use for this comparison is the
number of “violations” of the theory’s claims resulting when the parameters are set
in a certain way (e.g., whether pronominalization choices are in accordance with Rule
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Poesio et al. Centering: A Parametric Theory
1). In this section we discuss how we set about performing such comparison, the data
we used, our annotation methods, and how the annotation was used.
3.1 Evaluating the Claims of Centering against a Corpus
A preliminary question we had to address is what are in fact the main claims of the
theory. As discussed in Section 2, of the seven claims mentioned in Grosz, Joshi, and
Weinstein (1995), Constraint 1, Rule 1, and Rule 2 are the ones that can actually be
verified using a corpus; we concentrated on these. Because several variants of these
three claims have been proposed, we evaluated a few of these variants as well.
11
The second important question is how these three claims are meant to be inter-
preted and what we can expect a corpus to tell us about them. The proponents of
centering are quite clear that the theory does not state “hard” facts about language,
that is, the kind of facts whose violation leads to ungrammaticality judgments. Con-
straint 1, Rule 1, and Rule 2 are meant to be preferences which, when followed, lead
to texts that are easier to process.
12
The mere presence of a few exceptions to a claim
does not, therefore, count as a falsification. For one thing, we should expect centering
preferences to interact with other constraints (a point not emphasized enough in the
centering literature). And for another, there may be no way of expressing a particular
piece of information without violating some such preferences.
13
So at best, we can
expect the three claims to be verified in a statistical sense: that is, that the number
of utterances that verify such claims will be significantly higher than the number of
utterances that violate them—and in fact, we may find that for some claims, even
statistical significance will not be achieved. As a result, we evaluated each claim using
statistical tests; the tests we used are the sign test for Constraint 1 and Rule 1, and the
Page test for Rule 2 (Siegel and Castellan 1988).
It is also important to keep in mind that a corpus cannot tell us whether “vi-
olations” actually result in processing difficulties: This can be determined only by
behavioral studies such as reading-time experiments. So we should make it absolutely
clear that minimizing violations cannot and should not be the only deciding factor in
theorizing about centering. Nevertheless, the combinatorics of the problem make it im-
possible to compare the parameter instantiations in any other way. Furthermore, this
form of evaluation is also the most systematic way to identify other preferences and
constraints that may interact with centering. We return to these issues in Section 5.
3.2 The Data
The data used in this work are texts from the GNOME corpus, which currently in-
cludes texts from three domains. The museum subcorpus consists of descriptions of
museum objects and brief texts about the artists who produced them.
14
The pharma-
ceutical subcorpus is a selection of leaflets providing patients with legally mandatory
11 In this version of the article, we assume that the CB is defined by Constraint 3. For the results with
alternative definitions of CB, see the extended technical report or the companion Web site.
12 Beaver (2004) argues—correctly, in our opinion—that in one of the best-known pronoun resolution
algorithms based on centering, that proposed by Brennan, Friedman, and Pollard (1987), Rule 1 is
effectively used as a hard constraint, a problem fixed by Beaver’s own optimality-theoretic
reformulation of the algorithm. It is nevertheless quite clear that in the theory, Rule 1 has the status of
a preference.
13 This point is especially important from an NLG perspective: see, e.g., Karamanis (2003). We will return
to this issue in Section 5.
14 The museum subcorpus extends the corpus collected to support the ILEX and SOLE projects at the
University of Edinburgh. ILEX generates Web pages describing museum objects on the basis of the
perceived status of its user’s knowledge and of the objects she has previously looked at (Oberlander et
al. 1998) The SOLE project ILEX with concept-to-speech abilities, using linguistic information to control
intonation (Hitzeman et al. 1998).
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Computational Linguistics Volume 30, Number 3
information about their medicines.
15
The GNOME corpus also includes tutorial dia-
logues from the Sherlock corpus collected at the University of Pittsburgh (Di Eugenio,
Moore, and Paolucci 1997). Each subcorpus contains about 6,000 NPs. Texts from the
first two domains were used for the main experiments reported here. The third sub-
corpus was used for the segmentation experiments discussed in the extended technical
report available on the Web site.
The data used for this study have two characteristics that make them of particular
interest. First of all, they cover genres not previously considered in studies on centering
and more similar to those that “real” NLP applications have to contend with. At the
same time, they are strongly entity-centered (see, e.g., Knott et al [2001] for an analysis
of the museum data), so the hypotheses about coherence formulated in centering are
likely to play an important part in the way these texts are constructed.
3.3 Annotation
The previous corpus-based investigations of centering theory we are aware of (Walker
1989; Passonneau 1993, 1998; Byron and Stent 1998; Di Eugenio 1998; Hurewitz 1998;
Kameyama 1998; Strube and Hahn 1999) were all carried out by a single annotator
annotating her or his corpus according to her or his own subjective judgment. One of
our goals was to use for this study only information that could be annotated reliably
(Passonneau and Litman 1993; Carletta 1996), as we believe this will make our results
easier to replicate. The price we paid to achieve replicability is that we couldn’t test
all proposals about the computation of centering parameters proposed in the litera-
ture, especially those about segmentation and about ranking, as discussed below. The
annotation followed a detailed manual, available on the companion Web site. Eight
paid annotators were involved in the reliability studies and the annotation. In the
following we briefly discuss the information that we were able to annotate, what we
didn’t annotate, and the problems we encountered; for more details, we refer readers
to the extended version of the article and the Web site.
A systematic comparison among different ways of setting the parameters would
be prohibitively expensive with traditional psychological methods, but it’s not easy
to do with corpus analysis, either. Obviously, it can’t be done by directly annotating
“utterances” or “CB” according to one way of fixing the parameters, as has been done
in most previous studies of centering theory (Byron and Stent 1998; Di Eugenio 1998;
Kameyama 1998; Passonneau 1993; Walker 1989). Instead, we annotated our corpus
with the primitive concepts used by different instantiations of the theory, that is, in-
formation that has been claimed by one or the other instantiation of centering to play
a role in the definitions of its basic notions. This includes, for example, how sentences
break up into clauses and subclausal units; grammatical function; and anaphoric re-
lations, including bridging references. An automatic script uses this information to
compute utterances, their CF ranking, and their CB, according to a particular way of
setting the parameters, and to compute statistics relevant to the three claims according
to that instantiation.
3.3.1 Utterances. In order to evaluate the definitions of utterance proposed in the
literature (sentences versus finite clauses), as well as the different proposals concerning
the “previous utterance” discussed above, we marked all spans of text that might be
claimed to update the local focus. This includes sentences (defined as all units of text
15 The leaflets in the pharmaceutical subcorpus are a subset of the collection of all patient leaflets in the
United Kingdom, which was digitized to support the ICONOCLAST project at the University of
Brighton, developing tools to support multilingual generation (Scott, Power, and Evans 1998).
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Poesio et al. Centering: A Parametric Theory
ending with a period, a question mark, or an exclamation point) as well as what we
called (discourse) units. Units include clauses (defined as sequences of text containing
a verbal complex, all its obligatory arguments, and all postverbal adjuncts) as well as
other sentence subconstituents that might independently update the local focus, such
as parentheticals, preposed prepositional phrases (PPs), and (the second element of)
coordinated VPs.
16
Sentences have one attribute, stype, specifying whether the sentence is declarative,
interrogative, imperative, or exclamative. The attributes of units include
• utype: whether the unit is a main clause, a relative clause, an appositive,
a parenthetical, etc.
• verbed: whether the unit contains a verb or not.
• ﬁnite: for verbed units, whether the verb is finite or not.
Marking up sentences proved to be quite easy; marking up units, on the other hand,
required extensive annotator training. The agreement on identifying the boundaries
of units, using the kappa statistic discussed in Carletta (1996), was κ = .9 (for two
annotators and 500 units); the agreement on features (two annotators and at least 200
units) was as follows: utype: κ = .76; verbed: κ = .9; ﬁnite: κ = .81. In total, the texts
used for the main study contain 505 sentences and more than 1,000 units, including
900 finite clauses
3.3.2 NPs. Our instructions for identifying NP markables derive from those proposed
in the MATE scheme for annotating anaphoric relations (Poesio, Bruneseaux, and Ro-
mary 1999), in turn derived from DRAMA (Passonneau 1997) and MUC-7 (Chinchor
and Sundheim 1995). In the GNOME corpus, NPs are marked by <ne> (‘Nominal en-
tity’) elements. In total, the texts used for this study contain 3,345 NPs. These include
586 pronouns, among which are 217 third-person personal and possessive pronouns,
23 demonstratives, and 308 second-person pronouns; 1,290 definite NPs, including 554
the-NPs, 250 possessive NPs, and 391 proper nouns; 1,119 indefinite NPs, including
745 bare NPs and 269 a-NPs; and 350 other NPs, including 117 quantified NPs and
114 coordinated NPs.
We annotated 14 attributes of <ne> elements specifying their syntactic, semantic,
and discourse properties (Poesio 2000). Those relevant to the study discussed here
include the following:
• The np type, cat, with values such as a-np, that-np, the-np, and pers-pro.
• The agreement features num, per, and gen, used to identify contexts in
which the antecedent of a pronoun could be identified unambiguously.
• The grammatical function gf. Our instructions for this feature are derived
from those used in the FRAMENET project (Baker, Fillmore, and Lowe
1998); see also http://www.icsi.berkeley.edu/˜framenet/. The values are
subj, obj, predicate (used for postverbal objects in copular sentences, such
as This is (a production watch)), there-obj (for postverbal objects in
there-sentences), comp (for indirect objects), adjunct (for the argument of
PPs modifying VPs), gen (for nps in determiner position in possessive
NPs), np-compl, np-part, np-mod, adj-mod, and no-gf (for nps occurring by
themselves—eg., in titles).
16 Our instructions for marking up such elements benefited from the discussion of clauses in Quirk and
Greenbaum (1973) and from Marcu’s (1999) proposals for discourse units annotation.
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The agreement values for these attributes are as follows: cat: .9; gen: .89; gf: .85; num:
.84; per: .9. We encountered problems even with supposedly “easy” information such
as number and gender, but especially so with semantic attributes (see the annotation
manual available on the Web site). We were, however, able to mark up the attributes
relevant for this study in a reliable fashion. One exception is that we weren’t able
to reach acceptable agreement on a feature of NPs often claimed to affect ranking,
thematic roles (Sidner 1979; Cote 1988; Stevenson, Crawley, and Kleinman 1994); the
agreement value in this case was κ = .35. As a result, we were not able to evaluate
ranking functions based on thematic roles.
3.3.3 Anaphoric Information. In order to determine whether a CF of an utterance is
realized directly or indirectly in the following utterance, it is necessary to annotate
the anaphoric relations that CFs enter into, including both identity relations and, in
order to compute indirect realization, associative relations (Hawkins 1978). This type
of annotation raises, however, a number of difficult (and sometimes unresolved) se-
mantic issues (Poesio 2004). As part of the MATE and GNOME projects, an extensive
analysis of previously existing schemes for so-called “coreference annotation,” such
as the MUC-7 scheme, was carried out, highlighting a number of problems with such
schemes, ranging from issues with the annotation methodology to semantic issues.
Although some of these schemes, like DRAMA, allow the marking of associative re-
lations, none of them analyze which among such relations can be reliably annotated
(Poesio, Bruneseaux, and Romary 1999; Poesio 2000). The semantic problems with
these schemes include the inappropriate use of the term coreference to cover semantic
relations such as that between an intensional entity like the temperature that may take
different values at different time points and these values (as in the price of aluminum
siding rose from $3.85 to $4.02) or between a quantifier and a variable the quantifier
binds, in which neither may corefer (as in none of the meetings resulted in an agreement
between its participants (van Deemter and Kibble 2000; Poesio 2004). In MATE, a general
scheme was developed which includes a fine-grained repertoire of semantic relations,
such as binding and function value (Poesio, Bruneseaux, and Romary 1999). For the
GNOME corpus, we adopted a simplified version of the MATE scheme, as for our
purposes it’s not essential to mark all semantic relations between entities introduced
by a text, but only those that may establish a “link” between two utterances. So for
example, it is in general unnecessary in our case to mark a relation between the subject
of a copular sentence and its predicate (e.g., between the price of aluminum siding and
either $3.85 or $4.02 in the example above). Also, our texts do not include any case
of bound anaphora, so it was not necessary to offer this option to our annotators.
In the GNOME corpus, anaphoric information is marked by means of a special
〈ante〉 element; the 〈ante〉 element itself specifies the index of the anaphoric expression
(a 〈ne〉 element) and the type of semantic relation (e.g., identity), whereas one or more
embedded 〈anchor〉 elements indicate possible antecedents.
17
(See (8).)
(8) <unit finite=‘finite-yes’ id=‘u227’>
<ne id=‘ne546’ gf=‘subj’> The drawing of
<ne id=‘ne547’ gf=‘np-compl’>the corner cupboard </ne></ne>
<unit finite=‘no-finite’ id=‘u228’>, or more probably
<ne id=‘ne548’ gf=‘no-gf’> an engraving of
<ne id=‘ne549’ gf=‘np-compl’> it </ne></ne>
17 The presence of more than one 〈anchor〉 element indicates that the anaphoric expression is ambiguous.
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Poesio et al. Centering: A Parametric Theory
</unit>,
.
.
.
