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Anaphoric Cues for Coherence Relations

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In this paper, we focus on the way how the rhetorical discourse structure of texts, in terms of coherence relations, and different types of referring expressions depend on each other. In particular, we concentrate on the impact the resolution of anaphora has on the derivation of coherence relations. We introduce an algorithm which combines such analyses and provide a preliminary evaluation of its empirical validity.
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Anaphoric Cues for Coherence Relations
Holger Schauer and Udo Hahn
Text Understanding Lab
Freiburg University, Germany
http://www.coling.uni-freiburg.de
Abstract
In this paper, we focus on the way how the rhetori-
cal discourse structure of texts, in terms of coherence
relations, and different types of referring expressions
depend on each other. In particular, we concentrate
on the impact the resolution of anaphora has on the
derivation of coherence relations. We introduce an
algorithm which combines such analyses and provide
a preliminary evaluation of its empirical validity.
1 Introduction
Models of discourse structure typically distinguish be-
tween the micro level of cohesion and the macro level
of coherence. A common means to establish cohe-
sion is by way of coreference (Halliday & Hasan 76).
In Example (1-b), the pronominal
“it”
refers to
“the
Vaio F190”
, just like the definite noun phrase
“the
notebook”
or the bridging anaphora
“the batteries”
[of
“the Vaio F190”
].1Such reference relations im-
pose accessibility constraints on the resolution of sub-
sequent anaphora, e.g.,
“weight”
in (1-c) should no
longer be accessible after (1-d) has been processed.
However, the referential relationships between objects
are usually semantically poor, i.e., finding the an-
tecedent for an anaphoric expression adds few, if any
significant semantic information to the analysis.
(1) a.
The Vaio F190

offers fine equipment.
b.
It

comes with a DVD-ROM drive and a 6
GB harddisk.
c.
Still
the notebook

has a weight of only 6
lbs.
d.
Its

14”-display shows very bright colors
with clear contrasts.
e.
The batteries

last two hours.
In contrast, work on the coherence of texts is con-
cerned with semantically rich relations among dis-
course entities as evidenced by coherence relations
like Cause or Evaluation.2For instance, (1-a) might
1The referee is marked by the lower index, while the type of
referring expression is indicated by the upper index, where

stands for pronominal anaphora,

for nominal anaphora and

for bridging anaphora.
2We draw on the repertoire of coherence relations as pro-
posed in the framework of Rhetorical Structure Theory (Mann &
be taken to Evaluate (1-b). Rhetorical Structure The-
ory [RST] (Mann & Thompson 88) distinguishes be-
tween relations that relate equally important units and
those that relate a more important (nucleus) and a less
important unit (satellite). Such structural prescrip-
tions lead naturally to a tree-like analysis of a text’s
rhetorical discourse structure.
Recent research on computing coherence relations
relies very much on so-called discourse cues, i.e.,
words or phrases explicitly hinting at a particular dis-
course relation (Knott & Dale 94; Marcu 97). The
conjunction
“still”
, e.g., in Example (1-c) can be taken
to indicate a Concession relation between (1-b) and
(1-c). In our work, however, we found that discourse
cues might not always be sufficient. Moreover, while
cue phrases may signal which coherence relation is
appropriate, they usually do not determine the target
unit to which a new unit should be attached. There-
fore, it may be rewarding to consider the possible con-
tribution of further cohesion devices to a text’s coher-
ence structure. While referring expressions are gen-
erally seen as such a cohesive device, there is only
little work on how coreference relations might influ-
ence the creation of the discourse structure in terms of
coherence relations. We address exactly this point.
2 Empirical Considerations
2.1 Reconsidering the Relevance of Cue Phrases
In a first round of experiments, we tested whether cue
phrases are a reliable indicator for the presence of co-
herence relations, as argued for by (Knott & Dale 94;
Marcu 97). We examined 37 texts, taken from a cor-
pus of German-language information technology test
reports. This gave us a total of about 6,850 text to-
kens, which we annotated manually using a version
of RSTTOOL (Marcu et al. 99) that we had previ-
ously augmented with methods for the annotation of
cue phrases and coreferences.
The RST analyses were performed by the first au-
thor and one student, based on the considerations from
Thompson 88). These relations appear emphasized and Capital-
ized.
Section 3. In case of annotation conflicts, the two
coders discussed and then consensually merged diver-
gent RST annotations. Finally, we ended up with 609
elementary units and 408 complex units, all related by
549 coherence relations.
Next, we determined the number of cue phrases ap-
plying an intentionally benevolent policy. Whenever
we found that the assignment of some coherence rela-
tion was probably due to such a phrase, we counted it
as justified by a cue phrase. For the 549 relations, a to-
tal of 118 cue phrases were identified on that assump-
tion. Still, some relations such as Joint provide only
weak semantic contributions and are never explicitly
marked by cue phrases. Hence, 95 occurrences of
such relations were also not taken into consideration.
This leaves us with

