Rhetorical Distance Revisited
A pilot study
Christian Chiarcos1
Department of Linguistics
Applied Computational Linguistics
University of Potsdam
chiarcos@ling.uni-potsdam.de
Olga Krasavina2
Department of Linguistics
Humboldt University of Berlin
krasavio@rz.hu-berlin.de
Abstract
We present a general parametrized framework to implement current approaches on referential
accessibility in discourse whose parameters are to be trained on coreference and rhetorically
annotated corpora. The structuring of discourse plays an important role in use of anaphoric devices.
The results obtained by B. Fox (Fox 1987) suggest strong interaction between the embedding of
utterances into discourse structure and anaphoric accessibility. Furthermore, the effect of several
cues indicating discourse organization has been proved empirically (Givόn 1990:374). Recently, this
effect was questioned (cf. Tetreault and Allen 2003). Their results, however, can be attributed to
either objective irrelevance of discourse structure on intersentential anaphora or to a need of a more
fine-grained empirical analysis. Moreover, theories claiming the importance of discourse structure
differ with respect to their assumptions on discourse structuring and its limiting force on the search
for the antecedent. We focus on three proposals – the stack model (Grosz and Sidner 1986), veins
theory (Cristea 1998), and the rhetorical distance approach (Kibrik 2000). A general framework for
theories of intersentential accessibility in discourse is outlined:




A minimal set of parameters as a general framework is proposed.
The theories are reconstructed on the basis of the parameters as different configurations,
following the lines of Chiarcos and Krasavina (2005b).
A pilot study for comparative empirical evaluation is presented, using the Potsdam
Commentary Corpus (Stede 2004), a German newspaper corpus.
The interaction of rhetorical and referential distance is analysed, emphasizing the effect of
rhetorical distance on long-distance anaphora.
1 Accessibility in discourse
1.1 Motivation
The impact of discourse structure on anaphora has previously been noted, cf. Fox (1987).
However, discourse structure per se has been a controversial issue until now. Currently, there
are works suggesting that there is no hierarchical structure in some discourse genres (Sibun
1992), that this structure is domain-specific (Mann and Thompson 1988, Webber et al. 2003),
or that it is a surface phenomenon induced by local associations (Britton 2001). Other
proposals admit the overall importance of hierarchical organization of discourse, but interpret
it differently. So there are several theories positing quasi-syntactic rules at the discourse level,
1
2
Christian Chiarcos’ work has been supported by the DFG (German Research Foundation), GRK 275, project number 5220 8303.
Olga Krasavina’s work has been supported by grant #03-06-80241 from the Russian Foundation for Basic Research.
i.e. veins theory [VT] (Cristea et al. 1998), the stack model (Grosz and Sidner 1986), and –
similar to the latter – the right-frontier constraint (Polanyi 1988, Webber 1991, Asher 1993).
Different approaches disagree regarding which entities have to be considered as accessible
and inaccessible. Here, we focus on the production (generation) perspective, rather than
interpretation (anaphora resolution) perspective. Therefore, we bring three theories, Grosz and
Sidner 1986, Veins Theory (Cristea 1998) and the rhetorical distance approach (Kibrik and
Krasavina 2005) to a common ground, replacing the binary accessibility criterion by graduate
measurement using the notion of rhetorical distance. The predictive force of these theories is
evaluated on the corpus data: Potsdam Commentary Corpus (Stede 2004), a German
newspaper corpus.
1.2 Accessibility and distance
One of the main linguistic constraints on the use of pronouns is referential distance (RefD).
The term originates from Givόn (1983). It is a measurement which assesses "... the gap, in
number of clauses backward, between the referent's current text-location and its last previous
occurrence" (Givόn 1995:352).
RefD has been used as one of several heuristic measures of topicality in numerous inquiries,
especially of such phenomena as voice, word order and anaphora - processes all infuenced by
mental activation state of discourse referents (e.g. Jacennik and Dryer 1992). It has been
applied in corpus and psycholinguistic studies (Ravnholt 1996, Mitkov 1998), machine
translation, anaphora resolution and summarization studies. There are observations about
correlations of RefD and other factors, e.g. the type of anaphoric relation – "direct or indirect,
object or event-based" (Ravnholt 1996). By far, RefD remains the most commonly accepted
method of measuring distance in discourse.
The concept of purely referential distance was criticized – mostly because of the structures
under consideration. Givόn considered clauses, but in fields of practical application, such as
anaphora resolution, utterances and even words were considered (Walker 1998, Strube 1998).
Besides this, the existence of trans-sentential segments has been emphasized, thus giving rise
to notions of “structural distance” (Ariel 1991). In her application of this previously rather
vaguely defined concept, Fox (1987) concluded: “It is not simple distance that triggers the
use of one anaphoric device over the other. Rather, it is the rhetorical organisation of that
distance that determines whether a pronoun or a full NP is appropriate.”
1.3 Rhetorical Structure Theory in a nutshell
Our study builds on the framework of RST, Rhetorical Structure Theory (Mann and
Thompson 1988), a descriptive framework for discourse-structural analysis of text. RST relies
on the notion of text spans (discourse segments) as constituents of discourse. These are
connected by several schemata according to the following principles (Mann and Thompson
1987, p. 7f.):