</unit>
<ante current="ne549" rel="ident"> <anchor ID="ne547"> </ante>
Work such as Sidner (1979) and Strube and Hahn (1999) as well as our own prelimi-
nary analysis, suggested that indirect realization can play a crucial role in maintaining
the CB. However, previous attempts at marking anaphoric information, particularly
in the context of the MUC initiative, suggested that while it’s fairly easy to achieve
agreement on identity relations, marking up associative relations is quite hard; this
was confirmed by studies such as Poesio and Vieira (1998). For these reasons, and to
reduce the annotators’ work, we marked only a few types of relations, and we specified
priorities. Besides identity (IDENT), we marked up only three associative relations: set
membership (ELEMENT), subset (SUBSET), and “generalized possession” (POSS), which
includes part-of relations as well as ownership relations. We marked only relations
between objects realized by noun phrases and not, for example, anaphoric references
to actions, events, or propositions implicitly introduced by clauses or sentences. We
also gave strict instructions to our annotators concerning how much to mark. (See
the annotation manual available on the Web site.) Furthermore, we specified prefer-
ences: For example, in Francois, the Dauphin, the embedding NP would be chosen as
an antecedent, rather than the NP in appositive position.
As expected, we found a reasonable (if not perfect) agreement on identity relations.
In our most recent analysis (two annotators marking the anaphoric relations between
200 NPs) we observed no real disagreements; 79.4% of the relations were marked up
by both annotators; 12.8% by only one of them; and in 7.7% of the cases, one of the
annotators marked up a closer antecedent than the other.
18
With associative references,
limiting the relations did curtail the disagreements among annotators (only 4.8% of the
relations are actually marked differently), but only 22% of bridging references were
marked in the same way by both annotators; 73.17% of relations were marked by only
one or the other annotator. So reaching agreement on this information involved several
discussions between annotators and more than one pass over the corpus (Poesio 2000).
3.3.4 Segmentation. According to Grosz and Sidner (1986), centering is meant to cap-
ture preferences only within discourse segments. A proper evaluation of the claims of
the theory would therefore require a corpus in which discourse segments have been
identified. Unfortunately, discourse segments are difficult to identify reliably (Passon-
neau and Litman 1993), and Grosz and Sidner (1986) do not provide a specification
of discourse intentions explicit enough that it can be used to identify the intentional
structure of texts—which, according to Grosz and Sidner, determines their segmenta-
tion. As a result, only preliminary attempts at annotating texts according to Grosz and
Sidner’s theory have been made.
For this reason, most previous corpus-based studies of centering either ignored
segmentation or used heuristics such as those proposed by Walker (1989): Consider
every paragraph as a separate discourse segment, except when its first sentence con-
tains a pronoun in subject position or a pronoun whose agreement features are not
18 In previous work (Poesio and Vieira 1998) we came to the conclusion that kappa, while appropriate
when the number of categories is fixed and relatively small, is problematic for anaphoric reference,
when neither condition applies, and may result in inflated values of agreement.
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matched by any other CF in the same sentence. We tested only heuristic methods as
well, using the layout structure of the texts as a rough indicator of discourse structure.
In this article we discuss only the results with the heuristic proposed by Walker. In
the extended technical report available on the Web site, we discuss the results with
other segmentation heuristics, as well as further results with the tutorial dialogues
subdomain of the GNOME corpus, independently annotated according to relational
discourse analysis (Moser and Moore 1996), a technique inspired by Grosz and Sid-
ner’s proposals, from which a Grosz and Sidner–like segmentation was extracted as
proposed in Poesio and Di Eugenio (2001).
3.4 Automatic Computation of Centering Information
The annotated corpus is used by Perl scripts that automatically compute the center-
ing data structures (utterances, CFs, and CBs) according to the particular parameter
instantiation chosen, find violations of Constraint 1, Rule 1, and Rule 2 (according to
several versions of Rule 1 and Rule 2), and evaluate the claims using the statistical
tests. The behavior of the scripts is controlled by a number of parameters, including
CBdef: which definition of CB should be used. (All the results discussed in this
article were computed using the definition in Constraint 3.)
uttdef: identify utterances with sentences, finite clauses, or verbed clauses.
previous utterance: treat adjunct clauses Kameyama-style or Suri and McCoy-
style.
realization: allow only direct realization, or allow indirect realization as well.
CF-filter: treat all NPs as introducing CFs, or exclude certain classes. At the mo-
ment it is possible to omit first- and second-person NPs and/or NPs in
predicative position (e.g., a policeman in John is a policeman).
rank: rank CFs according to grammatical function, linear order, a combination of
the two as in Gordon, Grosz, and Gillion (1993), or information status as
in Strube and Hahn (1999).
prodef: consider as R1-pronouns only third-person personal pronouns (it, they),
or include also demonstrative pronouns (that, these), and/or the second-
person pronoun (you).
segmentation: identify segments using Walker’s heuristics, or with paragraphs,
sections, or whole texts.
Among the many other script parameters whose effect will not be discussed here we
will just mention those that determine whether implicit anaphors in bridging refer-
ences should be treated as CFs, the relative ranking of entities in complex NPs, and
how to handle “preposed” adjunct clauses. (See the extended technical report on the
Web site.) The algorithm used to compute statistics concerning violations of the claims
is fairly straightforward, and we will therefore omit it here; the interested reader can
find a discussion in the extended technical report. The one additional complication that
we need to mention here is relative pronouns. As it could be argued that the decision
to generate a relative pronoun is primarily controlled by grammatical considerations,
we attempted to ignore them as much as possible, in the following sense. Our scripts
do not count an utterance as a violation/verification of Rule 1 from Grosz, Joshi, and
Weinstein (1995) if the only “pronoun” realizing a non-CB is a relative pronoun, or
the CB is realized only by a relative pronoun. What this means in practice is that the
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Poesio et al. Centering: A Parametric Theory
Table 1
Number of utterances and CFs with the vanilla instantiation.
Museum Pharmaceutical Total
Number of utterances 430 577 1,007
Number of utterances that are segment boundaries 91 134 225
Number of CFs 1,731 1,308 3,039
number of utterances examined to evaluate Rule 1 is generally less than the number
of utterances with a CB, as we will see shortly.
4. Main Results
Given the number of parameters, it is difficult, if not impossible, to discuss the results
with all instantiations. Instead, we begin by discussing the results with what we call
the “vanilla instantiation,” based on the settings for the parameters most often used
in discussions of the theory. We then examine the results obtained by varying the
definitions of utterance and realization. After establishing the “best” values for these
parameters, we consider the effect of alternative ranking functions. Additional results
are discussed in the extended technical report available on the companion Web site.
Readers who want to try out instantiations not discussed here should visit the Web
site.
4.1 The Vanilla Instantiation
What we call the “vanilla instantiation” is not an instantiation actually proposed in
the literature, but an attempt to come as close as possible to a “mainstream” instanti-
ation of centering by blending proposals from Grosz, Joshi, and Weinstein (1995) and
Brennan, Friedman, and Pollard (1987) and incorporating additional suggestions from
Kameyama (1998) and Walker, Joshi, and Prince (1998a). The vanilla instantiation is
based on the definition of CB from Grosz, Joshi, and Weinstein (1995) and uses gram-
matical function for ranking, as proposed there and in Brennan, Friedman, Pollard
(1987). Because Grosz et al. do not provide a definition of utterance, the vanilla instan-
tiation incorporates the hypothesis from Kameyama (1998) that utterances are finite
clauses and the characterization of “previous utterance” proposed there.
19
Concerning
realization, in the vanilla instantiation only third-person NPs introduce CFs, and a
discourse entity counts as “realized” in an utterance only if it is explicitly mentioned.
For the purposes of Rule 1, we mainly studied a “strict” definition of R1-pronoun
including only personal (and possessive) pronouns and relative pronouns and traces
(see Walker, Joshi, and Prince [1998a], page 4), but we also considered a “broader”
definition including the demonstrative pronouns this, that, these, and those. Relative
clauses are assumed to include a link to the NP they modify, possibly not explicitly
realized. The segmentation heuristic proposed by Walker (1989) is adopted. With the
parameters set in this way, the number of utterances and CFs in our corpus is as
shown in Table 1.
19 We simplified Kameyama’s hypothesis about relative clauses by considering only instantiations in
which they were treated as utterances both “locally” and “globally”, and ones in which they weren’t.
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Computational Linguistics Volume 30, Number 3
Table 2
Utterances and CBs with the vanilla instantiation.
Museum Pharmaceutical Total Percentage
Number of times at least one CF(U
n
) is realized in U
n+1
195 162 357 (35.4%)
Utterances that satisfy Constraint 1 (have exactly one CB) 189 157 346 (34.4%)
Utterances with more than one CB 6 5 11 (1.1%)
Utterances without a CB but are segment boundary 67 96 163 (16.2%)
Utterances without a CB 168 319 487 (48.4%)
4.1.1 Constraint 1. The statistics relevant to Constraint 1 (that utterances have exactly
one/at most one CB) are shown in Table 2. This table clearly indicates that the weak
version of Constraint 1 (Weak C1) is likely to be verified with the vanilla instantiation.
Even without counting segment boundaries, Weak C1 is verified by 833 utterances
out of 1,007 (82.7%) and violated by only 11 (1.1%): The chance that Weak C1 will
not hold with a different sample is p ≤ 0.001 by the sign test. (We will henceforth
write +833, −11 to indicate numbers of verifiers and violators.) On the other hand,
the strong version of C1—that every utterance has exactly one CB—is not likely to
hold with this instantiation: In our corpus, only 346 utterances (34.4%) have exactly
one CB, whereas 498 utterances (49.4%) have zero or more than one CB. With +346,
−498, the chance of error in rejecting the null hypothesis that Strong C1 doesn’t hold
is obviously much higher than 10%. The chance of error doesn’t go below 10% even
if we count the 163 utterances that do not contain references to CFs introduced in the
previous utterance but are segment boundaries and therefore are not governed by the
constraint. In other words, if the vanilla instantiation were the “right” way of setting
the parameters, we would have to conclude that in the genres contained in our corpus,
utterances are very likely to have a unique CB, but entity coherence does not play a
major role in ensuring that a text is coherent: only 35.4% of utterances in our corpus
would be “entity-coherent,” that is, would contain an explicit mention to an entity
realized in the previous finite clause.
The following example illustrates why there are so many violations of Strong
C1 with the vanilla instantiation. If we identify utterances with finite clauses, the
two sentences in (9) break up into five utterances, and only the last of these can be
considered in any sense to directly refer to the set of egg vases introduced in (u1).
20
(9) (u1) These “egg vases” are of exceptional quality: (u2) basketwork bases
support egg-shaped bodies (u3) and bundles of straw form the handles,
(u4) while small eggs resting in straw nests serve as the finial for
each lid. (u5) Each vase is decorated with inlaid decoration: ...
Clearly, there are two ways of “fixing” this problem. One is to claim that utterances
are best identified with sentences, in which case we would have only two utterances
in this example, one for each sentence. The other is to allow for indirect realization:
20 In fact, the anaphoric relation here is not identity; rather, the set of egg vases serves as domain
restriction for the quantifier in (u5). We were not able to mark this distinction reliably.
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Poesio et al. Centering: A Parametric Theory
(u2)–(u4) all contain implicit references to the egg vases, and therefore all will have a
CB if indirect realization is allowed. Both possibilities are considered below.
The fact that 11 utterances (1.1%) in the corpus have more than one CB (i.e., they
violate Weak C1 as well) is also worth noticing. The reason for the violation is that
in “classic” centering, ranking is only required to be a partial order (see, e.g., Walker,
Joshi, and Prince 1998a page 3),
21
so when two CFs with the same rank in U
i
are both
realized in U
i+1
, both become the CB. This is illustrated in (10), where we show the
XML markup so that the attributes of elements are visible:
(10) <unit finite=‘finite-yes’ id=‘u227’>
<ne id=‘ne546’ gf=‘subj’>The drawing of
<ne id=‘ne547’ gf=‘np-compl’>the corner cupboard</ne></ne>
<unit finite=‘no-finite’ id=‘u228’>, or more probably
<ne id=‘ne548’ gf=‘no-gf’> an engraving of
<ne id=‘ne549’ gf=‘np-compl’> it </ne></ne>
</unit>,
must have caught
<ne id=‘ne550’ gf=‘obj’>
<ne id=‘ne551’ gf=‘gen’>Branicki’s </ne> attention</ne>
</unit>
<unit id="u229" finite="finite-yes">
<ne gf="subj" id="ne552">Dubois</ne> was commissioned through
<ne gf="adjunct" id="ne553"> a Warsaw dealer </ne>
<unit id="u230" finite="finite-no"> to construct
<ne gf="obj" id="ne554"> the cabinet </ne>
for<ne gf="adjunct" id="ne555">the Polish aristocrat</ne>
</unit>
</unit>
<ante current=‘ne554’ rel=‘ident’><anchor antecedent=‘ne549’>
</anchor></ante>
<ante current=‘ne555’ rel=‘ident’><anchor antecedent=‘ne551’>
</anchor></ante>
In this example, two discourse entities introduced in utterance (u227) are realized in
utterance (u229):
22
the corner cupboard (realized in (u227) by (ne547) and (ne549) and in
(u229) by (ne554)) and Branicki (realized in (u227) by (ne551), and in (u229) by (ne555)).
As their grammatical functions are equivalent under the ranking proposed by Grosz
et al., (np-compl, for np-complement, and gen, for genitive—see the annotation manual
available on the Web site), these two CFs have the same rank in (u227), so they are both
CBs of (u229). The same problem occurs with coordinated NPs, both of which have
the same grammatical function. This problem with the vanilla instantiation can also
be “fixed” by requiring the ranking function to be a total order, which is easily done
by adding a disambiguation factor such as linear order, as done by Strube and Hahn.
On the other hand, the requirement that ranking be total has not been previously
discussed in the centering literature, and one might argue conversely that examples
such as the one above are arguments againts centering’s claim that utterances have
only one CB. We return to this issue in Section 5.
21 It’s not clear to us why ranking is required only to be partial, yet the CB is clearly claimed to be unique.
22 Neither (u228) nor (u230) is treated as an utterance as they are not finite.
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Computational Linguistics Volume 30, Number 3
Table 3
Transition statistics for the Brennan et al. version of Rule 2.