(61.2%) semantically rich co-
herence relations that remain lexically unmarked. At
least for our text sample, cue phrases do not seem to
constitute a sufficiently reliable indicator of a text’s
discourse structure. So, additional criteria for identi-
fying coherence relations need to be considered.
2.2 Interaction Patterns of Reference and
Coherence Relations
Referential relations between nominal expressions
can be established by different means, such as pro-
nouns (including relative pronouns), proper names or
definite noun phrases, all of which rely on some rela-
tion of object identity. A complementary phenomenon
are bridging anaphora (Hahn et al. 96), as illustrated
by
“the batteries”
[of
the Vaio F190
] in Example (1),
which establish a particular conceptual relation be-
tween the discourse entities involved. Also important,
in our sample at least, are set-member (sm) relation-
ships. In Example (2), the different monitor variants
are all members of the set
‘three new monitor models’
.
(2) a.
Panasonic presented
three new monitor
models

.
b.
The LC50

is the low-budget model of the
new 15”-series.
c.
The LC50S

has additional speakers and
an USB-connection.
d.
Dressed in black,
the LC50SG

is the best-
looking model.
These phenomena may even interact. A definite noun
phrase can be a bridging anaphora to an entity just
mentioned, but at the same time it can be object-
identical to a discourse entity mentioned earlier. We
annotated all referential relations in such cases.
Given that an entity is referred to more than once in
a text, which expression should be marked as coref-
erential? Does, e.g., the nominal anaphor
“the note-
book”
in (1-c) refer to the pronominal
“it”
in (1-b),
or directly to
“the Vaio F190”
in (1-a)? (Cristea et al.
99) argue that the referring expressions in a text can be
seen as forming an equivalence class of expressions
that all make reference to the same entity. For our
purposes, we concentrate on two distinguished mem-
bers of this class: If more than one antecedent was
available for a referring expression, we marked the
antecedent that was closest in terms of textual prox-
imity (
“it”
in (1-b)), and also the one that was closest
if one would follow a path along the discourse struc-
ture (
“The Vaio F190”
in (1-a); cf. also Figure 1).
Antecedent Anaphoric
expression
Anaphoric
expression
Referential chainwith regard to textual adjacency
Closest antecedent wrt. rhetorical discourse structure
(Unspecified) RST−Relation
Figure 1: Direct Antecedents and RST
This leaves us with the question under which con-
ditions a referential link between two expressions
should be counted as justifying the structural configu-
ration of a coherence relation. After all, it is not suf-
ficient to count how many units containing coreferen-
tial expressions can be found. According to RST, if
a text is coherent, it can be analyzed completely in
a tree that spans the entire text. Now, two units con-
taining coreferential expressions are obviously always
connected by some path from one unit to the other
along the coherence relations. It is, hence, necessary
to consider whether the relationship between two dis-
course units is really due to coreference or to other
factors. “Other factors” in our evaluation boil down to
considering merely cue phrases. If one of the corefer-
ential units also contained a cue phrase, we replaced
the anaphoric expression with a non-coreferential ex-
pression. If this would make a different unit to con-
nect to more plausible, then the cue phrase is likely to
justify the coherence relation, not the coreference re-
lation. As a second criterion, we checked whether the
elimination of the cue phrase leads to the same struc-
tural configuration or requires subsequent changes. If
the configuration of the discourse structure has to be
changed, again the coreferential relation does not af-
fect the discourse structure under scrutiny.
It has also been claimed that the referential struc-
ture of a text and its discourse structure, in terms
of coherence relations, interact in such a way that
anaphora resolution should obey the so-called right
frontier principle (Webber 91). This means that
anaphora may refer only to entities that are accessible
at nodes of the right frontier of the discourse structure
tree. For the right frontier principle to be applicable, it
is necessary to promote antecedent candidates of nu-
clei upward to the group node that spans the complex
unit formed by the coherence relation and its units in
order to be accessible at all.
2.3 Data on Interactions of Reference and
Coherence Relations
For the set of 37 texts, we identified a total of
494 referential relations, which were categorized as
329 cases of object-identity relations, 103 bridging
anaphors and 62 set-member relations. The 494 re-
ferring expressions relate 386 out of 609 (elementary)
discourse units (63.4%). This number is lower than
the one of referential expressions, because sometimes
a unit carries more than one referring expression.
From the 386 coreferential units, only 129 (33.4%)
are structurally adjacent, i.e., the anaphoric unit bear-
ing the referring expression is directly connected (path
length=1) to the antecedent unit (cf. Figure 1). This
means that traversing the paths between the remain-
ing 257 coreferential units involves looking for an-
tecedents in group nodes, according to the right fron-
tier principle. Interestingly enough, from these 257
cases, 67 coreferential units are only reachable if one
violates the right frontier principle, i.e., the antecedent
is not part of a common parent group node.
Considering the 386 coreferential units and 118 cue
phrases, 53 units which contained a referring expres-
sion also contained a cue phrase. In 33 of these cases,
the complex units that can be justified by the occur-
rence of a cue phrase are formed by the clauses of sin-
gle sentences. In Example (3-b), the cue
“although”
and the syntactic construction establish a local Con-
cession relation.
(3) a.
The LC90S

