Current Theories of Centering for 
Pronoun Interpretation: 
A Critical Evaluation 
Andrew Kehler* 
SRI International 
We review the fundamental concepts of centering theory and discuss some facets of the pro- 
noun interpretation problem that motivate a centering-style analysis. We then demonstrate some 
problems with a popular centering-based approach with respect to these motivations. 
1. Introduction 
A central claim of centering theory (Grosz, Joshi, and Weinstein, 1995 henceforth GJW) 
is that certain entities mentioned in an utterance are more central than others, and 
that this property imposes constraints on a speaker's use of different types of ex- 
pressions to refer to them. To articulate some of these constraints, they define several 
fundamental centering concepts and propose rules based on them that should be fol- 
lowed by a speaker in producing coherent discourse. This work has led to several 
analyses employing centering theory and extensions of it, particularly in the area of 
pronoun interpretation (Kameyama 1986; Brennan, Friedman, and Pollard 1987; Di Eu- 
genio 1990, 1996; Walker, Iida, and Cote 1994; Strube and Hahn 1996, inter alia; see 
also citations within GJW, forthcoming papers in Walker, Joshi, and Prince in press, 
and psycholinguistic studies described in Hudson-D'Zmura 1989, Gordon, Grosz, and 
Gilliom 1993, and Brennan 1995). 1 In this squib, we discuss some facets of the pro- 
noun interpretation problem that motivate a centering-style analysis, and demonstrate 
some problems with a popular centering-based approach with respect to these moti- 
vations. 
2. Overview of Centering 
Centering theory is motivated by two related facts about language that are not ex- 
plained by purely content-based models of reference and coherence (cf. Hobbs \[1979\]): 
(1) that the coherence of a discourse does not depend only on semantic content but 
also on the type of referring expressions used, and (2) the existence of garden path ef- 
fects, in which pronouns appear to be resolved before adequate semantic information 
has become available: 
Pronouns and definite descriptions are not equivalent with respect to 
their effect on coherence. We conjecture that this is so because they 
* Artificial Intelligence Center, 333 Ravenswood Avenue, Menlo Park, CA 94025. E-mail: 
kehler@ai.sri.com 1 A draft of GJW, which revised and expanded ideas presented in Grosz, Joshi, and Weinstein (1983), 
was circulated as far back as 1986. Therefore some of the works described here as extending the work 
contained therein are dated prior to the published version. 
(~) 1997 Association for Computational Linguistics 
Computational Linguistics Volume 23, Number 3 
engender different inferences on the part of a hearer or reader. In 
the most pronounced cases, the wrong choice will mislead a hearer 
and force backtracking to a correct interpretation. (Grosz, Joshi, and 
Weinstein 1995, p. 207) 
GJW exemplify the first of these motivations with passages (1) and (2). Passage (1) is 
presumed to be in a longer segment that is currently centered on John. 
(1) a. He has been acting quite odd. (He=John) 
b. He called up Mike yesterday. 
c. John wanted to meet him quite urgently. 
The third sentence in this passage is quite odd, presumably because the more central 
element (John) is not referred to with a pronoun whereas the less central element 
(Mike) is. This passage can be compared to the similar passage in (2). 
(2) a. He has been acting quite odd. (He=John) 
b. He called up Mike yesterday. 
c. He wanted to meet him quite urgently. 
Although the propositional content expressed by these two passages is the same (the 
only difference being the expression used to refer to John in the subject of the third 
sentence), passage (2) is not jarring in the way that (1) is. 
GJW exemplify the second of these motivations with passage (3). 
(3) a. Terry really goofs sometimes. 
b. Yesterday was a beautiful day and he was excited about trying out his 
new sailboat. 
c. He wanted Tony to join him on a sailing expedition. 
d. He called him at 6AM. 
e. He was sick and furious at being woken up so early. 
Sentence (3e) causes the hearer to be misled: whereas common sense considerations 
indicate that the intended referent for He is Tony, hearers tend to initially assign Terry 
as its referent. Such examples suggest that more is involved in pronoun interpretation 
than simply reasoning about semantic plausibility. In particular, they suggest that 
hearers assign referents to pronouns before interpreting the remainder of the sentence. 