completeness: The set contains one schema application that contains a set of text
spans that constitute the entire text.
connectedness: Except for the entire text as a text span, each text span in the analysis
is either a minimal unit or a constituent of another schema application of the analysis.
uniqueness: Each schema application consists of a different set of text spans, and
within a multi-relation schema each relation applies to a different set of text spans.
2
Figure 1. Example of a rhetorical tree (Fox 1987)

adjacency: The text spans of each schema application constitute one text span. Taken
together, these principles ensure RST analyses to be trees with text spans (discourse
segments) interpreted as nodes. Then, we refer to a text span consisting of several subconstituents their parent, with the sub-constituents being its children. Accordingly,
parents are located above their children in the graph.
A central aspect of RST is the investigation of nuclearity in discourse, i.e. the asymmetries
between the text spans that make up a more complex structure. Some elements, called nuclei,
are more important to the writer’s purpose, less easy to substitute and more necessary for the
understanding of a text. Unlike nuclei, satellites can be replaced without any significant
change to the text function. They depend in their meaning on other elements.
According to their nuclearity, two basic prototypes of schemata are distinguished:
mononuclear (subordinating) rhetorical relations with one nucleus and one satellite,
multinuclear (coordinating) rhetorical relations with several nuclei, but not satellites.
Minimal text spans, the terminal nodes of the tree, are referred to as elementary discourse
units (EDUs) here. EDUs are usually clauses (cf. Carlson et al. 2003). An example tree is
given in Figure 1, with three EDUs, A, B and C, where A and B form, connected by a
CIRCUMSTANCE relation, a larger discourse segment A-B. In turn, A-B and C are connected by
an EVIDENCE relation.
3
1.4 The impact of discourse structure on anaphora
Fox (1987) admits that under short distances (1-2 clauses) between a pronoun and its
antecedent, pronouns are mostly predicted by referential distance. However, not all types of
pronouns can be explained this way. Rather, the hierarchical structure of discourse seems to
affect the usage of pronouns. The tree in Figure 1 is an example of a “return-pop”, i.e. a type
of discourse tree, where a given proposition has some relation to the proposition on the upper
level of the discourse tree, rather than to the immediately preceding proposition. While B is
sequentially closer to C than A, it can be accessed discourse-structurally only by making a
detour over A. So, C is closer to A discourse-structurally. This can explain occurrences of
pronouns, which refer to clauses other than immediately preceding ones. Furthermore, Fox
shows that the approach suggested by Givόn (1983) produces overgeneration, because the
influence of the discourse-structural devices such as the beginning of a new rhetorical unit is
ignored. In the latter case, devices of higher explicity, i.e. full descriptions, rather than
pronominal forms, are preferred.
The most prominent family of approaches to consider is based on the right-frontier constraint
(Webber 1991, Asher 1993) that formulates a necessary condition for pronominal reference
(or anaphoric relations in general): anaphoric reference is possible only to those nodes that
directly dominate (or structurally precede) the actual segment. A classical formulation has
been given with the focus-stack model by Grosz and Sidner (1986). Here, anaphoric
accessibility is a consequence of the interplay of attentional and intentional structure:


The intentional structure induces a global hierarchical structuring of the text, where
different discourse segments are related by either coordinating SATISFACTIONPRECEDENCE or subordinating DOMINANCE relations, both are mono-directional.
The attentional structure then is defined as a stack induced by the intentional structure.
It comprises the potential antecedents of anaphors occurring in the current segment
that are grouped together in ”focus spaces” where each focus space is associated with
a dominating (or the actual) segment. Whenever a new segment is opened, the actual
focus space is pushed into the stack, if it is closed, it is popped out. Thus, focus spaces
are ranked according to the number of DOMINANCE relations between their segment
and the actual one.
Accessibility of a discourse segment for antecedent search depends on the depth of this
fragment in the stack. Projected to the RST tree, the DOMINANCE relation can be interpreted as
subordinating relations in the RST, as suggested by Moser and Moore (1996).
Another important theory is Veins Theory (Cristea et al. 1998). It states that the accessibility
of antecedents depends on so-called “veins” computed by special rules applied on an RSTlike graph. The status of a discourse unit – nucleus or satellite – plays the determining role,
but the relative order of discourse segments is taken into account as well. The type of
rhetorical relation is of no importance at all. Against the right-frontier proposals, veins theory
is directly built on RST. There, a crucial difference, as opposed to Grosz and Sidner (1986) is
the existence of left satellites that lack a formal representation in discourse structure.
Kibrik (2000) proposed a measurement of rhetorical distance, which is calculated using the
shortest path from an anaphor to its antecedent along the rhetorical tree. Although referential
4
distance also plays a certain role, Kibrik claims that rhetorical distance is a stronger factor
licensing the use of pronouns vs. definite NPs.
The theories presented so far share important common insights:




