A Hierarchical Account of Referential Accessibility
Nancy IDE
Department of Computer Science
Vassar College
Poughkeepsie, New York 12604-0520 USA
ide@cs.vassar.edu
Dan CRISTEA
Department of Computer Science
University “Al. I. Cuza”
Iasi, Romania
dcristea@infoiasi.ro
Abstract
In this paper, we outline a theory of
referential accessibility called Veins
Theory (VT). We show how VT addresses
the problem of "left satellites", currently a
problem for stack-based models, and show
that VT can be used to significantly reduce
the search space for antecedents. We also
show that VT provides a better model for
determining domains of referential
accessibility, and discuss how VT can be
used to address various issues of structural
ambiguity.
Introduction
In this paper, we outline a theory of referential
accessibility called Veins Theory (VT). We
compare VT to stack-based models based on
Grosz and Sidner's (1986) focus spaces, and
show how VT addresses the problem of "left
satellites", i.e., subordinate discourse segments
that appear prior to their nuclei (dominating
segments) in the linear text. Left-satellites pose
a problem for stack-based models, which
remove subordinate segments from the stack
before pushing a nuclear or dominating
segment, thus rendering them inaccessible. The
percentage of such cases is typically small,
which may account for the fact that their
treatment has been largely overlooked in the
literature, but the phenomenon nonetheless
persists in most texts. We also show how VT
can be used to address various issues of
structural ambiguity.
1 Veins Theory
Veins Theory (VT) extends and formalizes the
relation between discourse structure and
reference proposed by Fox (1987). VT
identifies “veins” over discourse structure trees
that are built according to the requirements put
forth in Rhetorical Structure Theory (RST)
(Mann and Thompson, 1987). RST structures
are represented as binary trees, with no loss of
information. Veins are computed based on the
RST-specific distinction between nuclei and
satellites; therefore, RST relations labeling
nodes in the tree are ignored. Terminal nodes
in the tree represent discourse units and non-
terminal nodes represent discourse relations.
The fundamental intuition underlying VT is
that the distinction between nuclei and
satellites constrains the range of referents to
which anaphors can be resolved; in other
words, the nucleus-satellite distinction induces
a domain of referential accessibility (DRA) for
each referential expression. More precisely, for
each anaphor a in a discourse unit u, VT
hypothesizes that a can be resolved by
examining referential expressions that were
used in a subset of the discourse units that
precede u; this subset is called the DRA of u.
For any elementary unit u in a text, the
corresponding DRA is computed automatically
from the text's RST tree  in two steps:
1. Heads for each node are computed bottom-
up over the rhetorical representation tree.
Heads of elementary discourse units are
the units themselves. Heads of internal
nodes, i.e., discourse spans, are computed
by taking the union of the heads of the
immediate child nodes that are nuclei. For
example, for the text in Figure 1,
1
 with the
rhetorical structure shown in Figure 2,
2
 the
head of span [5,7] is unit 5. Note that the
head of span [6,7] is the list <6,7> because
both immediate children are nuclei.
2. Using the results of step 1, Vein
expressions are computed top-down for
each node in the tree, using the following
functions:
-  mark (x), which returns each symbol in a
string of symbols x marked with
parentheses.
-  seq(x,y), which concatenates the labels in
x with the labels in y, left-to-right.
-  simpl(x), which eliminates all marked
symbols from x, if they exist.
The vein of the root is its head. Veins of
child nodes are computed recursively, as
follows:
•  for each nuclear node whose parent
has vein v, if the node has a left non-
nuclear sibling with head h, then the
vein expression is seq(mark(h), v);
otherwise v.
• for each non-nuclear node with head h
whose parent node has vein v, if the
node is the left child of its parent, then
seq(h,v); otherwise, seq(h, simpl(v)).
                                                       
1
 Figure 1 highlights two co-referential equivalence
classes: referential expressions surrounded by
boxes refer to “Mr. Casey”; those surrounded by
ellipses refer to “Genetic Therapy Inc.”.
2
 The rhetorical structure is represented using the
conventions proposed by Mann and Thompson
(1988).
One of the conjectures of VT is that the vein
expression of a unit (terminal node), which
includes a chain of discourse units that contain
that unit itself, provides an “abstract” or
summary of the discourse fragment that
contains that unit. Because it is an internally
coherent piece of discourse, all referential
expressions (REs) in the unit preferentially
find their referees within that sub-text.