Details of Centering. In GJW's centering theory, each utterance Un in a discourse has 
exactly one backward-looking center (denoted Co(U,z)) and a partially ordered set of 
forward-looking centers (denoted Cf(Un)). Roughly speaking, Cf(U~) contains all enti- 
ties referred to in U~; among these is Cb(Un). Following Brennan, Friedman, and Pol- 
lard (1987), we refer to the highest-ranked forward-looking center as Cp(U,). 2 Cb(Un+D 
2 The issues pertaining to how the ordering of entities in Cf(U~) is determined have not been completely 
resolved. For the examples discussed in this paper, we can use the hierarchy of grammatical relations 
given by Brennan, Friedman, and Pollard (1987), in which the grammatical subject is ranked above all 
other grammatical relations (object, object2, and so forth). 
468 
Kehler Centering for Pronoun Interpretation 
is by definition the most highly ranked element of Cf(U,) realized in U~+I. Three in- 
tersentential relationships between a pair of utterances U, and Un+l are defined: 
. 
. 
. 
Center Continuation: Cb(Un+l) = Cb(Un) = Cp(Un+l). In this case 
Cb(Un+1) is the most likely candidate for Cb(Un+2). 
Center Retaining: Cb(Un4-1) = Cb(Un), but Cb(Un+l) 7 t Cp(Un+l). In this 
case Cb(Un+l) is not the most likely candidate for Cb(Un+2). 
Center Shifting: Cb(Un+l) # Cb(U,). 
The following rules are proposed in GJW: 
Rule 1 
If any element of Cf(Un) is realized by a pronoun in utterance Un+l, then Cb(Un+l) 
must be realized as a pronoun also. 
Rule 2 
Sequences of continuations are preferred over sequences of retaining; and sequences 
of retaining are to be preferred over sequences of shifting. 
The use of Rule 1 is illustrated by the oddness of passage (1) as compared to 
passage (2), because in (lc) the Cb (John) is not pronominalized whereas a non-Cb 
(Mike) is. The examples GJW give to illustrate Rule 2 are shown in passages (4) and 
(5). 
(4) a. John went to his favorite music store to buy a piano. 
b. He had frequented the store for many years. 
c. He was excited that he could finally buy a piano. 
d. He arrived just as the store was closing for the day. 
(5) a. John went to his favorite music store to buy a piano. 
b. It was a store John had frequented for many years. 
c. He was excited that he could finally buy a piano. 
d. It was closing just as John arrived. 
Like passages (1) and (2), passages (4) and (5) express the same propositional con- 
tent, yet they are not equally coherent. Whereas passage (4) consists of a sequence of 
Continue relations centered on John, passage (5) is marked by movements between 
Continuing and Retaining, which gives the effect that the passage flips back-and-forth 
between being about John and being about his favorite music store. 
Rule 1 is presented as a constraint on center realization, and Rule 2 as a con- 
straint on center movement. As formulated, the predictions these rules make about 
the preferred referents of pronouns are fairly limited. 3 For instance, Rule 1 makes no 
3 GJW do not make any specific proposals for using Rules 1 and 2 for pronoun interpretation. In 
Section 3, we discuss a particular utilization of these rules for pronoun interpretation proposed by 
Brennan, Friedman, and Pollard (1987). An apparently popular misconception attributes this utilization 
to GJW, however neither the draft nor final versions of GJW put forth such a proposal. See also GJW 
(1995, p. 215, footnote 16). 
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Computational Linguistics Volume 23, Number 3 
Table 1 
Transitions in the BFP algorithm. 
G(uo+I) = G(u°) G(un+~) # G(un) 
or unbound Cb(Un) 
Cb(Unq-1) = Cp(Unq-1) 
Cb(Un+l ) # Cp(Unq-1) 
Continue Smooth-Shift 
Retain Rough-Shift 
predictions about the preferred referents of the pronouns in sentence (3d), nor does 
it predict the garden path effect in sentence (3e); in each case the rule is satisfied 
assuming either possible assignment of referents to the pronouns. 4 
3. The BFP Algorithm 
Brennan, Friedman, and Pollard (1987, henceforth BFP) describe an algorithm for pro- 
noun interpretation based on centering principles, which is also utilized in Walker, 
Iida, and Cote (1994, henceforth WIC). In addition to Rule 1, BFP utilize Rule 2 in 
making predictions for pronominal reference. They augment the transition hierarchy 
by replacing the Shift transition with two transitions, termed Smooth-Shift and Rough- 
Shift, which are differentiated on the basis of whether or not Cb (U,+I) is also Cp (U,+I).5 
3a. Smooth-Shift: Cb(Un+l) = Cp(Un+l), Cb(Un+l) ~;~ Cb(Un). 