Depending on the rhetorical structure, an accessibility domain is constructed
(sequence of dominating segments in stack model, veins, paths).
An EDU is regarded as accessible iff. it is included in this domain.
The relative degree of accessibility of an antecedent-EDU can be calculated
considering the shortest path between an anaphor and a potential antecedent.
The distance between an anaphor and its potential antecedent on this path corresponds
to the likelihood that it serves as an antecedent.
We suggest that theory-dependent accessibility judgements can be modelled by assigning
weights to edges on this path depending on their respective types. Thus, such edge weights
are interpreted as parameters of a generalized framework of discourse-structural accessibility.
We provide a minimal set of parameters and show how to reconstruct the theories as different
configurations. The configurations are compared and generalizations are proposed. Finally,
we present a pilot study on the German newspaper corpus – the Potsdam Commentary Corpus
(Stede, 2004).
2 A parametrized framework
2.1 Trees and paths
Our approach builds on the following basic conventions:





We consider binary trees.
A node n CONTAINS a referring expression
o if it is an EDU and subsumes the expression, or
o if one of n’s direct children contains it.
We treat EDGES as elementary building blocks of path construction.
We consider vertical edges only, i.e. relations between a child and a parent node in the
rhetorical tree. No direct links between different child nodes are allowed.
We say, an edge POINTS FROM one node n1 TO another node n2 if
o n1 is the child node of n2 and n1 contains the anaphor (ASCENDING edge) or
o n1 is the parent node of n2 and n2 contains the antecedent (DESCENDING edge).
The underlying intuition is to construct an acyclic path, i.e. a sequence of edges, pointing
from one EDU A containing the anaphor to another EDU B containing a potential antecedent,
henceforth represented as A → B. Edges not on the path, i.e. pointing to/from text spans that
contain neither antecedent nor anaphor, are excluded.
In the following section, we sketch a minimal taxonomy of edge types that provides
parameters for the general framework. Note that we ignore the type of relation beyond the
distinction of mononuclear (asymmetric) and multinuclear (symmetric) relations.
5
2.2 Parameters
The intention of this paper has been to propose a minimal set of parameters as a base for the
comparison of previous approaches. This restriction is even more important for empirical
studies. Since corpora annotated with discourse structure and coreference are rare and small,
the number of parameters has to be minimized to prevent sparse-data problems.
In addition to the distinction between ascending and descending edges in the path to be
constructed, we suggest the following parameters to define necessary distinctions among
edges: whether a relation is mononuclear or multinuclear whether the child node serves as
satellite or nucleus of the dominating node (for a multinuclear relation, all child nodes are
defined as nuclei) whether the child node is left-most or right-most of the children (we
assume binary trees). As a convention, these four features of edges are encoded by edgelabels in the following way:




the first two letters denote nuclearity of the underlying discourse relation, i.e. mo
(mononuclear) or mu (multinuclear)
the third letter denotes the sequential position of the child node, i.e. l (left) or r (right)
the fourth letter denotes the type of the child node, i.e. s (satellite) or n (nucleus):
fifth letter denotes the direction of the edge, i.e. whether it is ascending a or
descending d
For example, mulnd denotes a multi-nuclear discourse relation, with the antecedent
(descending) in the left-most (nuclear) child-node, while morsa corresponds to a mononuclear discourse relation, with the anaphor (ascending) in the satellite that is the right-most
child node. Then, a path in a rhetorical tree can be represented as a sequence of edge labels,
beginning at the position of an anaphor and ending at the EDU containing the antecedent.
RHETORICAL DISTANCE (RhetD) between referential expressions in two EDUs is then defined
as the weighted sum of occurrences of labels in the path between them. A theory of
path(α,β)
=
(m
molna, morsa, mol nd, molnd, molnd)
rhet-dist(α,β) = wmolna + wmorsa + wmolnd + wmolnd + wmolnd
acc(α,β)
iff. rhet-dist(α,β) < τ
Figure 2: Example analysis
6
accessibility can then be represented by the choice of weights and threshold. An EDU B is
accessible from another EDU A if its RhetD is below an accessibility threshold τ:
accessible(A,B) iff. rhet-dist(A,B) < τ
The higher the RhetD of a potential antecedent node is, the lower is its relative degree of
accessibility.
3 Reconstructing previous attempts
Here, we present a set of parameters that is capable of achieving locally optimal
approximations and is thus adequate with respect to the stack model, veins theory and Kibrik
and Krasavina’s concept of rhetorical distance. Finally, a minimal set of parameters is used as
a basis for the comparative evaluation of the theories. We illustrate the adequacy of this
proposal by assigning different weightings to our set of parameters as configurations which
generate the necessary distinctions.
3.1 Grosz and Sidner (1986)
Previous interpretations of Grosz and Sidner’s model in RST terms (Moser and Moore 1996,
Tetreault and Allen 2003) agreed on the rough correspondence between RST-nuclearity and
DOMINANCE by Grosz and Sidner (1986), thus equating DOMINANCE relations with
mononuclear (subordinating) RST relations and SATISFACTION-PRECEDENCE with multinuclear
(coordinating) RST relations. This analysis is consistent with the partial mapping from Grosz
and Sidner’s model onto RST that has been suggested by Moser and Moore (1996:414),
where embedded segments in Grosz and Sidner (1986) are analyzed as satellites in RST. This
partial mapping has been extended by Marcu (2000:527f.) who proposed an isomorphic
mapping between DOMINANCE and RST-subordination, and a (mono-directional)
homomorphism transforming SATISFACTION-PRECEDENCE into multinuclear relations.
Nevertheless, RST structures and those assumed by Grosz and Sidner differ with respect to
their granularity. So, it seems that an interpretation of Grosz and Sidner’s discourse structure
and rhetorical structure in the sense of Mann and Thompson can be problematic. Generalizing
over these insufficiencies, we summarize the Grosz and Sidner (1986) model as follows:3