Museum Pharmaceutical Total (Percentages)
Establishment 96 93 189 (18.8%)
Continuation 37 33 70 (7.0%)
Retain 22 16 38 (3.8%)
Smooth Shift 22 15 37 (3.7%)
Rough Shift 18 5 23 (2.3%)
ZERO 87 81 168 (16.7%)
NULL 148 334 482 (47.9%)
Total 430 577 1,007
4.1.2 Rule 2. The statistics relevant for Brennan et al.’s version of Rule 2 are shown
in Table 3. The most obvious consideration suggested by this table is that the three
most frequent transitions in our corpus are ones that either have not been previously
discussed in the Centering literature or have been discussed only in a limited way. By
far the most frequent transition (47.9% of the total) is NULL: following up an utterance
without a CB with a second one, also without a CB. (Examples include (u3), (u4), and
(u5) in (9).) We found this transition discussed only in Passonneau (1998). The second
most common transition (18.8%) is Kameyama’s Establishment (the transition between
an utterance without a CB and one with a CB), followed by its reverse, the ZERO
transition (between an utterance with a CB and one without), never mentioned in the
literature. (An example of ZERO is (u2) in (9).) If we ignore NULL, Establishments,
and ZEROs, the preferences are roughly as predicted by Brennan et al.: The Page test
for ordered alternatives (Siegal and Castellan 1988, pages 184–188) indicates a chance
of less than .001 that the four transitions are equally likely. But only the differences
between CON and RET/SSH, and between SSH and RSH, are significant; and there
are more Shifts (SSH + RSH) than Retains.
23
Grosz et al.’s formulation of Rule 2 in terms of sequences also roughly holds,
except that there are too few sequences for the results to be considered significant,
as shown in Table 4. As we’ll see again in Section 5, in our corpus there seems to
be a preference for avoiding repetition; this tendency is confirmed by the numbers in
the table, which indicate a dispreference for maintaining the same CB for too long or
for maintaining it in the most salient position, at least at the level of finite clauses:
EST/CON sequences are twice as common as sequences of Continuations. As for
the claim that Retaining transitions prepare for Shifts, the figures do not lend much
support to the idea: Retains are more frequently followed by Continuations than by
Shifts, and almost as frequently by other Retains.
Of the other formulations of Rule 2, the version based on a preference for cheap
transition pairs over expensive ones proposed by Strube and Hahn is not verified with
the ranking function used in the vanilla instantiation—which is not, we should em-
23 Similar results were obtained by Passonneau (1998).
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Poesio et al. Centering: A Parametric Theory
Table 4
Rule 2 statistics considering sequences of transitions.
Museum Pharmaceutical Total
Continuation Sequences 10 6 16
Continuation/Retain 9 3 12
Establishment/Continuation 17 18 35
Retain Sequences 15 3 8
Retain/Continuation 7 7 14
Retain/Smooth Shift 3 2 5
Retain/Rough Shift 4 1 5
Smooth Shift Sequences 2 1 3
Rough Shift Sequences 2 1 3
Null Sequences 95 228 323
Other 290 312 602
Table 5
Cheap and expensive transitions with the vanilla instantiation.
Museum Pharmaceutical Total
Cheap transitions 76 63 139
Expensive transitions 263 380 643
Cheap transition pairs 21 14 35
Expensive transition pairs 162 234 396
phasize, the one assumed by Strube and Hahn themselves.
24
Ignoring the 225 segment
boundary utterances, we find 396 pairs of expensive transitions and 35 pairs of cheap
transitions, as shown in Table 5. These statistics mean that in only 139 cases out of
357 (the total number of entity-coherent utterances with this instantiation; see Table 2),
CB(U
i
) is predicted by CP(U
i−1
). We do find that 219 utterances, the majority (61.3%)
of entity-coherent ones, are “salient” in the sense of Kibble (2001)—that is, their CB is
the same as their CP.
4.1.3 Salience and Pronominalization. The statistics for pronominalization are shown
in Table 6. As noted above, our corpus contains 217 uses of third-person pronouns, 23
demonstratives, and 78 complementizers.
25
In this instantiation we take R1-pronouns
to include only personal pronouns and complementizers, for a total of 295 R1-pronouns.
If we identify utterances with finite clauses, 61 personal pronouns (28.1%) have their
24 Similar results were found for dialogues by Byron and Stent (1998).
25 We will use the term complementizer to indicate relative pronouns and relative traces.
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Computational Linguistics Volume 30, Number 3
Table 6
R1-pronouns in the corpus with the vanilla instantiation.
Museum Pharmaceutical Total
Total number of R1-pronouns 200 95 295
Number of personal pronouns 144 73 217
Number of complementizers 56 22 78
Table 7
cbs and pronominalization with the vanilla instantiation.
Museum Pharmaceuticla Total (Percentage)
Total number of realizations of CBs 211 163 374
Total number of CBs realized as R1-pronouns 138 68 206 (55.1%)
CBs realized as personal pronouns 85 48 133 (35.6%)
CBs realized as complementizers 53 20 73 (19.5%)
CBs not realized as R1-pronouns 73 95 168 (44.9%)
Total number of R1-pronouns that do not realize CBs 58 23 81 (27.5%)
Personal pronouns that do not realize CBs 55 21 76 (35.0%)
Complementizers that do not realize CBs 3 2 5 (6.4%)
antecedent in the same utterance, and 28 (13%) are “long-distance pronouns” (Hitze-
man and Poesio 1998) whose antecedent is in neither the same nor the previous utter-
ance.
Table 7 shows that the relation between pronominalization and CB with the vanilla
instantiation is not straightforward: Only 55.1% of the 374 mentions of CBs
26
are
pronominalized. And if relative clause complementizers were not included among
the R1-pronouns (on the grounds that the decision to use a complementizer is primar-
ily dictated by grammatical, rather than discourse, considerations), more CBs would
be realized as non-R1 pronouns (171, 44.9%) than as R1-pronouns (137, 35.9%). On the
other hand, 73% of R1-pronouns do refer to the CB.
27
Table 8 analyzes pronominalization in terms of the three versions of Rule 1 we
are considering.
28
Given the figures in Table 7, it should already be clear that the
stronger version of Rule 1 we considered, always pronominalize the CB—generalizing
the proposal by Gordon, Grosz, and Gillion (1993) to the less restrictive definition of
CB given by Constraint 3—is not verified: In fact, 55% of utterances violate it. The two
other versions of Rule 1 we are considering, however—Rule 1 (GJW 83), pronominalize
26 Even though only 357 utterances have a CB with this instantiation, a CB may be realized more than
once in an utterance.
27 Earlier versions of these findings led to the development of the pronominalization algorithm in
Henschel, Cheng, and Poesio (2000).
28 As discussed in Section 3, what is counted here are utterances that verify or violate Rule 1. Not all
utterances are considered: of the 346 utterances that have exactly one CB, 72 are ignored by the script
in that the only realization of an R1-pronoun is done via a relative pronoun or trace, so only 274 (27.2%
of the total number of utterances) are considered relevant for Rule 1.
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Poesio et al. Centering: A Parametric Theory
Table 8
Evaluation of the different versions of Rule 1 with the vanilla instantiation.
Museum Pharmaceutical Total (Percentage)
GJW 95–utterances that satisfy 130 135 265 (96.7%)
GJW 95—utterances that violate 7 2 9 (3.3%)
GJW 83—utterances that satisfy 117 105 222 (81%)
GJW 83—utterances that violate 20 32 52 (19.0%)
Gordon—utterances that satisfy 77 45 122 (44.5%)
Gordon—utterances that violate 60 92 152 (55.5%)
the CB if it’s the same as the CB of the previous utterance, and especially Rule 1 (GJW
95), pronominalize the CB if anything else is—are verified by most utterances.
There are two classes of violations of Rule 1 (GJW 95): possessive pronouns and
pronouns referring to “global topics”. In (11), CB(u3), PRODUCT-X, is realized as a
proper noun, whereas a possessive pronoun is used to refer intrasententially to the
baby.
29
(11) (u1) Infants and children must not be treated continuously with
PRODUCT-X for long periods
(u2) because it may reduce the activity of the adrenal glands, and so
lower resistance to disease.
(u3) Similar effects on a baby may occur after extensive use of
PRODUCT-X by its mother during the last weeks of pregnancy
(u4) or when she is breastfeeding the baby.
In the pharmaceutical leaflets, several violations of Rule 1 are found toward the end
of text, when pronouns are sometimes used to realize the product described by the
leaflet. For example, it in the following example refers to the cream discussed by the
leaflet, not mentioned in the previous two utterances.
(12) (u1) A child of 4 years needs about a third of the adult amount. (u2) A
course of treatment for a child should not normally last more than five
days (u3) unless your doctor has told you to use it for longer.
What we seem to observe here is a conflict between the “global” preference to real-
ize the “main character” of a discourse as a pronoun, and the “local” preference to
pronominalize the locally most salient entity, as identified by the CB.
30
By the end of
a leaflet, the product discussed in the leaflet has been mentioned a number of times,
so that it is salient enough to justify pronominalization even when it is not in CF list.
We saw in Table 7 that although there are only 9 violations of Rule 1 from Grosz,
Joshi, and Weinstein (1995), 81 R1-pronouns do not realize CBs. The majority of the
29 The problem of intrasentential pronouns in Centering is discussed, e.g., in Walker (1989), Tetreault
(2001), and Poesio and Stevenson (forthcoming).
30 See also Giouli (1996) and Byron and Stent (1998).
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Computational Linguistics Volume 30, Number 3
72 cases of pronouns that do not refer to the CB but do not violate Rule 1 fall into
two classes: (1) R1-pronouns used in utterances without a CB (the majority) and (2)
R1-pronouns used in utterances in which the CB is pronominalized as well—as in the
following example, in which both the microscope and the amateur scientist are realized
(by a personal pronoun and a relative trace) in the relative clause (u2):
(13) (u1) This microscope belonged to an amateur scientist,
(u2) who would have used it to explore the mysteries of the natural
world.
82.6% of demonstrative pronouns in the corpus do not realize the CB, which is what
one would expect on the basis of, for example, Gundel, Hedberg, and Zacharski (1993),
and Passonneau (1993). This suggests that treating demonstrative pronouns as R1-
pronouns would not lead to improvements with respect to Rule 1. On the other hand,
because there are only 23 demonstrative pronouns in the corpus, such a change would
be unlikely to drastically affect the results. And indeed, with a broader definition of
R1-pronoun that includes demonstrative pronouns, we find a few more violations of
Rule 1 (GJW 95) (11 instead of 9) and a few less violations of Rule 1 (Gordon et al.) (148
instead of 152) and of Rule 1 (GJW 83) (50 instead of 52), but none of these differences
is significant. The results reported in the rest of the article are all obtained with the
“narrow” definition of R1-pronoun that does not include demonstratives.
31
4.1.4 Differences Among the Domains. The texts in the museum domain seem to be
more in agreement with the predictions of the theory than the texts in the pharmaceu-
tical domain. This is especially the case for Rule 1. There are fewer personal pronouns
in the texts in the pharmaceutical domain (73 of 1,308 CFs, [5%], as opposed to 144
of 1,731 [8%] for the museum domain), and whereas in the museum domain 40.3%
(85/211) of CB realizations are done via personal pronouns (65.4% if we consider all
R1-pronouns), in the pharmaceutical domain only 29.4% (48/163) are (41.7% for R1-
pronouns). The percentage of utterances satisfying the strong version of Constraint
1 is much higher in the museum domain (44.0%, 189/430) than in the pharmaceuti-
cal one (27.2%, 157/577), and the percentage of utterances with no CB that are not
segment boundaries is much higher in this second domain (55.3%, 319/577) than in
the first (39.1%, 168/430). Finally, almost 72% of utterances in the pharmaceutical do-
main are NULL or ZERO transitions (415/577), whereas just 54.6% are in the museum
domain (235/430); the percentage of EST and CON is also higher in the museum
domain (133/430, 31%, versus 126/577 [21.8%]). These differences are in part due to
the large number of second-person pronouns you in the pharmaceutical domain, so
that the statistics for Constraint 1 improve if we treat the entities referred to by these
pronouns as CFs, as we will see below. A second reason for these differences is that
layout plays a much more important role in the pharmaceutical domain, providing a
different way of achieving coherence. (See Section 5.)
4.2 Varying the Utterance Parameters
We now begin to explore alternative parameter settings. As always, space constraints
prevent a full discussion of all the instantiations. In this article, we discuss the results
with most of the variants quite briefly and analyze at some length only the instantiation
31 The relation between demonstrative NPs in general and the CB in our corpus is analyzed in detail in
Poesio and Nygren-Modjeska (2003).
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Poesio et al. Centering: A Parametric Theory
that identifies utterances with sentences; the results are summarized with graphs.
The extended technical report available on the companion Web site contains a more
extensive discussion of some of the variants; interested readers are also encouraged
to try further instantiations on the Web site. In this subsection we consider how the
definition of utterance (parameter uttdef) and the value of the parameter previous
utterance affect the claims.
4.2.1 Treating Coordinated Verb Phrases as Utterances. Many researchers working
on spoken dialogues or NLG assume that each element of a coordinated VP counts
as a separate utterance: that is, that in We should send the engine to Avon and hook it to
the tanker car, the coordinate VP hook it to the tanker car is actually a separate utterance.
Treating coordinated VPs as separate utterances in our corpus would of course result
in more utterances (1,041 vs. 1,007), which of course would lead to worse results unless
these utterances were treated as containing an implicit trace. If we do so, we obtain
slightly (but significantly) better results for Strong C1 (48% violations instead of 49%),
and nonsignificant differences for Rule 1 and Rule 2 (with slightly higher numbers of
Continuations and slightly lower number of Retains).