3b. Rough-Shift: Cb(Un+l) # Cp(Un+l), Cb(U~+I) # Cb(U~). 
They redefine Rule 2 as follows: 
Rule 2 
Transition states are ordered. CONTINUE is preferred to RETAIN is preferred to 
SMOOTH-SHIFT is preferred to ROUGH-SHIFT. 
The resulting transition definitions are summarized in Table 1. 
Given these definitions, their algorithm (as described in WIC) is defined as follows: 
1. 
2. 
. 
GENERATE possible Cb-Cf combinations 
FILTER by constraints, e.g., contra-indexing, sortal predicates, centering 
rules and constraints 
RANK by transition orderings 
The pronominal referents that get assigned are those which yield the most preferred 
relation in Rule 2, assuming Rule 1 and other coreference constraints (gender, num- 
ber, syntactic, semantic type of predicate arguments) are not violated. This strategy 
4 A case in which Rule 1 does make a prediction is given in example (i); assigning Sam as the referent of he 
causes a violation whereas assigning John does not. 
(i) a. John introduced Bill to Sam. 
b. He seemed to like Bill. 
I thank an anonymous reviewer for bringing this example to my attention. 5 The terms Smooth-Shift and Rough-Shift were introduced in WIC. 
470 
Kehler Centering for Pronoun Interpretation 
correctly predicts that He and him in sentence (3d) refer to Terry and Tony respec- 
tively, since this assignment results in a Continue relation whereas the Tony/Terry 
assignment results in a less-preferred Retain relation. Their rules also account for the 
oddness of sentence (3e), since assigning he to Tony results in a Smooth-Shift whereas 
assigning he to Terry results in a Continue. Therefore, the algorithm makes the correct 
predictions regarding example (3), one of the central motivating examples of centering 
theory. 
Problems with the BFP Algorithm. The fact that the BFP algorithm predicts the garden 
path effect exhibited by sentence (3e) is particularly indicative that it embodies the 
motivations for centering theory. As we noted in Section 2, such effects distinguish 
centering-based approaches from purely content-based models of reference and coher- 
ence (Hobbs 1979, inter alia). As Brennan (1995) explains: 
While knowledge-based theories often succeed in resolving referring 
expressions in this manner \[=using semantic information and world 
knowledge, without taking advantage of the kinds of syntactic con- 
straints that centering uses\], they do not model human discourse pro- 
cessing. An entirely knowledge-based algorithm would not reproduce 
an addressee's immediate tendency to interpret a pronoun as cospec- 
ifying the backward center, even when this results in an implausible 
interpretation. (Brennan 1995, p. 145) 
However, other examples demonstrate that the BFP algorithm also cannot model an 
addressee's immediate tendency to interpret a pronoun, and therefore cannot properly 
account for the pronoun interpretation preferences that result from such tendencies. 
To illustrate, we consider a modification to passage (3), shown in passage (6), with 
three possible follow-ons (6el-e3). 
(6) a. Terry really gets angry sometimes. 
b. Yesterday was a beautiful day and he was excited about trying out his 
new sailboat. 
c. He wanted Tony to join him on a sailing expedition, and left him a 
message on his answering machine. \[Cb=Cp=Terry\] 
d. Tony called him at 6AM the next morning. \[Cb=Terry, C,=Tony\] 
el. He was furious for being woken up so early. 
e2. He was furious with him for being woken up so early. 
e3. He was furious with Tony for being woken up so early. 
Sentence (6d) constitutes a Retain, in which CF(U6d) is Tony and Cb(U6d) is Terry. 
Retains often result in an ambiguity based on whether a subsequent subject pronoun 
refers to Cb(U,,) (resulting in a Continue) or to C,(U,) (resulting in a Smooth-Shift). 