Referees that do not appear in the DRA are
possible, but are more difficult to process, both
computationally and cognitively (see Section
2.2). This conjecture expresses the intuition
that potential referees of the REs of a unit
depend on the nuclearity of previous units:
both a satellite and a nucleus can access a
previous nuclear node, a nucleus can only
access another left nuclear node or its own left
satellite, and the interposition of a nucleus
after a satellite blocks the accessibility of the
satellite for any nodes lower in the hierarchy.
1. Michael D. Casey, a top Johnson & Johnson
manager, moved to Genetic Therapy Inc., a
small biotechnology concern here,
2. to become its president and chief operating
officer
3. Mr. Casey, 46, years old, was president of
J&J’s McNeil Pharmaceutical subsidiary,
4. which was merged with another J&J unit,
Ortho Pharmaceutical Corp., this year in a
cost-cutting move.
5. Mr. Casey succeeds M. James Barrett, 50, as
president of Genetic Therapy.
6. Mr. Barrett remains chief executive officer
7. and becomes chairman.
8. Mr. Casey said
9. he made the move to the smaller company
10. because he saw health care moving toward
technologies like the company’s gene
therapy products.
11. I believe that the field is emerging and is
prepared to break loose,
12. he said.
Figure 1: MUC corpus text fragment
The DRA of a unit u is given by the units in
the vein that precede u. For example, for the
text and RST tree in Figures 1 and 2, the vein
expression of unit 3, which contains units 1
and 3, suggests that anaphors from unit 3
should be resolved only to referential
expressions in units 1 and 3. Because unit 2 is
a satellite to unit 1, it is considered to be
“blocked” to referential links from unit 3. In
contrast, the DRA of unit 9, consisting of units
1, 8, and 9, reflects the intuition that anaphors
from unit 9 can be resolved only to referential
expressions from unit 1, which is the most
important unit in span [1,7] and to unit 8, a
satellite that immediately precedes unit 9.
Figure 2 shows the heads and veins of all
internal nodes in the rhetorical representation.
In general, co-referential relations (such as the
identity relation) induce equivalence classes
over the set of referential expressions in a text.
When hierarchical adjacency is considered, an
anaphor may be resolved to a referent that is
not the closest in a linear interpretation of a
text. However, because referential expressions
are organized in equivalence classes, it is
sufficient that an anaphor is resolved to some
member of the set. This is consistent with the
distinction between "direct" and "indirect"
references discussed in (Cristea, et al., 1998).
1 2 3 4
5
67
8
9
10
11 12
13-??
??-??
H = 1 9 *
V = 1 9 *
H = 1
V = 1 9 *
H = 9
V = 1 9 *
H = 1
V = 1 9 *
H = 5
V = 1 5 9 *
H = 1
V = 1 9 *
H = 3
V = 1 3 5 9 *
H = 6 7
V = 1 5 6 7 9 *
H = 9
V = 1 9 * 
H = 9
V = 1 9 *
H = 9
V = 1 (8) 9 *
H = 10
V = 1 9 10 *
H = 11
V = 1 9 10 11 *
H = 3
V = 1 3 5 9
DRA  = 1 3
H = 9
V = 1 (8) 9
DRA = 1 8 9 
Figure 2: RST analysis of the text in Figure 1
2 VT and Stack-based Models
Veins Theory claims that references from a
given unit are possible only in its DRA, i.e., that
discourse structure constrains the areas of the
text over which references can be resolved. In
previous work, we compared the potential of
hierarchical and linear models of discourse--i.e.,
approaches that enumerate potential antecedents
in an undifferentiated window of text linearly
preceding the anaphor under scrutiny--to
correctly establish co-referential links in texts,
and hence, their  potential to correctly resolve
anaphors (Cristea, et al., 2000). Our results
showed that by exploiting the hierarchical
discourse structure of texts, one can increase the
potential of natural  systems to correctly
determine co-referential links, which is a
requirement for correctly resolving anaphors. In
general, the potential to correctly determine co-
referential links was greater for VT than for
linear models when one looks back 4 elementary
discourse units. When looking back more than
four units, the linear model was equally
effective.
Here, we compare VT to stack-based models of
discourse structure based on Grosz and Sidner's
(1986) (G&S) focus spaces (e.g., Hahn and
Strübe, 1997; Azzam, et al., 1998). In these
approaches, discourse segments are pushed on
the stack as they are encountered in a linear
traversal of the text. Before a dominating
segment is pushed, subordinate segments that
precede it are popped from the stack.