by Panasonic is a 19”- display.
b.
Although
its

screen size of 482 mm corre-
sponds to a conventional 21”-monitor,
c.
considerably less space is required.
In such a case, the cue phrase is stronger than the
referential link so that the cue phrase has to be ac-
counted for first, with subsequent consideration of the
referential links, i.e., linking the entire sentence ((3-b)
and (3-c)) to (3-a).
65 units (10.7%) bear only cue phrases, and 159
units (26.1%) carry neither coreference nor cue phrase
indications and, hence, seem to require a lot of world
knowledge and heavy inferencing.
Summing up, [386-33 =] 353 units (58.0% of the el-
ementary units) contain coreferential expressions that
justify the selection of the units of coherence rela-
tions.
3 Discourse Structure Analysis
3.1 RST Revisited
RST focuses on a ‘pre-realizational’ structure, i.e.,
it is not primarily concerned with concrete, surface-
bound text phenomena. So it is often difficult to judge
the appropriateness of a discourse structure as the au-
thor’s intention is rarely fully revealed, neither to hu-
man annotators nor to NLP systems.3This is espe-
cially true for judging which aspect of an utterance is
considered by the author to be most crucial, though
such an interpretation is at the heart of the theory.
Since RST does not account for any explicit cue
from which the rhetorical structure of the discourse
may be derived, referential constraints like the depen-
dency of an anaphoric expression on its antecedent are
disregarded, too.4While this is not an issue for RST
as a theory per se, it is a prerequisite for any system
that must compute a text’s discourse structure. Con-
sider, e.g., the following fragment repeated from Ex-
ample (1):
(4) a.
The Vaio F190