While the subject pronouns in follow-ons (6e1-e3) may all display this ambiguity to a 
certain degree, the preferences associated with them appear to be consistent among the 
three variants. 6 That is, the initial preference for the subject pronominal He in sentence 
6 The author and several informants prefer the subject pronoun to refer to Tony initially, causing a 
garden path effect in each case. Aside from this, there may be a subtle processing difference between 
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Computational Linguistics Volume 23, Number 3 
Table 2 
Centering analysis of sentences (6el-e3). 
Sentence Subject Referent Cb(U7el) Cp(U7ei) Result Preference 
6el Terry Terry Terry Continue Terry 
Tony Tony Tony Smooth-Shift 
6e2 Terry Tony Terry Rough-Shift Tony 
Tony Tony Tony Smooth-Shift 
6e3 Terry Tony Terry (#) Rule 1 Violation ?? 
(Rough Shift) 
Tony Tony Tony (*) Condition C 
Violation 
(6e0 does not appear to be affected by the subsequent inclusion of the phrases with 
him in variant (6e2) and with Tony in variant (6e3). This accords with the observation 
that hearers have an immediate tendency to resolve subject pronouns based on the 
existing discourse state, before the entire sentence is interpreted. 
Within the BFP algorithm, however, the ways in which these follow-ons are ana- 
lyzed differ radically, as summarized in Table 2. In follow-on (6e0, assigning He=Terry 
results in a Continue whereas assigning He=Tony results in a Smooth-Shift, and so 
Terry is preferred. In follow-on (6e2), assigning He=Terry results in a Rough-Shift 
whereas assigning He=Tony again results in a Smooth-Shift, and so Tony is preferred. 
The reason for this difference is attributable solely to the fact that the pronoun him 
occurs in (6e2): because there are two non-coreferring pronouns in (6e2), one must refer 
to Tony, and because Tony is Cp(U6d), by definition Tony is Cb(U6e2) instead of Terry. 
Finally, in sentence (6e3), the assignment of He=Terry results in a Rule 1 violation--the 
Cb Tony is not pronominalized whereas Terry is--putting it in the company of highly 
awkward examples such as passage (1). If we ignore this violation, the resulting tran- 
sition is again a Rough-Shift, the lowest-ranked relation. (The assignment of He=Tony 
is ruled out by a syntactic constraint violation.) 
These varied results are inconsistent with the aforementioned facts concerning 
these passages in both empirical and theoretical respects. Empirically, the results are 
counter to the more consistent preferences associated with the subject pronouns in each 
case. Theoretically, such consistency is just what one would expect given a hearer's 
immediate tendency to resolve subject pronouns based on the existing discourse state. 
In either regard, it is unclear why the inclusion of the phrases with him in variant (6e2) 
and with Tony in variant (6e3) should lead to such varied predictions for the subject 
pronoun. In fact, the example illustrates a general property of the BFP algorithm: that 
the preferred assignment for a pronoun in such examples, even in subject position, 
cannot be determined until the entire sentence has been processed. This property re- 
sults from the fact that determining the transition type between a pair of utterances 
Un and Un+l requires the identification of Cb(Un+l), and a noun phrase (pronominal 
or not) can occur at any point in the utterance that will alter the assignment of Cb(Un+l). 
This is what occurs in the analysis of passage (6): whereas the Cb of sentence (6el) is 
these sentences in that any garden path in sentence (6e3) may be resolved earlier than in (6el) and (6e2), 
specifically, at the point at which Tony is reached. This is a result of the fact that syntactic constraints on 
coreference can be used to eliminate the possibility of He referring to Tony at that time, whereas in the 
other cases it is semantic information that comes later in the sentence that eliminates Tony as a referent. 