Antecedents for REs appearing in the segment
on the top of the stack are sought in discourse
segments in the stack below it. Therefore, in
cases where a subordinate segment a precedes a
dominating segment b, a reference to an entity in
a by an RE in b is not resolvable. Special
provision could be made in order to handle such
cases—e.g., subsequently pushing a on top of
b—but this would violate the overall strategy of
resolving REs appearing in segments currently
on the top of the stack.
The special status given to left satellites in VT
addresses this problem. For example, one RST
analysis of (1) proposed by Moser and Moore
(1996) is given in Figure 3. Moser and Moore
note that the relation of an RST nucleus to its
satellite is analogous to the dominates relation
proposed by G&S (see also Marcu, 2000). As a
subordinate segment preceding the segment that
dominates it, the satellite is popped from the
stack before the dominant segment (the nucleus)
is pushed in the stack-based model, and therefore
it is not included among the discourse segments
that are searched to resolve co-references.
3
Similarly, the text in (2), taken from the MUC
annotated corpus (Marcu, et al., 1999), was
assigned the RST structure in Figure 4, which
presents the same problem for the stack-based
approach: the referent for this in C2 is to the
Clinton program in A2, but because it is a
subordinate segment, it is no longer on the stack
when C2 is processed.
(1) A1. George Bush supports big business.
B1. He's sure to veto House Bill 1711.
Figure 3: RST analysis of (1)
                                                       
3
 Note that Moser and Moore (1996) also propose an
informational RST structure for the same text, in
which a « volitional-cause » relation holds between
the nucleus a  and the satellite b, thus providing for a
to be on the stack when b is processed.
 (2) A2. Some of the executives also signed letters on
behalf of the Clinton program.
B2. Nearly all of them praised the president for
his efforts to pare the deficit.
C2. This is not necessarily the package I would
design,
D2. said Martin Marietta's Mr. Augustine.
E2. But we have to attack the deficit.
Figure 4: RST analysis of (2)
2.1 Validation
To validate our claim, we examined 23
newspaper texts with widely varying lengths
(mean length = 408 words, standard deviation
376). The texts were annotated manually for co-
reference relations of identity (Hirschman and
Chinchor, 1997). The co-reference relations
define equivalence relations on the set of all
marked references in a text. The texts were also
annotated manually with discourse structures
built in the style of Mann and Thompson (1988).
Each analysis yielded an average of 52
elementary discourse units. Details of the
annotation process are given in (Marcu et al.,
1999).
Six percent of all co-references in the corpus are
to left satellites. If only co-references pointing
outside the unit in which they appear (inter-unit
references) are considered, the rate increases to
7.76%. Among these cases, two possibilities
exist: either the reference is unresolvable using
the stack-based method because the unit in
which the referent appears has been popped from
the stack, or the stack-based algorithm finds a
correct referent in an earlier unit that is still on
the stack. Twenty-two percent (2.38% of all co-
referring expressions in the corpus) of the
referents that VT finds in left satellites fall into
B1A1
evidence
A2-B2
background
elaboration-addition
A2 B2
C2-D2-E2
antithesis
C2-D2
attribution
C2
D2
E2
the first category. For example, in text fragment
(3), taken from the MUC corpus, the co-
referential equivalence class for the pronoun he
in C3 includes Saloman Brothers analyst Jeff
Canin in B3 and he in A3. The RST analysis of
this fragment in Figure 5 shows that both A3 and
B3 are left satellites. A stack-based approach
would not find either antecedent for he in C3,
since both A3 and B3 are popped from the stack
before C3 is processed.
(3) A3. Although the results were a little lighter than
the 49 cents a share he hoped for,
B3. Salomon Brothers analyst Jeff Canin said
C3. he was pleased with Sun's gross margins for
the quarter.
Figure 5: RST analysis of (3)
In cases where stack-based approaches find a co-
referent (although not the most recent
antecedent) elsewhere in the stack, it makes
sense to compare the effort required by the two
models to establish correct co-referential links.
That is, we assume that from a computational
perspective (and, presumably a psycholinguistic
one as well), the closer an antecedent is to the
referential expression to be resolved, the better.
We have shown elsewhere (Cristea et al., 2000)
that VT, compared to linear models, requires
significantly less effort for DRAs of any size.
We use a similar strategy here to compute the
effort required by VT and stack-based models.