4.2.2 Using All Verbed Clauses Instead of Just the Finite Ones. A second extension
of the definition of utterance is to treat as utterances all clauses with a verb, including,
for example, the infinitival to-clause in John wants to visit Bill. The results with such an
instantiation, as well, crucially depend on our grammatical assumptions. With such
a definition, we get of course many more utterances (1,267 instead of 1,007), most of
which, like the example infinitival clause just given, do not contain explicit mentions
of the argument in subject position; so again, if we didn’t assume that traces are
present in such clauses, we would find significantly more violations of Strong C1 (685
instead of 498). Using a crude mechanism for tracking traces (adding a trace referring
to the subject of the matrix clause to all nonfinite complement clauses), we still find a
larger number of violations (598) than with the vanilla instantiation, but because the
number of utterances is much greater, these violations represent a significantly lower
percentage of the total (47% instead of 49%). We find no significant differences in the
number of violations of Rule 1. As for Rule 2, this change results in significantly fewer
NULL transitions (45.0% instead of 47.9%) and significantly more EST (22.1% instead
of 18.8%) and SSH (5.6% instead of 3.7%).
4.2.3 Restricting Finite Clauses. In general, the best results for C1 are obtained by
considering larger chunks of text as a single utterance, thus reducing the number of
utterances. In particular, fewer violations are obtained by not considering as utter-
ances finite clauses that occur as parentheticals, as subjects (as in That John could do this
to Mary was a big surprise to me), and as matrix clauses with an empty subject (as in
It is likely that John will arrive tomorrow). This merging only reduces the overall num-
ber of utterances from 1,007 to 972, but the result is a simultaneous reduction in the
violations of Strong C1 from 498 to 469 (48.2%) (which is significant by the binomial-
proportions test, though still not enough for Strong C1 to be verified) and an increase
in the number of utterances that satisfy Rule 1 (GJW 95) to 281. The violations of Rule
1 are also reduced to 8 (2.8%) (not significant). (There are virtually no changes for Rule
2.) Because of these small improvements, in the rest of the article we always exclude
these occurrences when discussing the results with finite clauses as utterances; we
refer to this instantiation as “vanilla−”.
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Computational Linguistics Volume 30, Number 3
4.2.4 Relative Clauses. Relative clauses turned out to be one of the most complex
problems we had to face. The reader may recall that Kameyama tentatively proposes
(without empirical support) that relative clauses have a “mixed” status: They should
be locally treated as updating the local focus, but at the global level they should
be merged with the embedding utterance. This proposal, however, seems to assume
that the local focus may be updated with the content of certain utterances some time
after they have been first processed, which is a rather radical change to the basic
assumptions of the framework. In this study, we simply compared an instantiation
in which relative clauses are treated as utterances with one in which they are not. In
addition, we considered treating relative clauses as adjuncts (i.e., as not embedded) and
treating them as complements (embedded).
32
The figures reported so far were obtained
by treating relative clauses as utterances and as akin to adjuncts.
33
Not treating relative
clauses as separate utterances results in a 6.5% reduction in the number of utterances
with respect to vanilla− (908 instead of 972) and in fewer violations of Strong C1 (452
[439 utterances without a CB, 13 with two CBs] instead of 469 [457 and 12]); however,
the percentage of violations is higher (49.7% vs. 48.2%). The number of violations of
Rule 1 also stays the same (8 [2.7%]). From the point of view of Rule 2, a lot of relative
clauses seem to function as EST, since their number goes down by almost 15%, to
17.3% (from 190 to 157); we also see a 30% reduction in SSH and an increase in NULL,
to 50.6% of the total. Everything else stays the same.
In purely numerical terms, then, not treating relative clauses as separate utterances
would not improve the results. Furthermore, and most important, we feel that not
treating finite relative clauses as separate utterances would make it very difficult to
maintain the principle that utterances are identified with finite clauses. For these
reasons, in the rest of the article we will continue to count relative clauses as finite
clauses.
4.2.5 Suri and McCoy’s Definition of Previous Utterance. As discussed in Section 2,
Suri and McCoy (1994) suggested that after- and before-clauses behave more like em-
bedding elements (i.e., like complements) than like coordinating ones, and Cooreman
and Sanford (1996) found evidence supporting this treatment for when clauses, as well.
The previous utterance parameter of our script can be used to compare this proposal
with Kameyama’s. When this parameter is set “Kameyama-style,” adjunct clauses are
treated as not embedded, so that, in (14), the previous utterance for (u3) is (u2). (This
was the setting used for the results discussed so far.) When the parameter is set to
(generalized) Suri and McCoy, adjunct clauses are treated as embedded, so that the
previous utterance for (u3) is (u1):
(14) (u1) John woke up (u2) when Bill rang the door.
(u3) He had forgotten the appointment.
Using Suri and McCoy’s definition of previous utterance results in a small but sig-
nificant reduction in the number of violations of Strong C1, in small improvements
concerning R1 (GJW 95), and in small, but not significant, improvements for Rule 2. As
far as Strong C1 is concerned, 20 utterances that violate Strong C1 with Kameyama’s
32 The difference matters when the relative clause occurs at the end of an embedding clause, as in John
wanted a photograph of the man that Bill had seen entering the building at night. He ...
33 We also remind the reader that our script treats all relative clauses as containing a link referring to the
entity modified by the relative, even when the clause does not contain an explicit relative pronoun or
complementizer, so that they never violate C1.
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Poesio et al. Centering: A Parametric Theory
definition satisfy it under Suri and McCoy’s, but 9 utterances become violations (by
the sign test, +20, −9, p ≤ .03). The reduction is not, however, sufficient for Strong
C1 to be verified (+355, −458). With Rule 1, we find that the number of utterances
that verify the GJW 95 version increases (+287), but the number and percentage of
violations stays the same (8 [about 2%]).
We should note, however, that the differences between Kameyama’s and Suri’s
definition of previous utterance have mostly to do with a type of clause that was
discussed only briefly by Kameyama and not at all by Suri and McCoy: relative clauses,
as in (15):
(15) (u1) This brooch is made of titanium,
(u2) which is one of the refractory metals.
(u3) It was made by Anne-Marie Shillitoe, an Edinburgh jeweller, in 1991.
If the “generalized Kameyama” definition of previous utterance is adopted, the pre-
vious utterance for (u3) is the relative clause, (u2); this causes a violation of Strong
C1. In the ‘generalized Suri and McCoy’ instantiation, by contrast, the relative clause
is treated as embedded; this seems to be the better approach. If relative clauses were
not treated as separate utterances or were treated as embedded in both instantiations,
we would find an equal number of violations, although about 20 violations would be
different in each instantiation. One example in which the difference does have to do
with the way adjuncts are handled is (7). PRODUCT-Z is not mentioned in the adjunct
if-clause, and therefore Strong C1 is violated if (u2) is taken as previous utterance for
(u3). In this case, Suri and McCoy’s proposal works better than Kameyama’s.
(7) (u1) You should not use PRODUCT-Z
(u2) if you are pregnant or breast-feeding.
(u3) Whilst you are receiving PRODUCT-Z ....
Conversely, in the following example, the adjunct clause, as you may damage the patch
inside, introduces the entity the patch, which is then referred to in (u3), so treating
the adjunct (u2) as embedded leads to a violation of C1. In this case, Kameyama’s
definition of previous utterance gives the right result:
(16) (u1) Do not use scissors
(u2) as you may damage the patch inside.
(u3) Take out the patch.
Given that these improvements are significant, if small, in the rest of the article, we
will use Suri and McCoy’s definition when uttdef is set to finite clause. However, our
discussion, and especially the contrast between (7) and (16), gives further support to
the idea that utterances may be best identified with sentences. We consider this setting
next.
4.2.6 Sentences. The setting of uttdef with the most dramatic impact on Strong C1
is that which identifies utterances with sentences. The reasons for this have already
been illustrated with (9): If utterances are identified with sentences, there are only two
utterances in that example, both containing references to the egg vases. The reduction
in violations is such that with this instantiation more utterances verify Strong C1
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Computational Linguistics Volume 30, Number 3
Table 9
Statistics relevant to Constraint 1 when utterances are identified with sentences.
Museum Pharmaceutical Total (Percentage)
Number of times at least one CF(Un) is realized in Un+1 131 147 278 (41.6%)
Utterances that satisfy Constraint 1 (have exactly one CB) 126 138 264 (39.5%)
Utterances with more than one CB 5 9 14 (2.1%)
Utterances without a CB but segment boundary 65 80 145 (21.7%)
Utterances without a CB 75 171 246 (36.8%)
than violate it, although not so many as to ensure verification at the 5% level.
34
The
statistics relevant to Constraint 1 with this definition of utterance are shown in Table 9.
Although Strong C1 is still not verified if we consider all 669 segments of text that
contain NPs, the number of utterances that satisfy Strong C1 (264) is slightly larger
than the number of those that don’t (260).
However, identifying utterances with sentences also has several negative (if small)
effects. The main among these is that the number of violations of Rule 1 goes up:
In the case of Rule 1 (GJW 95), by 50%, from 8 to 12. The reason for this increase is
in part simply that more utterances have a CB; but in some cases, the problem could
be viewed as the CB’s not being updated quickly enough. Consider the following
example:
(17) (s1) The engravings for these rooms, showing the wall lights in place,
were reproduced in Diderot’s Encyclopedie, one of the principal works
of the Age of Enlightenment. (s2) An inscription on the Getty Museum’s
drawing for one of these wall lights explains (cl3) that it should hang
above the fireplace.
The pronoun it in sentence (s2) violates Rule 1 if utterances are viewed as sentences,
but not if they are viewed as clauses. This is because in the first case (s2) has a single
CB, the wall lights, whereas with the vanilla− instantiation clause, (cl3) is a separate
utterance, with CB one of these wall lights. Because the number of violations is still quite
small, both Rule 1 (GJW 95) and Rule 1 (GJW 83) are still verified (+252, −12; and
+209, −55, respectively, as opposed to +287, −8 and +243, −52, with the vanilla−
instantiation, Suri setting),
35
although Rule 1 (Gordon et al.) still isn’t (+97, −167).
Note also that with this instantiation, the number of CBs realized by R1-pronouns
(129) is much smaller than the number realized by other types of NPs (209).
34 There is one complication: Many CFs are introduced not in sentences, but in in titles and other layout
elements that do not have a sentential format, such as Chandelier or Side effects. In order not to leave
these CFs “stranded,” the scripts also treat as an utterance every unit that contains an NP which is not
contained in any sentence, just as we did for the vanilla instantiation. This means, however, that the
number of utterances is much larger than the number of sentences (669 instead of 505), and that Strong
C1 is not verified, even though it would be if only the 505 sentences were considered (the sign test
would then show p ≤ 0.001 for Strong C1).
35 The number of utterances to be tested of course varies depending on whether utterances are identified
with finite clauses (295) or sentences (264).
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Poesio et al. Centering: A Parametric Theory
Table 10
Rule 2 statistics with sentences as utterances.
Museum Pharmaceutical Total (Percentage)
Establishments 54 68 122 (18.2%)
Continuations 28 33 61 (9.1%)
Retain 22 23 45 (6.7%)
Smooth Shift 7 12 19 (2.8%)
Rough Shift 20 11 31 (4.6%)
ZERO 52 66 118 (17.6%)
NULL 88 185 273 (40.8%)
The results for Rule 2 are not that different from those obtained with finite clauses,
but we do observe more Continuations and fewer NULLs. The statistics are shown
in Table 10. Note the much greater number of Rough Shifts than of Smooth Shifts,
although the ranking suggested by Brennan et al. is still verified by the Page test.
There are still too few sequences to truly test the version of Rule 2 proposed
by Grosz et al., but the preferences are roughly verified. As for the version of Rule
2 proposed by Strube and Hahn, there still 10 times as many expensive-expensive
sequences (191) as cheap-cheap ones (18).
4.2.7 Interim Summary. The effect of the changes in the definition of utterance and
previous utterance on Strong C1 and Rule 1 are summarized in Figure 1 and Figure 2,
respectively. As the figures show, most such changes have fairly small effects, even
though the effects are often significant. The one exception is identifying utterances
with sentences; treating all clauses as utterances also has a positive impact, provided
that we assume nonfinite clauses contain an implicit realization of the subject of the
matrix clause.
Even though identifying utterances with sentences leads to much better results for
Strong C1, we will not simply abandon the hypothesis that utterances may coincide
with finite clauses. This is in part for theoretical reasons, such as the fact that in
other theories of discourse in which “units” are assumed, such as RST, these units
are generally finite clauses. Also, identifying utterances with sentences leads to small,
but significant, increases in the number of violations of Rule 1 (from 8 in the vanilla
instantiation [2.8%] to 12 [4.5%]) and in the number of Rough Shifts (from 2.9% to
4.6%). We will also see in a moment that there are other ways of changing the vanilla
instantiation that satisfy Strong C1, so identifying utterances with sentences is not
strictly necessary.
In the rest of the article we will, therefore, study the effect of changes to other
parameters both on instantiations in which utterances are identified with finite clauses
(henceforth, u = f ) and on instantiations in which they are identified with sentences
(u = s).
4.3 Realization
In this section we discuss the effect of changes in the values of the realization param-
eters: realization and CF-filter.
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Figure 1
The effect of utterance parameters on Strong C1: A summary.
Figure 2
The effect of utterance parameters on Rule 1 (GJW 95): A summary.
4.3.1 IF: Indirect Realization + u = f . Examples such as (9) indicate that another
way to reduce the number of violations of Strong Constraint 1 is to allow for indirect
realization: Then the bridging references to the egg vases in (u2), (u3), and (u4) would
make them the CB of these utterances. And indeed, if we modify the “best” among the
u = f instantiations (vanilla−, using our generalization of Suri and McCoy’s proposal
to determine the previous utterance) to allow for indirect realization, the reduction in
violations to Strong C1 is such that with 525 utterances (54.0%) having exactly one CB
and 325 having zero or more than one (33.4%), Strong C1 is verified by the sign test
(+525, −325).