ascending from a nucleus and descending into a nucleus is always possible
ascending from a satellite is always possible
descending into a satellite node is not permitted
Then, the Grosz and Sidner (1986) configuration assigns every descending satellite edge (i.e.
molsd, morsd) the weight w molsd, morsd = 1, everything else the weight 0. If we
now compare the values calculated for rhetorical distance in the Grosz and Sidner (1986) –
configuration to the original binary criterion of accessibility, we find that an EDU is
accessible iff. its rhetorical distance is lower than 1, otherwise it is not. So, the accessibility
threshold τ is set to 1.
Note that Grosz and Sidner’s model cannot account for left satellites according to Cristea et al. (1998). One could assume
that left satellites in RST are not in a DOMINANCE relation, but in a SATISFACTION-PRECEDENCE relation or part of the same
discourse segment the nucleus belongs to as well. However, this interpretation conflicts with Marcu’s and Moser/Moore’s
view. With respect to the situation of n-ary branching relations, where sequential order among satellites does not necessarily
imply SATISFACTION-PRECEDENCE relations, another solution is to apply Marcu’s mapping onto left-branching satellites as
well, though such configurations could not have been expressed in the original Grosz and Sidner (1986) proposal.
3
7



The vein of the root is its head;
Let v be the vein of a non-terminal node with left child L (head hl and right child R (head hr);
The vein of L and R is defined as follows:
type of relation
nuclearity
veins of child nodes
L
R
L
R
multinuclear
NUC
NUC
v
v
mononuclear
NUC
SAT
v
v’ ◦ hr
mononuclear
SAT
NUC
v ◦ hr
(hl) ◦ v
Here, x ◦ y will produce a flat list comprising the heads enumerated in x and y according to
their respective linear order; x’ means to remove all elements marked by parentheses from
the vein x.
Table 1: Veins Theory schematically
3.2 Veins Theory
Veins Theory (Cristea et al. 1998) is a generalization of Centering Theory (Grosz et al. 1995)
that extends the applicability of centering rules by defining larger domains of accessibility
within a discourse tree. These domains, VEINS, are derived as follows:
1. In a bottom-up manner, a head is assigned to every node in the tree
(a) if an EDU is a terminal node, its head is its unique ID label,
(b) if an EDU has one nuclear child node (mononuclear node), its head is the head
of its nucleus
(c) if an EDU has several nuclear child nodes (multinuclear node), its head is the
concatenation of the heads of its nuclear children.
2. Then, the vein is calculated top-down using the heads derived so far, see Fig. 2
3. For an EDU with label u, all EDUs that are in the vein of u and precede u
sequentially are defined as accessible.
The rules can be interpreted as follows:



Nuclei are always accessible (m
mulna, murna, mulnd, murnd, molna,
morna, molnd, mornd).
Right satellites are inaccessible as antecedents (m
morsd).
Left satellites (m
molsd) are accessible only from the subtree dominated by the
corresponding nucleus, but not from right-branching satellite nodes (m
morsa).
Thus, the combination of molsd and morsa has to be prohibited. Further, multiple morsa
edges are allowed, while multiple molsd edges are not. We assign molsd a large constant as
a weight and morsa a small one, with wmolsd + wmorsa as the threshold of accessibility; morsd
is always inaccessible, thus, it must be given a weight larger than wmolsd + wmorsa. Every other
type of edge is accessible. A limitation of our proposal is its local character. As an example,
descending into a satellite is always impossible except in the root node. To approximate this
behaviour, we assign every descending edge a small additional weight (smaller than wmorsa).
8
3.3 Kibrik’s measurement of rhetorical distance
The underlying idea in Kibrik’s approach is that given a pair of EDUs with one containing a
potential antecedent and the other one containing a potential anaphor, a path is constructed
pointing from the potential anaphor to the potential antecedent. Then, rhetorical distance is
given by the number of transitions on this path.
In contrast to our proposal, these paths are not directly based on the rhetorical structure a text
has, but are taken from a simplified ”transition graph”. For mononuclear relations, a transition
is given if both nucleus and satellite child are on the path. Thus, mononuclear edges from/to
nuclei do not contribute to rhetorical distance (wmolna, molnd, morna, mornd = 0) whereas
mononuclear edges from/to satellites are counted (wmolsa, molsd, morsa, morsd = 1).
The handling of multinuclear relations is slightly more complex. For the transformations
needed there, Kibrik (2000) proposed certain rules which resulted in a heavy transformation
of the tree. In a later paper (Kibrik and Krasavina 2005), some modifications were suggested.
The method can be summarized in two rules:


move along the graph towards the nearest antecedent and count how many horizontal
jumps you make
when one jump penetrates into a symmetrical structure or makes a step out of it, a
penalty of 0.5 is added
As a result,


3.4
satellites are less accessible than nuclei in mononuclear relations
nuclei in multinuclear relations are less accessible than nuclei in mononuclear
relations.
Comparison
As a first result, we can now compare our reconstructions of the three theories. With respect
to the parameters all theories have in common, we obtain the configurations in Figure 3.
Reinterpreting the absolute weights as partial orders (cf. Fig. 4), we find – not unsurprisingly
– a great deal of compatibility, especially among less accessible relations, morsd, molsd,
indicating that descending into a satellite is quite a costly operation. Additionally, ascending
from the nucleus of a mononuclear relation (m
molna, morna) seems to be least problematic,
with multinuclear relations being intermediate. Generally, ascending is assumed to be easier
than descending, cf. Grosz and Sidner (1986), according to whom this restriction is the core
effect of discourse structure on referential accessibility.


For comparison of the approaches, theory-specific parameters can be safely ignored.
The stack model in its original formulation by Grosz and Sidner cannot be applied to
RST-like discourse structure in a straight-forward way. However, our adaption is
consistent with previous proposals (Mooser and Moore 1996, Marcu 2000, Tetreault
and Allen 2003).
9

Veins Theory involves both global and local optimization that is not covered
completely by the minimal set of parameters applied so far. In contrast to the
limitations with respect to Grosz and Sidner, this restriction seems to be intrinsic to an
approach that does not take the relative order of edges into consideration. Thus, we
achieve a local approximation only. Whereas an algorithm using pairs of edges is
likely to perform better, we restrict our attention to the minimal set of parameters for
the purpose of comparison.
All theories are compatible with the ranking of edge labels illustrated in Fig. 4.
RST structure
edge
G&S
VT
K&K
molna
0
0
0
molnd
0
0.01
0
molsa
0
0
1
molsd
1
1
1
morna
0
0
0
mornd
0
0.01
0
morsa
0
0.05
1
morsd
1
2
1
mulna
0
0
0.5
mulnd
0
0.01
0.5
murna
0
0
0.5
murnd
0
0.01
0.5
threshold
τ<1
τ < 1.05
n.a.
Figure 3. Edge labels and their corresponding weights, according to Grosz and Sidner (1986), Cristea et al. (1998)
and Kibrik and Krasavina (2005).
10
morsd
≥ molsd
morsd
higher RhetD
(less accessible)
≥
morsa
≥
mulnd
murnd
≥
mulna
murna
≥
morna
molna
lower RhetD
(highly accessible)
The effect of molsa, molnd and mornd is controversial.
Figure 4. Rankings of edge labels
4 Towards an empirical evaluation
Having provided a general framework, we perform a comparative analysis of the theories with
respect to their predictive power, namely on the use of full descriptions (proper names,
definite descriptions4) and pronouns (personal pronouns, possessive pronouns, demonstrative
pronouns, pronominal adverbs) on 134 texts from the Potsdam Commentary Corpus (PCC,
Stede 2004). The PCC is a collection of German newspaper commentaries annotated for
morpho-syntax (using the TIGER format, cf. Brants and Hansen 2002), coreference (Chiarcos
and Krasavina 2005b), rhetorical structure (Reiter and Stede 2003), information structure
(Götze 2003), and discourse connectives (Stede 2004).
As the focus of theories on discourse-structural accessibility lies on anaphoric references
beyond the current clause. We excluded trivial cases from consideration, i.e. when anaphor
and antecedent occur in the same EDU. Thus, precision and recall can only be compared
relative to each other only, rather than with respect to the overall data.5
The results obtained so far are preliminary, but give hints on directions for further research.
One of the most important results was that distance measures alone cannot sufficiently
account for the distribution of referring expressions (This is illustrated by rather nonsatisfying results for recall and precision, cf. Tab.2 and 3). Still, this is not unexpected, as a
low degree of rhetorical or referential distance is usually assumed to be a necessary condition
for pronominalization, but not a sufficient one. Rather, both veins theory and stack model are
closely interrelated with Centering Theory, where additional constraints on the use of
pronouns are formulated in terms of surface properties of the antecedent (Grosz et al. 1995).
Similarly, Kibrik (2000) considered other factors affecting the use of pronouns as well.
However, we leave the task to investigate the interaction between surface cues, referential
distance and different views on rhetorical distance for forthcoming research. Instead, we focus
on the impact of rhetorical distance alone.
4.1 Predicting referential accessibility
For the investigation of referential accessibility in general, we distinguish two major classes
of anaphors, full descriptions and pronouns and compare the different configurations of
rhetorical distance in terms of
4
Note that ''description'' is used in its syntactic sense, here. It denotes noun and prepositional phrases not being
pronominal, but involving at least one nominal lexeme.
5
For pronominalization, both precision and recall are higher due to the overwhelming majority of pronouns
among short-distance references.
11