472 
Kehler Centering for Pronoun Interpretation 
Terry assuming He refers to Terry, the occurrence of him later in the sentence in (6e2) 
and similarly Tony in (6e3) causes the Cb to be Tony, thus changing the bindings that 
constitute the various transition possibilities, and in this case, the predicted preferred 
referents. To be clear, this is not an issue regarding the efficiency nor the cognitive 
reality of BFP's particular algorithm; in fact neither BFP nor WIC make any claims to 
these effects. The problem lies more generally in their proposal to utilize Rule 2 along 
with the definition of Cb(Un+l) to interpret pronouns--any algorithm incorporating 
this proposal will have to process an entire sentence before determining the preferred 
referents of pronouns; no reordering of processing within the BFP algorithm can alter 
this fact. The need to process an entire sentence to recover pronoun assignments, how- 
ever, is one that GJW and Brennan (1995) argue against in motivating centering over 
purely content-based models of reference and coherence. That is, this very property 
renders such an approach incapable of modeling the preferences associated with an 
addressee's immediate tendency to interpret pronouns, as example (6) demonstrates. 7 
Preferences and Other Intersentential Relationships. The motivations for centering cited 
by GJW and Brennan (1995) reflect the intuition that salience plays a central role 
in pronoun interpretation. What remains at issue is the manner in which salience is 
utilized by the pronoun interpreter. In the previous section we argued that BFP's use 
of Rule 2 along with the transition definitions and definition of Cb does not provide 
the correct utilization. In fact, the only aspects of Un and Un+ 1 utilized by the BFP 
algorithm are the identities of Cb(U,), Cp(Un), Cb(Un+l), and Cp(U~+I), as well as the 
types of expressions used to refer to them. Here, we argue that this is also insufficient. 
There is a well-known contrast between passages that are coherent by virtue of 
being a narration, as is the case for sentence (7c) and follow-on (7d), versus those 
coherent by virtue of parallelism, as is the case for sentence (7c) and follow-on (7d'). 
(7) a. The three candidates had a debate today. 
b. Bob Dole began by bashing Bill Clinton. 
c. He criticized him on his opposition to tobacco. 
d. Then Ross Perot reminded him that most Americans are also anti- 
tobacco. 
d'. Then Ross Perot slammed him on his tax policies. 
The preferred referent for the pronoun in example (7d) is Bob Dole, whereas the 
preferred referent for the pronoun in example (7d') is Bill Clinton. However, each 
passage shares sentences (7a-c), and therefore Cp(UTc) and Cb(U7c) are the same for each 
follow-on. Furthermore, each follow-on contains a new subject (Ross Perot, who will be 
7 In order to model this tendency in the BFP algorithm, one might consider a strategy in which provisional 
referents are assigned to pronouns while proceeding left-to-right in the current utterance. 
Under such a strategy one could assume that Cb(Un+ 1) is computed incrementally using the 
assumption that no additional elements will appear in Un+l that are more highly ranked in Cf(Un). 
Then, garden paths would be predicted when this assumption does not hold and the assignment of Cb (Un+1) 
must be changed, in addition to those caused by semantic influences such as in sentence (3e). 
Again, however, this strategy would treat follow-ons (6el) and (6e2) quite differently. This strategy 
would predict no garden path effect for follow-on (6el), since it assigns Terry as the referent of he and 
sticks with it. On the other hand, (6e2) should be much worse because two garden paths would be 
predicted: one for changing Cb(Un+I) from Terry to Tony when the pronoun him is processed, and 
another for the semantic information subsequently preferring Terry. This difference does not appear to 
be reflected in the actual judgements for these two examples (in both cases we find a similar garden 
path effect), although experimental evidence would be required to confirm these judgements. 
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Computational Linguistics Volume 23, Number 3 
the new Cp) and an object pronoun (the referent of which will be the new Cb). Therefore, 
because the relevant Cb and Cp relations are the same, a BFP-style approach cannot 
distinguish between these cases, s These examples show that pronominal reference 
preferences are affected by additional types of intersentential relationships that may be 
identifiable at the time a pronoun is encountered; proposals along these lines include 
preference-ranking schemes (e.g., Kameyama \[1996\]) and systems in which salience 
and the process of determining coherence relations interact (e.g., Kehler \[1995\]). 
4. Conclusions 
The pronoun resolution preferences that result from an addressee's immediate ten- 
dency to interpret a pronoun motivate pursuing a centering-based approach. How- 
ever, certain examples demonstrate that BFP's utilization of the centering rules does 
not model this tendency, which in turn limits the ability of their algorithm to account 
for the data. Furthermore, data has been presented that shows that in addition to the 
salience factors utilized by BFP, additional types of intersentential relationships must 
be taken into account. 
Acknowledgments 
The author thanks Barbara Grosz, David 
Israel, Megumi Kameyama, Christine 
Nakatani, Gregory Ward, and four 
anonymous reviewers for helpful comments 
and discussions. This research was 
supported by National Science 
Foundation/Advanced Research Projects 
Agency Grant IRI-9314961 to SRI 
International and National Science 
Foundation Grant IRI-9404756 to Harvard 
University. 