36
36 The number of utterances is obviously not affected by changes in the realization parameters.
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Poesio et al. Centering: A Parametric Theory
Table 11
Rule 2 statistics with indirect realization, 4u = f .
Museum Pharmaceutical Total (Percentage)
Establishments 75 95 170 (17.5%)
Continuations 49 40 89 (9.2%)
Retain 76 51 127 (13.1%)
Smooth Shift 39 25 64 (6.6%)
Rough Shift 60 37 97 (10%)
ZERO 60 78 138 (14.2%)
NULL 46 241 287 (29.5%)
However, allowing for indirect realization has a negative effect on other claims,
just as the change to u=s does. The first negative effect is that the number of utter-
ances with more than one CB almost doubles, from 13 with the “generalized Suri and
McCoy” instantiation (1.3%) to 22 (2.3%). This is because by increasing the number
of “persistent entities,” we increase the chance of their having an equivalent ranking
in the previous utterance. The number of violations of Rule 1 exactly doubles: from
8 with the Suri and McCoy instantiation to 16. But because with indirect realization
more utterances have a CB, the number of utterances that matter for the purposes of
Rule 1 also increases, from 295 to 467, so that the percentage of violations to Rule 1
does not change that much. With indirect realization, 3.4% of utterances violate Rule
1 (GJW 95), as opposed to 2.7% with generalized Suri and direct realization. As a
result, Rule 1 (GJW 95) (+451, −16) and Rule 1 (GJW 83) (+318, −149) are still verified,
whereas Rule 1 (Gordon et al.) still isn’t (+136, −331). An example of a pronoun that
becomes a violation of Rule 1 (GJW 95) if we allow CFs to be indirectly realized is
shown in (18). The NP one stand in (u42) realizes a bridging reference to the discourse
entity introduced by the NP the two stands in (u39), which is therefore realized in (u42),
and thus becomes its CB, but it is not pronominalized.
(18) (u39) The two stands are of the same date as the coffers, but were
originally designed to hold rectangular cabinets.
(u42) One stand was adapted in the late 1700s or early 1800s century to
make it the same height as the other.
Finally, the change to indirect realization has a big impact on the statistics for Rule 2,
shown in Table 11. On the positive side, the number of NULL transitions goes down
significantly (to less than 30%), and the percentages of the four “classic” transitions
go up. However, the greatest increases are in the number of RET (from 3.8% to 13.1%)
and RSH (from 2.6% to 10.0%). The fact that there are many more RET than CON and
many more RSH than SSH means that this is the first instantiation for which Rule 2
(BFP) is not verified by a Page test. The reason for this can be seen in (18): Because
implicit realizations are implicit NP modifiers (i.e., one stand is interpreted as one of the
two stands), they are never CPs of an utterance. (Rule 2 [Strube and Hahn] still isn’t
verified, although the percentage of cheap transitions increases from 154/747, [20.6%]
to 207/747 [27.7%]).
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Computational Linguistics Volume 30, Number 3
Table 12
Statistics about Strong C1 with u = s and indirect realization
MUSEUM PHARMA TOTAL
Number of times at least one CF(U
n
) is realized in U
n
+ 1 194 222 416 (62.2%)
Utterances that satisfy Constraint 1 (have exactly one CB) 184 206 390 (58.3%)
Utterances with more than one CB 10 16 26 (3.9%)
Utterances without a CB that are segment boundaries 47 55 102 (15.2%)
Utterances without CB 30 121 151 (22.6%)
Below, we indicate the instantiations with u=f, Suri and McCoy-style treatment of
adjuncts, and direct realization as DF and those with the same settings, but indirect
realization, as IF.
4.3.2 IS: Indirect Realization +u = s. As one might expect, the results for Constraint
1 get even better if indirect realization is combined with the u=s setting. As shown
in Table 12, With this instantiation (henceforth, IS) 390 utterances out of 669 (58.3%)
satisfy Strong C1, and 177 (26.5%) violate it—significantly better than the instantiation
with u=s and direct realization (henceforth, DS). On the other hand, the number of
utterances with more than one CB almost doubles again (and with respect to the DS
instantiation), to 26 (3.9%) from 14 (2.1%).
The number of violations of Rule 1 (GJW 95), as well, doubles again with respect to
the DS instantiation, from 12 (4.5%) to 26 (6.7% of the 390 utterances with a CB and an
R1-pronoun). While this number of violations isn’t enough to invalidate Rule 1 (GJW
95) (+364, −26), it is three times the number of violations with the vanilla instantiation.
As for what we called Rule 1 (Gordon et al.), even with this instantiation more than
75% of utterances violate it: +97, −293.
37
The results with Rule 2 are comparable to those obtained with the IF instantiation.
Just as in that case, Rule 2 (BFP) is not verified according to a Page test, even though
there is a great reduction in the number of NULL transitions (to 23.2%). The percentage
of RET is even greater than with IF (114 [17.0%], almost twice the percentage of CON
[9.4%]) as is that of Rough Shifts (100 [14.9%], almost three times the percentage of
Smooth Shifts [5.2%]). If we ignore segment boundaries, cheap transitions are 136/444,
30.6% of the total (as opposed to 22.0% with DS and 27.7% with IF).
4.3.3 Second-Person CFs. Second-person pronouns (henceforth, PRO2s) are generally
assumed to be used deictically rather than anaphorically (see, e.g., Di Eugenio 1998).
37 Some readers might think that the additional violations of Rule 1 obtained with instantiations IF and IS
(such as the one in example (18)) shouldn’t really count as violations of Rule 1, because bridging
references such as one stand contain an implicit reference to the two stands, that is, are semantically
equivalent to one of the two stands, and it is these implicit anaphors that satisfy Rule 1. One of the
parameters not discussed here, bridges policy, controls whether these implicit anaphoric references are
treated as R1-pronouns. It turns out that doing this actually results in more violations of Rule 1, because
most bridging references do not refer either to the CB of the present utterance or the CB of the
previous one (see Poesio 2003), and every bridging reference not referring to the CB may cause a
violation. In fact, treating these implicit anaphoric references as R1-pronouns (hence, as CFs) also
dramatically increases the number of utterances with more than one CB, as well as the number of
Rough Shifts. For details, see the extended report and the companion Web site.
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Poesio et al. Centering: A Parametric Theory
However, it has been suggested in recent work that especially in dialogue, they may
actually realize CFs (Byron and Stent 1998).
38
In our corpus, and especially in the phar-
maceutical domain, PRO2s are very numerous and often seem to play an important
role in maintaining the coherence of the discourse. And in fact, allowing PRO2s to
count as realizations of CFs does reduce the number of violations of Strong C1 with
both the u = f and the u = s instantiations of the theory, both with direct and with
indirect realization. Even with DF (and the Suri-McCoy setting of the previous utter-
ance parameter), allowing PRO2s to count as CFs is sufficient on its own to verify
Strong C1: The museum domain is not affected, but in the pharmaceutical domain,
the number of utterances that satisfy Strong C1 increases from 164 to 273, so that in
total 464 utterances satisfy C1 and 367 violate it, which makes the constraint verified
(by the sign test, p ≤ .03). With DS, if we treat PRO2s as CFs, 332 utterances verify
Strong C1, and 214 don’t (as opposed to +264, −260 when PRO2s are not treated as
CFs). Allowing for indirect realization we get even better results: With IF, we get +623,
−242, a significant improvement even over the instantiation with direct realization and
PRO2s; with IS, we get +439, −145.
The results with Rule 2 are also improved by treating PRO2s as CFs. The percent-
age of NULL transitions is greatly reduced (for DF, down to 35.0% [from 47.6%]; for
DS, to 30.8% [from 40.8%]; for IF, to 18.2% [from 29.5%]; for IS, to 15.1% [from 23.2%]).
As a result, the percentage of “continuous” transitions (Kibble 2001)—EST, CON, RET,
SSH, and RSH—increases. However, RSH and SSH increase, as well as EST and CON:
In the IF instantiation with PRO2s, EST are the most common transition (20.2%), but
in the IS instantiation, RSH are (18.4%). Because of these increases, treating PRO2s as
realizations of CFs does not fix the problem with rule 2 (BFP) observed above: the
Rule still isn’t verified with IF and IS. There are no significant changes with Rule 2
(Strube and Hahn).
The results with Rule 1 crucially depend on whether we do or do not consider
second-person pronouns as R1-pronouns. In either case, letting PRO2s realize CFs
results in more violations of Rule 1 (GJW 95), both in absolute and in relative terms,
because more utterances have a CB and therefore count as violations or verifications of
the rule. But if we don’t consider PRO2s as R1-pronouns, then the increase in violations
is small: for DF, from 8 (2.7%) to 12 (2.9%); for DS, from 12 (4.5%) to 17 (5.1%); for IF,
from 16 (3.4%) to 20 (3.5%); and for IS, from 26 (6.7%) to 31 (7.1%). If we treat PRO2s as
R1-pronouns, however, the percentage of violations of Rule 1 (GJW 95) almost triples
for the u=f instantiations and doubles for the u=s ones: 31 violations for DF (7.6%), 38
for DS (11.4%), 51 for IF (9.1%), and 67 for is (15.3%). (Of course, in all of these cases,
Rule 1 [GJW 95] remains verified in a statistical sense.) The reason for this increase
in violations is that PRO2s do not seem to be very good indicators of the CB: About
half of PRO2s are not realizations of CBs, in all instantiations. Given these results,
it seems clear to us that it’s not a good idea to treat PRO2s as R1-pronouns; it’s less
clear whether to treat them as realizing cfs. As we find the position that PRO2s play a
deictic function convincing, in the rest of the article, we will not include their referents
among the CFs, but we will indicate where doing so would result in major differences.
The interested reader is advised to try the alternatives on the companion Web site.
4.3.4 Predicative NPs. The two alternative views considered so far about which en-
tities to realize both result in an increase in the number of CFs. What if we were to
38 Walker (personal communication) also observed that in Japanese, zero pronouns—often taken as
referring to the CB—are allowed to refer to second-person entities.
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Computational Linguistics Volume 30, Number 3
attempt to reduce the number of CFs instead? Prima facie, one would imagine this type
of modification to have a negative impact on C1, but perhaps some of the violations
of Rule 1 might disappear.
Among the NPs that might be thought not to introduce CFs, an obvious candidate
are predicative NPs, that is, NPs like a policeman in John is a policeman that play the role
of predicates in the logical form of an utterance. But in fact, because our annotators
were instructed to mark up John rather than a policeman as antecedent of subsequent
anaphoric expression in these examples, filtering away such NPs does not have any
positive result at all; on the contrary, it does have a significant (if small) negative
impact on Strong C1,
39
because in some cases the annotators had been forced to mark
up an NP in predicative position as the antecedent of an anaphoric expression against
the instructions. Two such examples are given below. Especially in the second case, it
is not clear how else the annotators could have marked the antecedent of Bjorg:
(19) a. An important artist in making these links has been Yasuki
Hiramatsu. His knowledge of metalcraft allows him to push and play
against the boundaries of what the material can physically do.
b. Two such jewellers are Toril Bjorg from Norway and Jacqueline Mina
from England. It may be unsurprising that Bjorg, as a Scandinavian,
should choose silver as her material.
In the following we will continue to treat predicative NPs as not introducing CFs.
4.3.5 Interim Summary. The realization parameters have an even greater impact than
the utterance parameters, especially on Strong C1 and Rule 2. Either allowing for
indirect realization or treating second-person pronouns as introducing CFs, is sufficient
for Strong C1 to be verified. When the two settings are combined, a large majority of
utterances verifies the constraint. On the other hand, allowing for indirect realization
also results in significant increases in the number of violations of Rule 1, although
overall the percentage of such violations remains pretty small. In addition, indirect
realization leads to such an increase in the number of RET and RSH that there are
fewer CON than RET and fewer SSH than RSH, and Rule 2 (BFP) is not verified by
any of the instantiations with indirect realization we have discussed. Treating PRO2s
as realizations of CFs, while sufficient to cause Strong C1 to be verified, has less of
an effect on Rule 2, but when we combine this setting with the IS instantiations, we
obtain an instantiation in which RSH is the most common transition. The effects of
the realization choices are summarized in Figures 3 and 4.
4.4 Ranking
4.4.1 Grammatical Function + Linear Disambiguation. We observed above that be-
cause grammatical function does not always specify a unique, most highly ranked CF,
when using that ranking function some utterances end up with more than one CB,
which causes the violations of the weak version of Constraint 1 seen above (up to 5.7%
of the total in the IF instantiation treating PRO2s as CF realizations). We also men-
tioned, however, that this problem can be fixed by requiring the ranking function to be
a total order, which, in turn, is easily done by adding a tie-breaking factor. Given the
results in Gernsbacher and Hargreaves (1988) and Gordon, Grosz, and Gillion (1993),
39 The difference is significantly larger for all the instantiations not treating PRO2s as CFs; larger, but not
significantly so, if PRO2s are treated as CFs.
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Poesio et al. Centering: A Parametric Theory
Figure 3
The effect of the realization parameters on the violations of Strong C1.
Figure 4
The effect of the realization parameters on the percentage of violations of Rule 1.
the most obvious disambiguating factor is linear order: Whenever two CFs are equally
ranked, assign to, say, the leftmost CF a higher rank. And indeed, we saw in Section 2
that linear order is used by Strube and Hahn (1999) to resolve ties, albeit in conjunction
with a ranking function other than grammatical function. In this section we evaluate
the ranking function obtained by adding linear order to grammatical function, which
we call GFTHERELIN.
40
The results with this ranking function are summarized in
Table 13.
40 The reason for the “there” in the function’s name is that the results can be slightly improved by a
further small change: ranking postcopular npsinthere-sentences (e.g., someone in There is someone at the
door) as subjects rather than objects. See, e.g., Sidner (1979).