precision (relative portion of correctly predicted expressions from predicted
expressions);
recall (relative portion of correctly predicted expressions from originally used
expressions);
f-measure (the harmonic mean of recall and precision);
χ2-test to test against the null hypothesis of independence.
Since Kibrik and Krasavina's model of rhetorical distance does not provide an accessibility
threshold, we applied different values of τ. Besides the theories, we tested a baseline defined
as the path length, i.e. the number of edges on the path, again with different τ-values.
G&S
VT
K&K
τ = 1.0
τ = 1.5
τ = 2.0
τ = 2.5
τ = 3.0
τ = 3.5
τ = 4.0
baseline
τ = 2.0
τ = 3.0
τ = 4.0
τ = 5.0
τ = 6.0
correct
predicted
173
209
total
predicted
418
523
total
recall precision
f
χ2
correct
282 61,35% 41,39% 49,43% 23.62, p<0.01
282 74,11% 39,96% 51,93% 38.01, p<0.01
17
171
193
234
243
258
261
45
350
413
574
638
733
759
282
282
282
282
282
282
282
6,03%
60,64%
68,44%
82,98%
86,17%
91,49%
92,55%
37,78%
48,86%
46,73%
40,77%
38,09%
35,20%
34,39%
10,40%
54,11%
55,54%
54,67%
52,83%
50,84%
50,14%
0.74, p=0.39
76.37, p<0.01
78.13, p<0.01
58.83, p<0.01
40.03, p<0.01
21.11, p<0.01
14.93, p<0.01
2
114
176
220
244
7
176
341
496
626
282
282
282
282
282
0,71%
40,43%
62,41%
78,01%
86,52%
28,57%
64,77%
51,61%
44,35%
38,98%
1,38%
49,78%
56,50%
56,56%
53,74%
0.04, p=0.85
109.03, p<0.01
98.95, p<0.01
80.29, p<0.01
48.05, p<0.01
Table 2. Predictions as to pronouns (personal pronouns and possessive pronouns) according to Grosz
and Sidner (G&S) reconstruction, veins theory (VT) reconstruction and Kibrik and Krasavina (K&K).
G&S
VT
K&K
τ = 1.0
τ = 1.5
τ = 2.0
τ = 2.5
τ = 3.0
τ = 3.5
τ = 4.0
baseline
τ = 2.0
τ = 3.0
τ = 4.0
τ = 5.0
τ = 6.0
correct
predicted
356
287
total
predicted
465
360
total
recall precision
f
χ2
correct
601 59,23% 76,56% 66,79% 23.62, p<0.01
601 47,75% 79,72% 59,73% 38.01, p<0.01
573
422
381
261
206
126
103
838
533
470
309
245
150
124
601
601
601
601
601
601
601
95,34%
70,22%
63,39%
43,43%
34,28%
20,97%
17,14%
68,38%
79,17%
81,06%
84,47%
84,08%
84,00%
83,06%
79,64%
74,43%
71,15%
57,36%
48,70%
33,56%
28,41%
0.74, p=0.39
76.37, p<0.01
78.13, p<0.01
58.83, p<0.01
40.03, p<0.01
21.11, p<0.01
14.93, p<0.01
596
539
436
325
219
876
707
542
387
257
601
601
601
601
601
99,17%
89,68%
72,55%
54,08%
36,44%
68,04%
76,24%
80,44%
83,98%
85,21%
80,70%
82,42%
76,29%
65,79%
51,05%
0.04, p=0.85
109.03, p<0.01
98.95, p<0.01
80.29, p<0.01
48.05, p<0.01
Table 3. Predictions as to full descriptions (proper names and definite NPs) according to Grosz and Sidner (G&S)
reconstruction, veins theory (VT) reconstruction and Kibrik and Krasavina (K&K).
12
correct
predicted
total
predicted
total
correct
recall
precision
f
χ2
RefD, τ = 1
RefD, τ = 2
RefD, τ = 3
117
247
259
174
462
597
282
282
282
41.49%
87.59%
91.84%
67.24%
53.46%
43.38%
51.32%
66.40%
58.93%
124.26, p<0.01
206.57, p<0.01
111.11, p<0.01
RefD, τ = 1
RefD, τ = 2
RefD, τ = 3
544
386
263
709
421
286
601
90.52% 76.73%
601
64.23% 91.69%
601
43.76% 91.96%
Table 4. Referential distance
83.05%
75.54%
59.30%
124.26, p<0.01
206.57, p<0.01
111.11, p<0.01
prn
full
Surprisingly, it turned out that the baseline (with τ=3 resp. τ =5) outperformed the established
theories, closely followed by Kibrik and Krasavina (2005) (τ=2), veins theory reconstruction
and stack model. This can be explained by the interaction of rhetorical distance and referential
distance, which is outlined in the following sentence.
4.2 Rhetorical and referential distance
For our pilot study, we considered sequential antecedents. Under this restriction, RhetD
seems to be generally ruled out by RefD, as illustrated in Tab 4.
Accordingly, we assume referential distance to be a main determinant of pronoun use in local
contexts. Thus, we concentrate on rhetorical distance as a device allowing for pronominal
reference where it is unexpected under a purely sequential account. To exclude cases that are
more properly explained by short-distance effects, we introduce a bias β to filter out cases
with referential distance smaller than β.
G&S
VT
K&K, τ = 1.5
K&K, τ = 2
baseline, τ = 3
baseline, τ = 4
baseline, τ = 5
RefD, τ = 1
RefD, τ = 2
RefD, τ = 3
RefD, τ = 4
RefD, τ = 5
RefD, τ = 6
# prn
# full NP
RefD bias β
β=0
49.43%
51.93%
54.11%
55.54%
49.78%
56.50%
56.56%
51.32%
66.40%
58.93%
55.52%
53.59%
51.36%
282
601
β=1
40.76%
42.22%
45.59%
45.99%
44.53%
47.36%
45.71%
n.a.
57.40%
48.30%
44.55%
42.64%
40.41%
165
544
β=2