DRAs for both models are treated as ordered
lists. For example, text fragment (4) reflects the
set of units on the stack at a given point in
processing one of the MUC texts; units D4 and
E4, in brackets, are left satellites and therefore
not available using the stack-based model, but
visible using VT. To determine the correct
antecedent of Mr. Clinton in F4 using the stack-
based model, it is necessary to search back
through 3 units (C4, B4, A4) to find the referent
President Clinton. In contrast, using VT, we
search back only 1 unit to D4.
 (4) A4. A group of top corporate executives urged
Congress to pass President Clinton's deficit-
reduction plan,
B4. declaring that it is superior to the only
apparent alternative: more gridlock.
C4. Some of the executives who attended
yesterday's session weren't a surprise.
  [ D4. Tenneco Inc. Chairman Michael Walsh, for
instance, is a staunch Democrat who
provided an early endorsement for Mr.
Clinton during the presidential campaign.
E4. Xerox Corp.'s Chairman Paul Allaire was
one of the few top corporate chief executive
officers who contributed money to the
Clinton campaign.   ]
F4. And others, such as Atlantic Richfield Co.
Chairman Lodwrick M. Cook and Zenith
Electronics Corp. Chairman Jerry Pearlman,
have also previously voiced their approval of
Mr. Clinton's economic strategy.
We compute the effort e(M,a,DRA
k
) of a model
M to determine correct co-referential links with
respect to a referential expression a in unit u,
given a DRA of size k (DRA
k
(u)) is given by the
number of units between u and the first unit in
DRA
k 
that contains a co-referential expression of
a. The effort e(M,C,k) of a model M to determine
correct co-referential links for all referential
expressions in a corpus of texts C using DRAs of
size k is computed as the sum of the efforts
e(M,a,DRA
k
) of all referential expressions a
where VT finds the co-reference of a in a left
satellite. Since co-referents found in units that
are not left satellites will be identical for both
VT and stack-based models, the difference in
effort between the two models depends only on
co-referents found in left satellites.
Figure 6 shows the VT and stack-based efforts
computed over referential expressions resolved
by VT in left satellites and k = 1 to 12.
Obviously, for a given k and a given referent a,
that no co-reference exists in the units of the
corresponding DRA
k  
In these cases, we consider
B3-C3
attribution
concession
A3
B3 C3
the effort to be equal to k. As a result, for small k
the effort required to establish co-referential
links is similar for both models, because both
can establish only a limited number of links.
However, as k increases, the effort computed
over the entire corpus diverges, with VT
performing consistently better than the stack-
based model.
Figure 6: Effort required by VT and stack-based
models
Note that in some cases, the stack-based model
performs better than VT, in particular for small
k. This occurs when VT searches back through n
adjacent left satellites, where n > 1, to find a co-
reference, but a co-referent is found using the
stack-based method by searching back m non-
left satellite units, where m < n. This would be
the case, if for instance, VT first found a co-
referent for Mr. Clinton In text (4) in D4 (2 units
away), but the stack-based model found a co-
referent in C4 (1 unit away since the left
satellites are not on the stack).
In our corpus, 15% of the co-references found in
left satellites by VT required less effort using the
stack-based method, whereas VT out-performed
the stack-based method 23% of the time. In the
majority of cases (62%), the two models
required the same level of effort. However, all of
the cases in which the stack-based model
performed better are for small k (k<4), and the
average difference in distance (in units) is 1.25.
In contrast, VT out-performs the stack-based
model for cases ranging over all values of k in
our experiment (1 to 12), and the average
difference in distance is 3.8 units. At k=4, VT
can determine all the co-referents in our corpus,
whereas the stack-based model requires DRAs of
up to 12 units to resolve them all. This accounts
for the marked divergence in effort shown in
Figure 6 as k  increases. So, despite the minor
difference in the percentage of cases where VT
out-performs the stack-based model, VT has the
potential to significantly reduce the search space
for co-referential links.
2.2 Exceptions
We have also examined the exceptions, i.e., co-
referential links that VT and stack-based models
cannot determine correctly. Because of the
equivalence of the stack contents for left-
balanced discourse trees, there is no case in
which the stack-based model finds a referent
where VT does not. There is, however, a number
of referring expressions for which neither VT
nor the stack-based model finds a co-referent. In
the corpus of MUC texts we consider, 12.3% of
inter-unit references fall into this category, or
9.3% of the references in the corpus if we
include intra-unit references.