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Computational Linguistics Volume 30, Number 3
Table 13
Summary of results for Strong C1, Rule 1 (GJW 95), and Rule 2 (BFP) with GFTHERELIN
ranking. ♠ indicates that a claim is not verified at the .05 level; ♦ that it’s not verified at the
.01 level.
Instantiation Strong C1 Rule 1 (GJW 95) Rule 2 (BFP) (Page test,
(Percentage violations) (Percentage violations) probability of not
being verified)
DF-predicate +352,−450 (46.3%) ♠ +291,−11 (3.6%) .001
DF-predicate+pro2 +465,−355 (36.5%) +403,−15 (3.6%) .001
DS-predicate +273,−249 (37.2%) ♠ +259,−14 (5.1%) .001
DS-predicate+pro2 +347,−197 (29.4%) +325,−22 (6.3%) .001
IF-predicate +529,−310 (31.9%) +463,−18 (3.7%) 1 ♠
IF-predicate+pro2 +635,−219 (22.5%) +325,−22 (3.7%) .05♦
IS-predicate +408,−157 (23.5%) +378,−30 (7.4%) .05♦
IS-predicate+pro2 +469,−113 (16.9%) +432,−37 (7.4%) 1 ♠
The table summarizes eight instantiations: DF, DS, IF, and IS, each in two variants
(including PRO2s and without them). For each instantiation, the table lists verifiers
and violations of Strong C1 and Rule 1 (GJW 95) and the percentage of violations, as
well as the results of the Page test for Rule 2.
Adopting GFTHERELIN as a ranking function doesn’t lead to major changes as far
as Strong C1 is concerned. This is because the only change from the results obtained
with simple grammatical function is that the utterances previously classified as having
two CBs get reclassified as having one, and with the instantiations that would benefit
the most from a reduction in Strong C1 violations—those based on DF—the number of
multi-CB sentences is fairly small, typically 1–2%, although this is enough to make the
improvement significant by the sign test with all instantiations. The improvements are
greater with the u=s instantiations, since with sentences it’s more common for more
than one CF to be realized in the same grammatical position; for example, in the IS
instantiations in which PRO2s are considered as realizations of CFs, we find that 5.7%
of utterances (38/669) have more than one CB. However, Strong C1 is already verified
with these instantiations, even with simple grammatical function.
As in all previous cases, better results with Strong C1 are counterbalanced by
worse results for Rule 1—although, again, not so much worse that Rule 1 ends up
not being verified. The results with the DF instantiations aren’t significantly worse:
For example, we find +291, −11 (3.6%) with the instantiation not including predicative
NPs and second-person pronouns, as opposed to +280, −9 for the same instantiation
with simple grammatical function ranking. The number of violations of Rule 1 is
significantly greater with the DS instantiation if PRO2s are treated as CF realizations:
+325, -22 (6.3%) vs. +310, -17 (5.2%). In two of the additional five violations of Rule
1, however, the problem is simply that by adding a disambiguation element, we turn
utterances whose CB is undefined (because more than one CF is equally ranked) into
utterances with a CB. One such example is (20):
(20) (s7) Intended to hold jewels or small precious items, the interiors of
this pair of coffers are lined with tortoiseshell and brass or pewter, with
secret compartments in the base.
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Poesio et al. Centering: A Parametric Theory
Table 14
Transition percentages for IS with GFTHERELIN ranking.
Museum Pharmaceutical Total (Percentage)
Establishments 47 60 107 (16.0%)
Continuations 28 44 72 (10.8%)
Retain 56 65 121 (18.1%)
Smooth Shift 8 24 32 (4.8%)
Rough Shift 48 28 76 (11.4%)
ZERO 43 58 101 (15.1%)
NULL 41 119 160 (23.9%)
(s8) The coffers are each decorated using techniques known as premiere
partie marquetry, a pattern of brass and pewter on a tortoiseshell ground,
and its reverse, contrepartie, a tortoiseshell pattern on a background of
pewter and brass.
With simple grammatical function, both the coffers and brass are CBs of (s8), which
is therefore treated by our script as not having a well-defined CB. As a result, the
pronominalization of a non-CB, premiere partie marquetry, is not counted as a violation.
(s8), however, becomes a violation with GFTHERELIN, since the coffers becomes its
only CB.
With the IF instantiation, the percentage of violations of Rule 1 (3.7%) is nonsignif-
icantly greater than the percentage with simple grammatical function (3.5%). The
percentage of violations with the two IS instantiations (7.4%) is significantly worse (at
the .01 level) than with simple grammatical function (6.7% and 7.1%, respectively).
Table 13 shows that using GFTHERELIN has a positive effect on the number
of violations of Rule 2 (BFP). Whereas with simple grammatical function, none of the
instantiations with indirect realization verifies Rule 2 (BFP) by the Page rank test, with
GFTHERELIN the IS instantiation does (although only at the .05 level), as does IF if
PRO2s are treated as CF realizations. (All direct realization instantiations still verify
the rule.) The main reason for this change is a significant reduction in the percentage
of RSH with GFTHERLIN, especially for the IF and IS instantiations: With IF we see
a reduction in RSH from 9.7% to 7.6%; with IS, from 14.6% to 11.4%. With the DS
instantiation the percentage of RET and RSH is about twice what we find with the
DF instantiation, just as we observed with simple grammatical function ranking, but
otherwise the results are pretty similar to those with DF. With the IF and the IS
instantiations, we get small but significant increases in CON and RET and a reduction
in RSH. In Table 14, we report the complete percentages for this instantiation, for
comparison with other ranking functions.
The change to GFTHERELIN hardly affects the relative percentages of cheap and
expensive transitions, so the results concerning Rule 2 (Strube and Hahn) do not
change.
The IS instantiation with GFTHERELIN ranking is the one in which all three claims
are verified without need to treat PRO2s as CF realizations, even though Rule 2 is
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Computational Linguistics Volume 30, Number 3
verified with this instantiation only at the .05 level. We will therefore concentrate on
this instantiation when making comparisons with the other ranking variants.
4.4.2 Linear Order. Among the ranking functions alternative to grammatical function,
perhaps the simplest is the one that ranks CFs in the order of their occurrence in the
utterance, from left to right. This ranking function was explicitly proposed by Rambow
(1993) to account for facts about scrambling in German, and effects of order of mention
have been observed by, among others, Gernsbacher and Hargreaves (1988), Gordon,
Grosz, and Gillion (1993), and Stevenson, Crawley, and Kleinman (1994).
Using linear order instead of GFTHERELIN has no effect at all on Constraint 1,
as one would expect, since all that matters for the constraint to be verified is whether
discourse entities are mentioned in successive utterances and whether the ranking
function is total. However, no significant differences were observed with Rule 1 (GJW
95), either: with IS, we find +378, −30, with linear order, as opposed to +377, −31,
with GFTHERELIN.
41
This is because linear order is a very good approximation of
grammatical function in English: Subjects tend to occur in first position, objects in
second position, etc. The one claim for which the differences are significant is Rule 2
(BFP): with IS, enough CON become RET and enough SSH become RSH that Rule 2
is no longer verified even at the .05 level. (The rule is still verified in the DF and the
DS instantiations.)
All in all, these results are not grounds to argue that linear order is a better rank-
ing function than GFTHERELIN;
42
however, because the differences are so small, they
also suggest that linear order (which is far easier to compute) might be a good ap-
proximation of grammatical-function ranking for practical applications working with
English.
4.4.3 Information Structure. Replacing GFTHERELIN with the ranking function pro-
posed by Strube and Hahn (1999) (henceforth, STRUBE-HAHN): rank hearer-old en-
tities more highly than inferrables, and these higher than hearer-old entities—cannot
and did not lead to different results for Strong C1, for the reasons already discussed
for linear-order ranking. Less expected was the fact that—again, just as in the case
of linear order—we didn’t find any significant differences with Rule 1 (GJW 95), ei-
ther, although with the IF and IS instantiations, we find one more violation than with
GFTHERELIN.
43
This doesn’t mean that the exact same utterances are violations in
both cases, rather, that the differences “balance out”. We already saw one example in
which STRUBE-HAHN ranking results in a violation of Rule 1, whereas GFTHERELIN
ranking doesn’t: This is the first sentence in (10), illustrating the kind of situations in
which a partial ranking may result in two CBs. We repeat that sentence in (21) and
include the preceding sentence:
(21) (s67) An inventory of Count Branicki’s possessions made at his death
describes both the corner cupboard and the objects displayed on its
shelves: a collection of mounted Chinese porcelain and clocks, some
embellished with porcelain flowers.
41 With IF the difference goes the other way: +463, −18, for GFTHERELIN, +463, −19, for linear order.
There are no differences at all with DF and DS.
42 This point is reinforced by a number of results from Gordon and collaborators (e.g., Gordon, Grosz,
and Gillion 1993; Gordon et al. 1999) suggesting that hierarchical position in the parse tree is a better
predictor of salience than linear order, as well as by results suggesting that for a range of languages,
linear order is much less effective–see, for example, Prasad and Strube (2000) for Hindi.
43 We discuss the results only with the version of Rule 1 proposed by Grosz, Joshi, and Weinstein (1995).
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Poesio et al. Centering: A Parametric Theory
Table 15
Transition percentages for IS with STRUBE-HAHN ranking.
Museum Pharmaceutical Total (Percentage)
Establishments 47 60 107 (16.0%)
Continuations 39 55 94 (14.1%)
Retain 50 53 103 (15.4%)
Smooth Shift 18 26 44 (6.6%)
Rough Shift 33 27 60 (9.0%)
ZERO 43 58 101 (15.1%)
NULL 41 119 160 (23.9%)
(s68) The drawing of the corner cupboard, or more probably an
engraving of it, must have caught Branicki’s attention.
As the corner cupboard is in object position, it gets higher ranking in (s67) than Count
Branicki, which is in NP-modifier position, which—while not explicitly discussed in
the centering literature—will presumably fall among the “other” cases. As a result,
the cupboard is the CB of (s68), and its pronominalization is predicted by Rule 1.
With STRUBE-HAHN ranking, Count Branicki is the highest-ranked entity of (s67), and
therefore the CB of (s68); hence the violation. Conversely, (22) is an example in which
GFTHERELIN and ranking results in a violation of Rule 1, while STRUBE-HAHN
ranking doesn’t:
(22) (s88) Christened by his contemporaries as ’the most skillful artisan in
Paris,’ Andr`e-Charles Boulle’s name is synonymous with the practice of
veneering furniture with marquetry of tortoiseshell, pewter, and brass.
(s89) Although he did not invent the technique, Boulle was its greatest
practitioner and lent his name to its common name: Boulle work.
In this example, Andr`e-Charles Boulle’s name, the subject of (s88), is ranked higher than
Andr`e-Charles Boulle, and is therefore the CB of (s89), in which, however, it is not
pronominalized, even though both Boulle and the technique he invented are. Notice
that (21) and (22) are almost stereotypical instances of the class of examples that led
Sidner (1979) to argue that two foci are needed, one for animated entities, and one for
the entities acted upon; we return to this issue in Section 5.
The one claim where STRUBE-HAHN ranking makes a clear difference is Rule 2
(BFP). About 20% of RET become CON and about 20% of RSH become SSH. Although
we still find more RET than CON and more RSH than SSH, these changes are sufficient
to cause Rule 2 (BFP) to be verified at the .01 level in all instantiations considered.
44
The
transition percentages with IS and STRUBE-HAHN ranking are presented in Table 15.
Even with IS, however—the instantiation closest to the one proposed by Strube
and Hahn—we still find many more expensive transitions (272) than cheap ones (172)
44 With DF and DS the number of RET and RSH goes down drastically, so that we do find more CON
than RET and more SSH than RSH, but we still find more SSH than RET.
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Computational Linguistics Volume 30, Number 3
and almost three times as many expensive-expensive sequences (137) as cheap-cheap
ones (56), so Rule 2 (Strube and Hahn) is not verified.
4.4.4 Summary. Because Strong C1 is the most problematic claim, it was to be expected
that the most studied parameter of centering, ranking, would have a smaller impact
than the utterance and realization parameters. It is nevertheless interesting that the
results for Rule 1 (GJW 95) are virtually identical under the three versions of ranking
we considered. More differences can be found for Rule 2 (BFP), which is not verified
by any instantiation with linear-order ranking and is verified only by a few instantia-
tions with GFTHERELIN. Adopting STRUBE-HAHN ranking does result in a greater
percentage of utterances being classified into one of the “continuous” classes and in a
lower probability of Rule 2’s (BFP) being falsified. Finally, not even these last changes
to parameter settings were sufficient to cause either Rule 1 (Gordon et al.) or Rule 2
(Strube and Hahn) to be verified.
5. Discussion
In this section we first discuss the effects of different parameter settings on the re-
sults obtained; we then analyze the claims of centering theory, draw a few theoretical
conclusions, and make some suggestions for further work (empirical and theoretical).
5.1 Setting the Parameters
5.1.1 Comparing Instantiations. A central goal of this study was to compare different
ways of instantiating centering’s parameters, and different versions of its claims, on a
single data set, also examining combinations not previously considered (e.g., whether
Brennan et al.’s version of Rule 2 would be verified when the parameters were set
as suggested by Strube and Hahn and vice versa. Our first interesting result in this
sense is that if the parameters are set in the most “mainstream” way (the “vanilla”
instantiation) only Rule 1 (GJW 95) and Rule 1 (GJW 83) are clearly verified. The results
concerning Constraint 1 are especially negative. As with this instantiation only 35% of
utterances are continuous—that is, CF(U
n
) ∩ CF(U
n−1
) negationslash= ∅ (Kibble 2000; Karamanis
2001)—only the weak version of Constraint 1 is verified. Strong C1, the best-known
formulation, and the one that in our view best captures the idea of “entity coherence,”
clearly doesn’t hold. Another interesting observation is that if ranking is required
only to be partial, some utterances end up with more than one CB: The percentage
of such utterances is only 1% with the vanilla instantiation but can be as high as 6%
with some instantiations. This is perhaps obvious, but to our knowledge, it had not
been previously discussed.