20.11%
18.34%
21.88%
20.51%
14.29%
18.02%
18.89%
n.a.
n.a.
14.12%
14.05%
14.92%
14.69%
35
386
β=3
20.80%
20.69%
28.92%
27.72%
20.00%
20.90%
22.86%
n.a.
n.a.
n.a.
10.53%
13.51%
13.53%
23
263
β=4
22.47%
20.00%
32.73%
27.27%
28.57%
30.43%
29.41%
n.a.
n.a.
n.a.
n.a.
14.08%
13.85%
18
196
β=5
20.29%
17.95%
33.33%
26.92%
36.36%
38.89%
28.57%
n.a.
n.a.
n.a.
n.a.
n.a.
11.11%
13
148
β=6
18.60%
16.33%
28.57%
24.24%
35.39%
34.78%
24.24%
n.a.
n.a.
n.a.
n.a.
n.a.
n.a.
9
93
Table 5. Interplay between referential distance (RefD) and rhetorical distance (RhetD).
13
We found that for the use of referring expressions, referential distance is a better predictor of
pronouns with antecedents within the last two clauses. This assumption is further supported
by the impressive performance of the baseline, with edge labels being ignored, for unbiased
data (β = 0).
For references beyond this point, i.e. with referential distance larger than 2, rhetorical distance
is a better indicator. Curiously, the theories seem to perform similarly (for β =2), though for
longer distances, a slight advantage of Kibrik and Krasavina's rhetorical distance might be
suspected. The data on long-distance pronominal anaphors is, however, too sparse to draw
any definite conclusions at this point, as illustrated by the seemingly better performance of the
base-line for pronouns with referential distance greater than 4.
So, this effect has to be investigated further using additional corpora from other languages
and heterogenuous registers. As we focused on one single corpus consisting of the newspaper
texts only, we cannot exclude annotation artifacts. Due to its limited size, the number of
long-distance pronouns is too low, so that we could make any commitments. In 134 texts
from the PCC, only 35 pronouns (12.4%) can be considered as long-distance anaphors.
4.3 Edges and expressions
Another aspect of our study was the comparison of the theories, as to the appropriateness of
the parameter weighting. To do so, we abstract over the frequency of edges, consider the
likelihood of a type of a referring expression r to occur on the path where a given edge label e
is present (Fig. 5) and compare relative differences with respect to the average edge frequency
per referring expression (Table 6). Edge labels preferred for long-distance anaphors are
excluded.
Figure 5. Portion of referring expressons per edge label.
14
morna
morsa
murna
molnd
molsd
mulnd
defnp
(+)
(–)
––
(–)
(+)
(+)
ne
=
=
+
(–)
+
–
prn
(–)
(+)
++
(+)
–
+
Deviation from the average
++ iff. ≥5%
+ iff. ≥ 2.5%
(+) iff. ≥ 0.5%
–
= iff.
strong preference
preference
slight preference
accordingly for dispreferences
derivation less than 0.5%
Table 6. Referring expressions per edge label: deviation from the average.
In Tab. 6, three groups of edge labels can be distinguished.
 edges with strong preferences (++) for pronouns, but strong dispreference (– –) for
definite descriptions
murna
 edges with preference (+) for pronouns, but not for (-,=) for definite descriptions and
proper names
mulnd
 edges without any preferences or with slight preferences only
morna, morsa, molnd
 edges with dispreference for pronouns, but (slight) preference for definite descriptions
and proper names
molsd
Thus, a ranking is observable as summarized in Fig. 6.
Whereas the results for molsd seems to conform assumptions underlying the theories as
reconstructed above, the differentiations made between the more accessible edge types are
different from the respective predictions. The higher frequency of murna edges for
pronouns than for definite descriptions can be explained by the constraint on the repetition of
full NPs at short distances, which results in their substitution by pronouns. Futher, we observe
that molsd seems to restrict usage of pronouns, in contrast to molnd and mulnd. Again,
this conforms the assumptions of the the stack model (Grosz and Sidner 1986) and veins
theory (Cristea et al. 1998), whereas the prediction of Kibrik and Krasavina (2005) is that the
patterns of molsa und molsd are identical.
molsd > morna, morsa, molnd > mulnd > murna
low accessibility
full NPs
high accessibility
pronouns
Figure 6. Observed ranking of edge labels.
15
Despite these problems, some predictions with respect to the ranking of edge labels (cf. Fig.
4) could now be verified empirically (see Fig. 6). Especially, it was not clear how molnd is
related to other edge labels. It is less accessible in VT reconstruction than mulna and