References 
Brennan, Susan E. 1995. Centering attention 
in discourse. Language and Cognitive 
Processes, 10:137-167. 
Brennan, Susan E., Marilyn W. Friedman, 
and Carl J. Pollard. 1987. A centering 
approach to pronouns. In Proceedings of the 
25th Meeting of the Association for 
Computational Linguistics, pages 155-162. 
Di Eugenio, Barbara. 1990. Centering theory 
and the Italian pronominal system. In 
Proceedings of the 13th International 
Conference on Computational Linguistics 
(COLING-90), pages 270-275. 
Di Eugenio, Barbara. 1996. The discourse 
functions of Italian subjects: a centering 
approach. In Proceedings of the International 
Conference on Computational Linguistics 
(COLING-96). 
Gordon, Peter C., Barbara J. Grosz, and 
Laura A. Gilliom. 1993. Pronouns, names, 
and the centering of attention in 
discourse. Cognitive Science, 17(3):311-347. 
Grosz, Barbara J., Aravind K. Joshi, and 
Scott Weinstein. 1983. Providing a unified 
account of definite noun phrases in 
English. In Proceedings of the 21st Conference 
of the Association for Computational 
Linguistics (ACL-83), Cambridge, MA. 
Grosz, Barbara J., Aravind K. Joshi, and 
Scott Weinstein. 1995. Centering: A 
framework for modelling the local 
coherence of discourse. Computational 
Linguistics, 21(2). 
Hobbs, Jerry. 1979. Coherence and 
coreference. Cognitive Science, 3:67-90. 
Hudson-D'Zmura, Susan. 1989. The Structure 
of Discourse and Anaphor Resolution: The 
discourse center and the roles of nouns and 
pronouns. Ph.D. thesis, University of 
Rochester. 
8 The BFP approach prefers Bob Dole as the referent for the pronoun in each case. Note that passage (7) 
with follow-on (7d') contradicts BFP's (page 157) and WIC's (page 223) claim that constraints based on 
structural parallelism, such as Kameyama's (1986) property-sharing constraint, are epiphenomena of 
BFP's ordering of the Cf and preference for Continue interpretations, since such constraints predict that 
Bill Clinton is the referent of him, not Bob Dole. Note also that an appeal to semantic plausibility 
factors to alter the preferences for example (7d') will not work, since it is at least as plausible that Perot 
would slam Dole on his tax policies as it is that he would slam Clinton. 
Suri and McCoy (1994) also provide minimal pairs that are problematic for BFP, which their 
algorithm correctly handles. However, their algorithm also cannot distinguish between the above pair, 
preferring Bill Clinton as the referent in both cases. 
474 
Kehler Centering for Pronoun Interpretation 
Kameyama, Megumi. 1986. A 
property-sharing constraint in centering. 
In Proceedings of the 24th Annual Meeting of 
the Association for Computational Linguistics, 
pages 200-206, New York. 
Kameyama, Megumi. 1996. Indefeasible 
semantics and defeasible pragmatics. In 
M. Kanazawa, C. Pifion, and H. de Swart, 
editors, Quantifiers, Deduction, and Context. 
CSLI, Stanford, CA, pages 111-138. 
Kehler, Andrew. 1995. Interpreting Cohesive 
Forms in the Context of Discourse Inference. 
Ph.D. thesis, Harvard University. 
Strube, Michael and Udo Hahn. 1996. 
Functional centering. In Proceedings of the 
34th Conference of the Association for 
Computational Linguistics (ACL-96), Santa 
Cruz, CA, June. 
Suri, Linda Z. and Kathleen E McCoy. 1994. 
RAFT/RAPR and centering: A 
comparison and discussion of problems 
related to processing complex sentences. 
Computational Linguistics (Squibs and 
Discussions), 20(2):301-317. 
Walker, Marilyn, Aravind Joshi, and Ellen 
Prince, editors. In press. Centering in 
Discourse. Oxford University Press. 
Walker, Marilyn A., Masayo Iida, and 
Sharon Cote. 1994. Japanese discourse 
and the process of centering. 
Computational Linguistics, 20(2). 
475 