As for Rule 2, with the vanilla instantiation the version proposed by Brennan et
al. is verified by a Page rank test, but arguably, the most striking fact about transitions
with this instantiation is the prevalence of NULL transitions (47.9%), Establishments
(18.8%), and ZEROs (16.7%). All together, the four types of transitions falling under
the remit of Rule 2 account for only 16% of utterances, and if Smooth Shifts and Rough
Shifts are counted together, with this instantiation there are more Shifts than Retains.
Other classifications and versions of the rule do not correlate much better with the
observed frequencies: For example, only 39% of entity-coherent transitions (139 out
of 357), and 14% of the total, are cheap in the sense of Strube and Hahn (1999) (i.e.,
CP(U
n−1
) predicts CB(U
n
)).
These findings concerning the vanilla instantiation should not, however, lead us
to conclude that the theory in general is not verified. Our second major finding is that
parameters do matter: that is, it is possible to set the parameters in such a way as to
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Poesio et al. Centering: A Parametric Theory
make all three claims verified in a statistical sense. However, because Strong C1 is the
claim with the largest percentage of violations, the parameters whose setting matters
the most when one is trying to find an instantiation in which all claims are satisfied
are those controlling utterance definition and CF realization. Considering a center as
realized in an utterance which contains an associative reference to that center is suf-
ficient for Strong C1 to be verified; identifying utterances with sentences instead of
finite clauses also has a strong positive effect. With the resulting instantiations (IF and
IS), Strong C1 is verified, as well as the two “basic” versions of Rule 1.
We also found, however, that there is a trade-off between Strong C1, on one side,
and Rule 1 and Rule 2, on the other: The changes to the utterance and realization
parameters just mentioned, while reducing the violations of Strong C1, increase those
of Rule 1 and Rule 2 (see, e.g., Table 13). Identifying utterances with sentences, or (to a
lesser extent) allowing indirect realization, results in statistically significant increases
in the number of violations of Rule 1—up to a total of 7.4% in the IS instantiation (see
Figures 2 and 4)—although Rule 1 (GJW 95) and Rule 1 (GJW 83) are so robust that
they are still verified, even in these instantiations.
45
These changes to the utterance
and realization parameters have an even greater impact on Rule 2 (BFP), which is
only weakly verified with the vanilla instantiation. With the IF and IS instantiations
and grammatical-function ranking, we find many more RSH than SSH and many
more RET than “pure” CON (i.e., without counting Establishments); indeed, in the IS
instantiation with GFTHERELIN ranking, RET are the second most common transition.
As a result, Rule 2 (BFP) is verified with is instantiations only at the .05 level, and with
IF instantiations only if second-person pronouns are counted as realizations of CFs.
On the positive side, with these instantiations a much greater percentage of utterances
(45%) are classified as either CON, RET, SSH, or RSH, and a further 16% as EST.
These results can be further strengthened by making one last change to the param-
eters: adopting the ranking function proposed by Strube and Hahn (1999) instead of
GFTHERELIN. With this instantiation, Rule 2 (BFP) is verified at the .01 level, rather
than only at the .05 level. This is because although the STRUBE-HAHN ranking func-
tion has no effect on Strong C1 (obviously) or R1 (more surprisingly), it does result in
some of the RET becoming CON and some of the SSH becoming RSH. Even though
we still find more RET than CON and more RSH than SSH, these changes are enough
to cause Rule 2 (BFP) to be verified at the .01 level with the IS instantiation. Strube
and Hahn’s own version of Rule 2 still isn’t verified, but this version of the rule is not
verified by any of the instantiations we evaluated. In other words, with the IS or IF
instantiation and STRUBE-HAHN ranking, all three claims of the theory are verified
at the .01 level.
The final observation concerning parameter settings is that issues not widely dis-
cussed in the centering literature had a greater impact on the theory’s claims in our
experiments than parameters such as the choice of ranking function or the definition
of previous utterance. Many of these issues, such as the treatment of second-person
pronouns and of empty categories, have to do with the general issue of which entities
should be included in the CF list. Considering second-person pronouns to be realiza-
tions of discourse entities is enough to make Strong C1 satisfied; we also found that
45 Perhaps the most spectacular demonstration of the trade-off between Strong C1 and Rule 1 can be seen
with the versions of the theory that adopt the definitions of CB proposed by Gordon, Grosz, and
Gillion (1993) and Passonneau (1993). (These instantiations are not discussed in this article, but can be
examined on the companion Web site.) By adopting a particularly restrictive definition of CB, these
versions succeed in reducing (indeed, eliminating, in the case of Passonneau) the violations of Rule 1,
but the price is that only a very few utterances have a CB.
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Computational Linguistics Volume 30, Number 3
a number of extensions to the definition of utterance, such as the inclusion of rela-
tive clauses and nonfinite clauses, led to much worse results unless reduced relative
clauses and nonfinite clauses were taken to include traces linking these clauses to the
clause in which they were embedded.
5.1.2 Minimizing Violations Should Not Be the Overriding Goal. We said in Sec-
tion 3 that we don’t think that minimizing violations should be the only factor taken
into account in deciding how to set parameters. Some violations are best accepted and
explained in terms of the interaction of centering preferences with other preferences.
(See below.)
Special care is needed when alternative definitions are supported by cross-linguistic
evidence or by the results of psychological studies. In the case of ranking, although
we didn’t find any significant differences between grammatical-function ranking and
linear-order ranking for English, one should keep in mind that such differences have
been found for other languages, especially more free-order ones. Prasad and Strube
(2000), for example, found that in Hindi the difference between grammatical-function
and linear-order ranking is significant, and Strube and Hahn (1999) found significant
differences between grammatical function and information structure in German. Con-
versely, before taking the evidence for a slight advantage of STRUBE-HAHN ranking
over grammatical-function ranking as conclusive, one needs to supplement our stud-
ies with psychological experiments reconciling these results with numerous results
indicating the important role played by grammatical function, especially subjecthood
(among others, Hudson, Tanenhaus, and Dell [1986]; Gordon, Grosz, and Gillion [1993];
Brennan [1995]). Information structure has also been found not to be appropriate for
languages including Greek, Hindi, and Turkish (Turan 1998; Prasad and Strube 2000;
Miltsakaki 2002). Similar considerations apply to the definition of previous utterance,
since we saw that a considerable amount of psychological evidence supports treating
adjuncts as embedded, at least when the syntactically embedded clause is at the end
of the sentence (Cooreman and Sanford 1996; Pearson, Stevenson, and Poesio 2000).
In the case of the definition of utterance, our results indicate that identifying utter-
ances with sentences, rather than finite clauses, leads to results much more consistent
with the claimed preference for discourses to be entity-coherent. While this result is
likely to be useful for a number of reasons and for different types of applications (e.g.,
text planners), we believe that further empirical and theoretical work is needed before
conclusions can be reached about when the local focus is updated. For one thing, most
analyses of discourse structure—for example, rhetorical structures theory (Mann and
Thompson 1988)–view clauses as the basic unit of discourse in written text. And in
spoken dialogue one can hardly find any complete sentences; in this case, the update
unit is much more likely to be a prosodic phrase of some sort.
5.2 The Claims of Centering, Revisited
5.2.1 Centering, Pronominalization, and Salience. One clear result of this work is that
centering’s claims about pronominalization—at least, those expressed by the versions
of Rule 1 proposed in Grosz, Joshi, and Weinstein (1995, 1983)–are very robust. Rule 1
(GJW 95) and Rule 1 (GJW 83) are verified with all parameter instantiations, and in a
very convincing way: In the instantiations we considered, the percentage of violations
of Rule 1 (GJW 95) never exceeds 8% of the total number of utterances.
On the other hand, one should keep in mind that these two versions of Rule 1
make very weak claims about pronominalization. All that Rule 1 (GJW 95) says is that
if we decide to pronominalize, then we should pronominalize the CB. This formulation
doesn’t address the real problem for a theory of pronominalization or, more generally,
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Poesio et al. Centering: A Parametric Theory
of NP form decision, which is to decide when a discourse entity should be realized
as a pronoun (Henschel, Cheng, and Poesio 2000). And our results also indicate that
simply strengthening Rule 1 to the form “pronominalize the CB,” which can be seen
as a generalization of the proposals in Gordon, Grosz, and Gillion (1993), would be
a very bad idea: Between 50% (with u = f ) and 60% (with u = s) of mentions of
the CB are not realized using a pronoun, and conversely, between 30% and 40% of
personal pronouns are not realizations of the CB. Examples like (12) illustrate one
type of situation in which a mismatch between the CB and pronominalization may
occur: By having been mentioned often in a discourse, a discourse entity may become
sufficiently salient (at the global level) to justify pronominalization even when it is
not the CB.
46
These observations suggest that the decision to pronominalize does not
depend only on whether a discourse entity is the CB but must involve a number of
further constraints and preferences.
47
5.2.2 CT as a Theory of Coherence: Constraint 1. Another result of this work is that
the validity of centering’s claims about local coherence—Constraint 1 and Rule 2—
depends on the choice of the parameters to a much greater extent than is the case for
the claims about pronominalization. Strong C1 does not hold for the vanilla instan-
tiation, although it does hold for any instantiation in which the implicit anaphoric
component of bridging references is treated as an indirect realization and for many
instantiations in which utterances are identified with sentences. But even under the
most favorable parameter instantiations, there are many more exceptions to Strong
C1 (between 20% and 25% of the total number of utterances) than we find even with
the instantiations which are worse for Rule 1 (7–8%). While the weak version of C1,
requiring only that there is at most one most salient entity per utterance, does hold
even with the vanilla instantiation and does capture the claim that utterances with a
unique CB are easier to process, a central aspect of centering since Joshi and Kuhn
(1979) and Joshi and Weinstein (1981), it says nothing about entity coherence’s being
what ensures local coherence.
Further light on entity coherence is shed by recent work on text planning, particu-
larly by Karamanis (2003), which suggests that when all alternative ways of extracting
a text plan from the propositions expressed by texts such as those we are studying
are considered, the actual ordering found in the texts tends to be in greater agreement
with centering’s preferences about entity coherence than with most of its alternatives.
After extracting the propositions
48
expressed by texts in the museum subdomain of
our corpus, Karamanis determined that although the sequence actually found in such
texts is not optimal as far as minimizing the violations to entity coherence (with the
instantiation he considers, more than 50% of the utterances violate Strong C1), approx-
imately 70% of the alternative orderings introduce even more violations.
If we accept that the texts in our corpus are coherent, these results suggest that
there must be other ways of achieving local coherence, apart from what we have
been calling here “entity coherence”. An obvious candidate for an additional, or
46 The role of global focus in the interpretation of pronouns needs further study. A few preliminary
observations can be found in Hitzeman and Poesio (1998).
47 The discrepancy between pronominalization and CB-hood in our corpus is analyzed in more detail by
Henschel, Cheng, and Poesio (2000), who propose an algorithm for pronominalization that takes into
account factors such as the presence of distractors matching the CB’s agreement features that may lead
to the decision not to pronominalize, as well as factors that may result in the pronominalization of a
non-CB. The algorithm achieves an accuracy of 87.8% in the museum domain.
48 More precisely, the lists of CF realized by each utterance with a DF instantiation, representing that
utterance’s arguments.
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Computational Linguistics Volume 30, Number 3
alternative, coherence-inducing device are rhetorical relations. Indeed, the claim that
“entity” coherence needs to be supplemented by “relational” coherence can be found
as far back as Kintsch and van Dijk (1978) and Hobbs (1979). This view is supported
by an analysis of our data. With the u=f instantiations, we find in the pharmaceutical
subdomain many examples in which successive utterances do not mention the same
entities, but the connection between clauses is explicitly indicated by connectives, as
in (23):
(23) (u1) This leaflet is a summary of the important information about
Product A.
(u2) If you have any questions or are not sure about anything to do with
your treatment,
(u3) ask your doctor or your pharmacist.
A more complex case are utterances in the museum subdomain that do not refer to
any of the previous CFs because they express generic statements about the class of
objects of which the object under discussion is an instance, or utterances that make
a generic point that will then be illustrated by a specific object. In (24), (u2) gives
background concerning the decoration of a cabinet:
(24) (u1) On the drawer above the door, gilt-bronze military trophies flank a
medallion portrait of Louis XIV. (u2) In the Dutch Wars of 1672–1678,
France fought simultaneously against the Dutch, Spanish, and Imperial
armies, defeating them all. (u3) This cabinet celebrates the Treaty of
Nijmegen, which concluded the war.
While the analysis of such cases in terms of rhetorical relations is more complex, it
seems clear to us that an analysis in terms of underlying semantic connections between
events or propositions is more perspicuous than one in terms of entity coherence.
While it is true that some of these violations could be fixed by adopting a broader
notion of bridging reference–for example, in (24) we might treat France as a bridge to
Louis XIV—this wider notion of bridging reference has proven to be very difficult to
identify in a reliable way.
Now, given that in an RST-style analysis, every discourse unit is connected by at
least one rhetorical link to at least another discourse unit, one might wonder whether
“entity coherence” is still needed once “relational coherence” is introduced. However,
Knott et al. (2001) convincingly argue that in RST, complete connectivity is usually
achieved by introducing relations such as “Elaboration” that, when looked at closely,
turn out really to be attempts to capture a notion of entity coherence. This work on
rhetorical relations is coming to a position symmetrical to our own: that a purely rela-
tional account is not sufficient, and a separate theory of entity coherence is necessary
(Knott et al. 2001).
49
5.2.3 Topic Continuity: Rule 2. Rule 2–stating a preference not just to keep talking
about the same objects, but to preserve their relative ranking—also seems much less
robust than Rule 1, irrespective of its formulation and of the instantiation.