murna, being at the same level as mulnd and murnd. According to Kibrik and Krasavina
(2005), molnd is grouped together with molna and morna, thus regarded to be more
accessible than murna and mulna. In the data we found that murna seems to be
dispreferred for definite descriptions indicating that Kibrik and Krasavina’s treatment of
molnd is possibly more appropriate. Besides this, we found that under molsd the choice of
definite descriptions is preferred, as predicted.
Besides this, we observe that proper names share features of both pronouns and definite NPs.
This may be due to the two-fold function of proper names: on the one hand, they serve as a
shortcut for unique identification of a referent; on the other hand they can be of high explicity,
which relates them to full NPs – the expressions at the lower end at the accessibility marking
scale (Ariel 1990).6 This can explain the seemingly higher frequency of murna edges for
proper names than for definite NPs (Fig. 5). We suspect proper names are used as a short
reference in this case, because the corresponding referents have been sufficiently described in
the previous discourse.
4.4 Final remarks
Rhetorical distance and referential distance co-operate
For short-distance references, we found a strong tendency for referential distance to be a more
appropriate predictor of pronominalization. Still, as this seemingly superiority might be due to
the restriction to sequential antecedents, not rhetorical ones, a comparative analysis
considering the respective rhetorical distance of all antecedents will be performed.
However, for long-distance anaphors, RefD is ruled out by RhetD, indicating that two
strategies are applied in parallel. Accoding to the greater number of short-distance references
performed by pronouns, RefD can be seen as a “default” measurement of referential
accessibility, whereas rhetorical distance comes into play in cases of long-distance anaphora.
In more technical terms, we suggest the combined application of Walker’s cache model
(1996) and Grosz and Sidner’s stack model (and related approaches) side by side. For
concrete application, this conforms to Tetrault and Allen’s Grosz and Sidner stack
approximation algorithm (Tetreault and Allen 2003), which follows Walker’s (2000) analysis
stating that reference can occur between two utterances even if they are split by a segment
boundary.
Comparative performance of theories of discourse structural accessibility
As rhetorical distance effects are observable for long-distance anaphors which make up about
12.41% of pronouns in our corpus, no definite conclusions can be made due to the sparsity of
data. Still, it seems that the theories under consideration show a similar performance, ruling
out the baseline (i.e. the length of a path). Further, these analyses have to be enriched by the
inclusion of other factors such as grammatical role of antecedent, a distinction of types of
rhetorical relations, etc. as distance measures formalize necessary conditions for the use of
pronouns, but no sufficient ones.
6
For further research, we suggest to emphasize the distinction between short and full names more explicitly.
16
(7.1)
(7.2)
Figure 7: Critical cases for veins theory reconstruction
Accordingly, accessibility is not the only criterion to be considered. Besides this, the effect of
interference or ambiguity of reference must be addressed, too, cf. Poesio et al. (2002).
Further questions
Note that our reconstruction of veins theory is locally adequate only. We find critical cases
such as those depicted in the partial trees in Fig. 7. In (7.1), the left-most node (A) is
inaccessible from the right-most (D) according to veins theory, whereas in (7.2) it is
accessible. However, the number of edge labels on the paths, and thus the calculated
rhetorical distance, is identical in both cases.
A minimal solution is to mark the neighbourhood of the root node, resulting in a set of 15
parameters (12 normal plus 3 left-descending edges at the root node), but a more intuitive
alternative is to assume such locality effects everywhere in the tree.
We did not distinguish different kinds of relations, but only different types of structures. It has
often been claimed that referential accessibility depends on the semantics of discourse
relations, too. An extended set of parameters could be a subject of later inquiries.
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19