offers fine equipment.
b.
It

comes with a DVD-ROM and a 6 GB
harddisk.
In classical RST, example (4-a) may stand in an Eval-
uation relation to (4-b). The definition of Evaluation
requires that the satellite evaluate the nucleus (cf. Fig-
ure 2).5However, this does not capture an obvious
case of structural dependency, viz. that the pronomi-
nal anapher
“it”
cannot be interpreted correctly with-
out the antecedent so (4-b) depends on (4-a).
In RST, this referential dependency can be ac-
counted for by analyzing (4-b) as giving Evidence
3(Mann & Thompson 88, p. 246) already acknowledge: “Dur-
ing analysis, judgments must be made about the writer or readers.
Since such judgments cannot be certain, they must be plausibility
judgments.”
4The same observation holds for syntactic constraints. As
(Webber et al. 99) point out, syntactic constraints that are associ-
ated with cue phrases also influence a text’s discourse structure.
5The depicted structures reflect standard RST schemata. The
arrow points at the nucleus.
Evaluation
Vaio F190 It
Figure 2: Structure of Evaluation
for (4-a) (cf. Figure 3). An Evidence relation ap-
plies when the hypothesis is the most important part,
i.e., the nucleus. Such an analysis, however, neglects
the attribute
“fine”
in (4-a), which is quite an explicit
evaluation.
Evidence
Vaio F190 It
Figure 3: Structure of Evidence
We therefore propose to change the focus of RST-
style theories and to incorporate such structural con-
straints within the representation of a text’s dis-
course structure. In Example (4), we introduce an
Evaluation-N(ucleus) relation which reflects that the
nucleus (4-a) evaluates the satellite (4-b). This pro-
posal covers the explicit structural dependency and al-
lows an analysis in terms of a relation which we con-
sider most adequate.
Evaluation−N
Vaio F190 It
Figure 4: Structure of Evaluation-N
3.2 Combining Coreference and Coherence
Relations within RST
In the annotated text sample, we found that when
two elementary discourse units contain coreferring
expressions, either these elementary units or the com-
plex discourse unit they participate in are usually con-
nected by a coherence relation which subordinates the
anaphoric unit. In the simplest case, this may be an
Elaboration relation, but further linguistic cues or in-
ferences might give rise to semantically “richer” re-
lations.6As we are mostly concerned with structural
configurations, accounting for these additional infer-
ences will not be an issue here (Schauer & Hahn 00).
6Section 5 shows that these cues or inferences are sometimes
strong enough to override the basic structural configuration, re-
sulting in a multi-nuclear configuration or even a subordination
of the unit which contains the antecedent.
When more than one coreference relation is in-
volved, things become more complex. Consider the
following example:
(5) a.
The LC90S
by Panasonic is a 19”-display.
b.
Although
its

screen size of 482 mm corre-
sponds to a conventional 21”-monitor,
c.
considerably less space is required.
d.
The device
can be attached to a video-
card via an USB-connector.
Obviously, the nominal anaphor
“the device”
in (5-d)
requires an antecedent. One reasonable choice could
be the pronominal
“its”
in (5-b), leading to a reso-
lution in terms of
“the LC90S”
. However, this is not
reflected in the discourse structure that seems most ap-
propriate (cf. Figure 5). The topic of (5-b) and (5-c)
(the
“size”
) is not further elaborated on in (5-d), so
one might say that a mini-segment boundary between
these two sentences is encountered. Hence, it would
also be incorrect to analyze (5-d) as an Elaboration of
(5a-c), because (5-d) elaborates only (5-a).
5a
5b
Elaboration
Concession
Elaboration
5c
5d
Figure 5: RST Analyses for Example (5)
Example (6) illustrates a preference for local at-
tachment.
(6) a.
Apple presented a new PDA,
the MessagePad
130
.
b.
The new display


has a surface that is
more durable than in prior versions.
c.
The background lighting