49 The respective role of entity coherence, relational coherence, and other forms of coherence in the
examples in our corpus is studied in more detail in Oberlander and Poesio (2002).
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Poesio et al. Centering: A Parametric Theory
As already noted, one of the most interesting observations about this aspect of
the theory concerns the classification of utterances used to formalize it (at least in
the earlier versions of the theory). With pretty much all parameter instantiations that
we tested, two of the most common transitions were the NULL transition (between
two utterances neither of which has a CB), previously considered only in Passonneau
(1998), and the ZERO transition (from an utterance with a CB to one without), which
as far as we can see has never been discussed before. Indeed, with the vanilla in-
stantiation, 84% of all utterances are either NULL, ZERO, or EST and therefore fall
outside the scope of Rule 2 in almost all its formulations. The question raised by this
finding is whether the theory has to be extended to cover such cases or whether they
have to be accounted for by other components of an overall theory of discourse (see
below).
Three versions of Rule 2 were tested in some detail.
50
The version of Rule 2 from
Grosz, Joshi, and Weinstein (1995), formulated in terms of sequences and stating a
preference for sequences of CON over sequences of RET over sequences of SHIFT
(which we tested by counting the number of sequence pairs), suffers from the prob-
lem that even with the “best” instantiations, fewer than one-third of sequence pairs
involve the same transition, and even fewer are sequences of the transitions consid-
ered by Grosz et al. Even in the instantiation which yields the best results for Rule 2
(BFP), IS with STRUBE-HAHN ranking, only 13% of sequence pairs are of the form
CON-CON/RET-RET/SH-SH, and altogether only 28% of sequence pairs involve only
transitions considered by Grosz et al. Keeping in mind that Rule 2 (GJW 95) applies
only to a minority of sequence pairs, we do find that with IS and STRUBE-HAHN
ranking, the number of CON-CON sequences (37) slightly exceeds the number of RET-
RET (35), which in turn exceeds the number of SH-SH (19, of which 16 are RSH-RSH).
This doesn’t hold with GFTHERELIN ranking, where RET-RET exceeds CON-CON
even if we treat EST as a type of CON; we find no significant difference between the
IF and the IS setting.
Rule 2 (BFP), formulated in terms of single transitions, accounts for larger per-
centages of the data (single utterances) and was found to be verified both with the
vanilla instantiation and with the “best” instantiations. However, we still observed a
large percentage of NULL transitions with most instantiations; we also found more
RET than CON and more RSH than SSH in most instantiations in which utterances
are identified with sentences or allow for indirect realization.
51
Finally, Strube and Hahn’s preference for sequences of cheap transitions over se-
quences of expensive ones isn’t verified by any of the instantiations we tested; in-
deed, in all instantiations we studied we found more expensive transitions than cheap
ones, meaning that the CP of one utterance generally doesn’t predict the CB of the
next.
These mixed results are in line with those of psychological experiments, which
so far haven’t found clear evidence supporting the claim that, say, Continuations
are easier to process than Shifts, let alone Retains (Gordon, Grosz, and Gillion
1993)
50 As noted earlier, an earlier version of Kibble’s proposal was also tested; the results can be viewed on
the companion Web site.
51 CON can be made the most frequent transition by merging EST and CON. We found, however, that
this merging leads to worse results as far as the correlation between the classification of transitions and
two of the linguistic phenomena for which the classification has been used: predicting the form of
subject NPs, and predicting segment boundaries. These results are discussed in the technical
report.
356
Computational Linguistics Volume 30, Number 3
5.3 Theoretical Consequences
While proposing modifications of centering is beyond the scope of this article, we
believe our results do have broad theoretical consequences worthy of further explo-
ration.
5.3.1 Clarification of the Claims and Identification of Further Parameters. Apart from
comparing different ways of setting the parameters already discussed in the literature,
our work had the more fundamental goal of clarifying the claims of centering theory
by identifying aspects that need to be made more precise. Our study raised a number
of questions about the definitions of the concepts used in centering not previously
examined in the literature or only discussed in passing.
Many of these questions have to do with realization, one of the least studied as-
pects of the theory. One such question is the status of entities realized as second-person
pronouns. Our results indicated that if PRO2s are not considered realizations of CF, or
if we treat them as R1-pronouns, we find many more violations of Strong C1 and Rule
1, respectively (although both claims are still verified). We also saw that the results
concerning Constraint 1 and Rule 1 depended on whether reduced relative clauses and
non-finite VPs were assumed to contain traces and whether or not these traces were
assumed to be R1-pronouns. More generally, we identified the need for a clear defi-
nition of “R1-pronoun”: that is, whether we should include traces in relative clauses,
the implicit anaphoric elements of bridging references, and demonstrative pronouns
among the “pronouns” to which Rule 1 applies. This question isn’t mentioned in the
literature we know of, yet our results indicate that, for example, treating the implicit
anaphoric elements of bridging references or second-person pronouns as R1-pronouns
is a very bad idea.
Some of the issues raised by this study are relevant only for certain parameter in-
stantiations. One example is the specification of grammatical function ranking beyond
the simplest cases: for example, whether postcopular NPs in there-clauses should be
treated as subjects or objects (our results suggest the former) or how nominal mod-
ifiers should be ranked (we treated them as adjuncts). An issue for instantiations in
which utterances are identified with finite clauses is what the previous utterance is
when an embedded finite clause is in the middle of another finite clause, rather than
at the end, as in the following example, from the Guardian:
(25) But Hutchinson, who appointed Ranieri last season, today said that he
spent 30 minutes with the Italian after the Blackburn match and that
resignation was never an issue.
5.3.2 Separating Entity Coherence from CB Uniqueness. Starting with Brennan, Fried-
man, and Pollard (1987) and, more recently, Beaver (2004) and Kibble (2001) there have
been attempts to “unpack” some of the original preferences proposed by centering.
We feel this work has greatly helped our understanding of the theory and believe that
it would be similarly useful to unpack Constraint 1 into two separate claims, as well:
one about uniqueness of the CB, and one about entity coherence.
The first function of (both versions of) Constraint 1 is to claim that the CB is
unique. We will call this claim CB uniqueness:
CB Uniqueness: Utterances have at most one CB.
We have argued throughout the article that Strong Constraint 1 has a second function
as well: to express a preference for utterances that do not occur at the beginning of a
357
Poesio et al. Centering: A Parametric Theory
segment to mention at least one of the objects included in the previous utterance. Fol-
lowing Kibble (2000) and Karamanis (2001), we will call this second half of Constraint
1 (entity) continuity:
(Entity) Continuity: CF(U
i−1
) ∩ CF(U
i
) negationslash= ∅
Weak C1 is CB uniqueness, whereas Strong C1 is CB uniqueness plus continuity.
5.3.3 A Hybrid View of Coherence. One clear conclusion suggested by our results is
that entity-based accounts of coherence need to be supplemented by accounts of other
factors that induce coherence at the local level. The most direct way to do this would
be to include in continuity a longer list of factors that may link an utterance to its
previous one and claim that in order for an utterance to be “locally coherent,” at least
one of these factors must be present. The resulting claim would take a form along the
following lines:
Hybrid Continuity For every utterance U
i
, at least one of the following must
hold:
1. CF(U
i−1
) ∩ CF(U
i
) negationslash= ∅;
2. There is a rhetorical relation RR such that RR(U
i−1
,U
i
).
52
3. U
i−1
and U
i
are temporally coherent in the sense, for
example, of Kameyama, Passonneau, and Poesio (1993).
4. ...(other factors)
A more sensible approach, especially as we don’t yet know all the factors affecting
coherence, would be to be more explicit about the scope of centering theory, viewing
it not as a comprehensive account of “local coherence,” but only as an account of the
contribution of entity coherence to local coherence. In other words, we could view
(Entity) Continuity as only one among the preferences holding at the discourse level.
A natural way to formalize this would be to include Entity Continuity among a set of
constraints like those proposed by Beaver, which would also have to include further
constraints specifying preferences for rhetorical and temporal coherence.
5.3.4 CB Uniqueness. We saw in Section 4 that it’s fairly easy to fix the problem of
utterances’ violating Weak C1, or CB uniqueness: All that is needed is to strenghten
the requirements on the ranking function and require it to be total, which in turn can
be easily done by adding a disambiguation factor to ranking functions that aren’t total
like grammatical function. Before doing this, however, we should ask whether this is
the conclusion we should draw from the finding that CB uniqueness will be violated
with partial ranking functions—or if instead we should allow for utterances to have
more than one CB.
When multi-CB utterances such as (10) are considered, it is not immediately ob-
vious that one discourse entity (the corner cupboard) is more salient than the other
(Branicki), especially since neither occupies a particularly salient position either in the
previous utterance (u227) or in the current one (u229). Notice also that both entities
have been mentioned before; and furthermore, one of them is animate (Branicki), the
52 This formulation was intentionally designed in such a way as to finesse the issue of whether RR
should be an informational-level relation between the eventualities expressed by the utterances or a
genuine rhetorical relation between the speech acts performed by them.
358
Computational Linguistics Volume 30, Number 3
other inanimate (the cupboard). In these respects, these examples are reminiscent of
the examples that led Sidner (1979) to argue for two foci—sentences with one an-
imate entity (typically in agent position) and an inanimate one (typically in theme
position), like Mortimer sold the book for 10 cents or Mary took a nickel from her toy bank
yesterday. Although the results from studies such as Gordon, Grosz, and Gillion (1993)
suggest that when two animate entities are considered, only one tends to show RNP
effects, we are not aware of any experiment testing materials like those discussed by
Sidner.
The hypothesis that topicality is not restricted to one entity per utterance has been
advanced by a number of researchers, although it is perhaps most clearly associated
with the work of Givon (1983). Within the centering literature, abandoning the claim
that we call “CB uniqueness” has been suggested by Gundel (1998) and, more radically,
in work such as Strube (1998), Gordon and Hendrick (1999), and Tetreault (2001) in
which the whole notion of CB is abandoned.
As seen in Section 2, the primary motivation for CB uniqueness is complexity-
theoretic arguments: Inference in monadic logics is less expensive than in normal
logics (Joshi and Kuhn 1979; Joshi and Weinstein 1981). Grosz and colleagues’s lin-
guistic evidence for CB uniqueness is contrasts like those in (3), showing that failing to
pronominalize certain entities (Susan, in that example) is a more serious problem than
failing to pronominalize others (Betsy). This claim is further supported by the evidence
concerning the Repeated Name Penalty (Gordon, Grosz, and Gillion 1993). However,
the RNP is observed only in a subset of the cases that would be considered as CB
mentions according to the definition provided by Constraint 3, and in the example we
are discussing (10), neither Branicki nor the cupboard occur in (u229) in a position that
would be subject to RNP effects according to Gordon et al. In other words, (some)
evidence used by Grosz et al. in support of CB uniqueness cannot be used to argue
that (u229) in (10) has a single CB. This evidence is also consistent with a different
solution to the problem raised by examples like (10): Instead of attempting to preserve
CB uniqueness by requiring the ranking function to be total, one could abandon CB
uniqueness, as suggested in Givon (1983) and Gundel (1998). In both cases, we would
need a separate theoretical account of RNP effects. More empirical evidence is needed
on this issue.
53
5.3.5 Variety. The third conclusion suggested by our results is that ensuring variety
seems to be as important a principle in discourse production as maintaining coher-
ence. This is suggested, first of all, by the fact that only slightly over half of CBs are
realized as R1-pronouns. It is also the case that CBs are hardly ever continued for
more than two or three utterances; that the same discourse entity is very unlikely
to be realized using the same type of NP twice in a row (even with pronouns, we
only have 58 pronoun-pronoun sequences—26% of the total); and that two-thirds of
all transition sequences involve two different transitions. In fact, we wonder whether
that the repeated name penalty observed by Gordon et al. might not be an instance of
this more general phenomenon.
53 One way to reconcile the different findings would be to use different conceptual tools to characterize
the connection between subsequent utterances. Each utterance satisfying Continuity would have one or
more links to the previous utterance, that we might call centers of coherence; Entity Continuity would
then become a preference for the set of centers of coherence to be nonempty. In particular situations,
may be experimentally identified using the RNP as a test, one of the centers of coherence may acquire
a particular status, leading to a preference for pronominalization. We may call this center the center of
salience, say. It would also be interesting to examine the connection between a solution along these
lines and Sidner’s solution involving two foci.
359
Poesio et al. Centering: A Parametric Theory
Acknowledgments
Special thanks to Nikiforos Karamanis,
Alistair Knott, Mark Liberman, Ruslan
Mitkov, Jon Oberlander, Tim Rakow, and
the other members of the GNOME project:
Kees van Deemter, Renate Henschel, Rodger
Kibble, Jamie Pearson, and Donia Scott. We
also wish to thank James Allen, Jennifer
Arnold, Steve Bird, Susan Brennan, Donna
Byron, Herb Clark, George Ferguson,
Jeanette Gundel, Aravind Joshi, Eleni
Miltsakaki, Rashmi Prasad, Ellen Prince,
Len Schubert, Harold Somers, Joel Tetreault,
Lyn Walker, and audiences at the ACL 2000,
the University of Pennsylvania, the
University of Rochester, CLUK, and the
University of Wolverhampton for comments
and suggestions. The corpus presented here
was annotated by Debbie De Jongh, Ben
Donaldson, Marisa Flecha-Garcia, Camilla
Fraser, Michael Green, Shane Montague,
Carol Rennie, and Claire Thomson, together
with the authors. A substantial part of this
work, including the creation of the corpus,
was supported by the EPSRC project
GNOME, GR/L51126/01. Massimo Poesio
was supported during parts of this project
by an EPSRC advanced fellowship. Barbara
Di Eugenio was supported in part by NSF
grant INT 9996195, in part by NATO grant
CRG 9731157. Janet Hitzeman was in part
supported by the EPSRC project SOLE,
GR/L50341.

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