can be controlled
with a switch.
In (6-c)
“the background lighting”
is a bridging
anaphor to the
“the new display”
which is, in turn,
a bridging anaphor to the
“MessagePad 130”
.
“The
new display”
, however, introduces a new discourse
entity that is distinct from, though part of, the
“Mes-
sagePad”
. So, unit (6-c) is subordinated to (6-b) (cf.
Figure 6), because the referential dependency of
“the
background lighting”
should be resolved as locally as
possible. In contrast, in Example (5) there is no such
mediated dependency between the anaphoric expres-
sions in (5-d) and (5-b).
Elaboration
Elaboration
6a
6c6b
Figure 6: RST Analyses for Example (6)
Summing up, the structural configurations that we
typically found illustrate a preference to connect a
new unit to the highest node (Example (5)) that pro-
vides direct antecedents for the referring expression in
the new unit (Example (6)).
4 From Coreferences to Coherence
The configurations described in the previous sec-
tion naturally lead to a combined account of deriv-
ing a text’s rhetorical discourse structure and resolv-
ing its referring expressions. Basically, the algo-
rithm we propose exploits the successful resolution of
anaphoric expressions in order to determine the tar-
get discourse unit to which a new unit should be con-
nected. This, in turn, restricts the set of units which
must be searched for resolving further referring ex-
pressions.
The algorithm (cf. Figure 7) requires several ca-
pabilities for anaphora resolution. First, for a given
unit candidate (a clause) a set of noun phrases need
to be identified that may be anaphoric expressions
(anaphoric expressions), basically pronouns
and definite noun phrases. Second, some resolution
process (match(ana cand,ante list)) is nec-
essary in order to check whether an anaphoric expres-
sion can be resolved considering a given list of possi-
ble antecedents. Third, while not essential for the al-
gorithm, we assume some ordering on the antecedent
lists (centers forward(clause)) in line with,
say, centering theory (Grosz et al. 95).
The basic data structure to operate on is a node of a
tree. Leaf nodes represent elementary discourse units.
Their data field holds a list of nominal expressions that
are accessible for coreference resolution at that node.
The algorithm loops through all clauses of a text,
building up both the discourse tree and the antecedent
lists incrementally. Basically, whenever a new clause
is considered, the right frontier of the tree is checked
for plausible antecedents. First, the lowest rightmost
node is checked (lowest right node(tree))
for possible antecedents. If there is none, its prede-
cessor on that rightmost branch of the tree is checked
(predecessor(node)). In order to determine the
target node to which the new unit should be con-
nected to, one has to find all anaphoric expressions
(ana cand), i.e., all nodes on the right frontier that
contain an antecedent for the anaphoric expressions in
the new unit.
When all antecedent nodes are determined, the
highest node that provides antecedents for all re-
solvable anaphoric expressions in the new unit is
taken as the target node (find highest node-
matching all), in accordance with the discussion
in the previous section.
If a new unit contains no referential expression,
then the algorithm makes no prediction. If the node to
connect to has been found, the new unit is connected
to it, i.e., the new unit is established as a satellite to
the target unit. This way, the new unit opens a new
right-most branch and, hence, becomes the lowest-
right node of the tree. So, the new right frontier con-
sists of the newly attached unit (with its antecedent
list), the modified node (still bearing the same an-
tecedent list) and its predecessors.
5 Evaluation of the Algorithm
In Section 2.1 we already mentioned that 37 German
technical reports were segmented into 609 elementary
units, leading to 549 relations and 408 complex units.
We evaluated the performance of the implemented al-
gorithm from Figure 7 by judging based on our in-
tuition in how many cases the algorithm predicted
a structure that matched the one we felt most appro-
priate, and in how many cases the predictions seemed
implausible.
Obviously, when a new unit contains no coreferring
expression, the algorithm makes no prediction. This
is the case for 145 units out of 609 new units (23.8%).
65 of those units contained cue phrases, while the re-
maining cases seem to require rather complex infer-
ences to compute the target unit and their relation.
The algorithm determined a node to connect a new
unit to in 464 cases (out of 609 elementary units).
This number is smaller than the number of corefer-
ring expressions because the new unit that needs to be
connected can contain more than one coreferring ex-
pression. In 297 cases (64.0%) the prediction was cor-
rect, i.e., the predicted target node was the one we also
found most appropriate in the manual annotations.
In 167 cases (36.0%), however, the predictions
seemed implausible. From these cases, 81 were due
t r e e : = t re e ( c e n t er s f o r w ar d ( f i r s t ( c l au se s ) ) , NIL )
c la us es : = r es t ( c l au se s )
fo r al l c l a us e : = c l a us e s do
an a nod es : = a rr ay of l i s t s of no de s .
fo r al l a na c an d : = a n ap h or i c e x p r e ss i on s ( c l a us e ) do
nod e : = l o w e s t r i g h t n o d e ( t r e e )
while node do
if match ( a na c an d , a n t e l i s t ( node ) ) then
ana node s [ an a ca nd ] := append ( ana n odes [ ana cand ] , node )
fi
nod e : = p re de ce ss o r ( no de )
done
done
t a r ge t n o d e : = f i n d h i g h e s t n o d e m a t c h i n g a l l ( a n a n od e s )
/
found at l e a s t one a nt e c e de nt node
/
if t a rg e t no d e then
/
con n ect new un i t to old node
/
co nn ect ( t a rg e t n od e , t r ee ( c en te r s f or wa r d ( c la us e ) , NIL ) )
fi
done
Figure 7: Algorithm for the Integrated Computation of Coreferences and Coherence Structure
to cue phrases. Interestingly, 75 out of these 81 are
intra-sentential cases, i.e., the related units are clauses
within a single sentence (cf. Example (5-b) and (5-c)).
No wonder then that such intra-sentential phenomena
need to be accounted for prior to dealing with coref-
erences. When one first accounts for intra-sentential
discourse structure and only then considers the coref-
erence relations, the prediction of the target unit to
which this complex unit should be related is correct in
62 out of these 75 cases. Thereby the algorithm would
correctly predict [464+62 =] 526 cases (86.4%).
We cautiously interpret these results in two ways:
Either, it can be taken as a hint that the minimal size
of discourse units should be the entire sentence. Or, it
may indicate that intra-sentential coherence relations
should not be seen as restricting the availability of ex-
pressions for further anaphora resolution.
6 Discussion of Related Work
(Vonk et al. 92) argue that overly specific definite
noun phrases may signal segment boundaries. Their
data also suggests that pronouns tend to be used when
other means to signal thematic shifts are available.
The evidence we found and the evaluation of our al-
gorithm indicate that such thematic shifts occur quite
frequently without overly specific noun phrases.
(Corston-Oliver 98) modifies the cue phrase ap-
proach of (Marcu 97) similar to us. However, he does
not consider how several coreference relations inter-
act with the resulting discourse structure. Also, it re-
mains unclear how the correct target node to attach to
is identified in his approach.
Segmented Discourse Representation Theory
(Asher 93) provides a framework for dealing with
discourse structure which incorporates referential
accessibility constraints, too. Asher, however, does
not rely on coreferences for establishing target units.
Rather the derivation of a coherence relation (and
thereby of the target unit to connect a new unit to)
relies on quite abstract connections between “events”.
While recognizing coreference relations certainly re-
quires domain knowledge and inference capabilities,
too, recognizing connections between events seems
a very hard task. In contrast, our approach is more
light-weight by design, though more feasible.
(Webber 91) argues for the resolution of discourse-
deictic references along the right frontier of a dis-
course structure. In order to establish that structure
two basic operations on trees are proposed. Webber,
though, makes no clear commitment when to choose
which operation and how the resolution of references
influences the tree’s construction. (Webber et al. 99)
apply the same basic two operations for incorporat-
ing cue phrases in a TAG-driven approach to discourse
structure. Our algorithm may well be integrated with
their approach, e.g., to account for the cases of intra-
sentential phenomena discussed in the evaluation sec-
tion. Our approach, however, is incompatible with
Webber’s with respect to a single though crucial point:
The operations from (Webber 91) cannot account for
the structures discussed for Example (5) in Section
3.2. After adjoining (5b-c) to the root of (5), one can
attach or adjoin (5-d) only to (5b-c) or to (5a-c). This
reflects, however, a continuation of either segment,
against which we have argued (5-d) elaborates only
on (5-a).
The work of (Cristea et al. 99) on coreference and
discourse structure, though based on the original RST
model, has already revealed that the resolution of ref-
erential expressions can considerably benefit from fol-
lowing a text’s discourse structure. As the proposed
modifications to RST exactly aim at referential de-
pendencies, we expect to earn even higher benefits for
anaphora resolution with analyses made along the line
of our approach.
7 Conclusion
Coherence relations, though sometimes signalled by
explicit cue words (Knott & Dale 94; Marcu 97),
are basically a representational construct at the level
of conceptual text representation. In order to cope
with those cases which are marked by referential con-
straints, we focused on the role of anaphoric expres-
sions, basically within the framework of RST (Mann
& Thompson 88). We set out to overcome its lack of
capturing referential dependencies and worked out an
approach in which the automatic derivation of a text’s
discourse structure is made dependent on the resolu-
tion of coreferring expressions.
We presented an algorithm which computes the dis-
course structure of a text by using the successful res-
olution of referring expressions as an indicator for de-
termining the target units of coherence relations to
which new units should be connected. Our evalua-
tion yielded plausible predictions of a text’s discourse
structure in 64% of the cases. The algorithm must be
extended to handle cue phrases as well. To realize this
extension, the algorithm just has to be delayed until
the (intra-sentential) cue phrases have been accounted
for. Such an extension would increase the level of
plausible predictions of discourse structure up to 86%.
The combined algorithm has been implemented in the
text understanding system SYNDIKATE(Hahn & Ro-
macker 00) which already provides means for han-
dling referential relations of object-identity and bridg-
ing anaphora (Hahn et al. 96).
8 Acknowledgments
H. Schauer was supported by a grant from DFG within the Grad-
uate Programme Human and Machine Intelligence.
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