Table 1 provides a summary of the types of
referring expressions for which co-referents are
not found in our corpus—i.e., no antecedent
exists, or the antecedent appears outside the
DRA.
4
 We show the percentage of REs in our
corpus for which VT (and the stack-based model
as well, since all units in the DRA computed
according to VT are in the DRA computed using
the stack-based model) fails to find an
antecedent, and the percentage of REs for which
VT finds a co-referent (in a left satellite) but the
stack-based model does not.
                                                       
4
 Our calculations are made based on the RST
analysis of the MUC data, in which we detected a
small number of structural errors. Therefore, the
values given here are not absolute but rather provide
an indication of the relative distribution of RE types.
0
20
40
60
80
100
120
12345678910112
DRA length (k)
Number of co-refs
Stack
VT
We consider four types of REs:
(1) Pragmatic references, which refer to entities
that can be assumed part of general
knowledge, such as the Senate, the key in the
phrase lock them up and throw away the key,
or our in the phrase our streets.
(2) Proper nouns, such as Mr. Gerstner or
Senator Biden.
(3) Common nouns, such as the steelmaker, the
proceeds, or the top job.
(4) Pronouns
Following (Gundel, et al., 1993), we consider
that the evoking power of each of these types of
REs decreases as we move down the list. That is,
pragmatic references are easily understood
without an antecedent; proper nouns and noun
phrases less so, and are typically resolved by
inference over the context. On the other hand,
pronouns have very poor evoking power, and
therefore a message emitter employs them only
when s/he is certain that the structure of the
discourse allows for easy recuperation of the
antecedent in the message receiver's memory.
5
Except for the cases where a pronoun can be
understood without an antecedent (e.g., our in
our streets), it is virtually impossible to use a
pronoun to refer to an antecedent that is outside
the DRA.
Type of RE VT Stack-based
pragmatic 56.3% 0.0%
proper nouns 22.7% 26.1%
common nouns 16.0% 39.1%
pronouns 5.0% 34.8%
Table 1: Exceptions for VT and stack-based models
The alignment of the evoking power of
referential expressions with the percentage of
exceptions for both models shows that the
predictions made by VT relative to DRAs are
fundamentally correct--that is, their prevalence
corresponds directly to their respective evoking
                                                       
5
 Ideally, a psycho-linguistic study of reading times to
verify the claim that referees outside the DRA are
more difficult to process would be in order.
powers. On the other hand, the almost equal
distribution of exceptions over RE types for the
stack-based model shows that it is less reliable
for determining DRAs.
Note that in all VT exceptions for pronouns, the
RST attribution relation is involved. Text
fragment (5) and the corresponding RST tree
(Figure 7) shows the typical case:
(5) A5. A spokesman for the company said,
B5. Mr. Bartlett’s promotion reflects the current
emphasis at Mary Kay on international
expansion.
C5. Mr. Bartlett will be involved in developing
the international expansion strategy,
D5. he said
The antecedent for he in D5 is a spokesman for
the company in A5, which, due to the nuclear-
satellite relations, is inaccessible on the vein.
Our results suggest that annotation of attributive
relations needs to be refined, possibly by treating
X said and the attributed quotation as a single
unit. If this were done, the vein expression
would allow appropriate access.
Figure 7: RST analysis of (5)
2.3 Summary
In sum, VT provides a more natural account of
referential accessibility than the stack-based
model. In cases where the discourse structure is
not left-polarized, at least one satellite precedes
its nucleus in the discourse and is therefore its
left sibling in the binary discourse tree. The vein
definition formalizes the intuition that in a
sequence of units a b c, where a and c are
satellites of b, b can refer to entities in a (its left
satellite), but the subsequent right satellite, c,
cannot refer to a due to the interposition of
nuclear unit b--or, if such a reference exists, it is
A5-B5
elaboration
attribution
A5 B5
C5-D5
attribution
D5C5
harder to process. In stack-based approaches to
referentiality, such configurations pose
problems: because b dominates a, in order to
resolve potential references from b to a, b must
appear below a on the stack even though it is
processed after a. Even if the processing
difficulties are overcome, this situation leads to
the postulation of cataphoric references when a
satellite precedes its nucleus, which is counter-
intuitive.
3 VT and Structural Ambiguity
The fact that VT considers only the nuclear-
satellite distinction and ignores rhetorical
labeling has practical ramifications for anaphora
resolution systems that rely on discourse
structure to determine the DRA for a given RE.
(Marcu, et al., 1999) show that over a corpus of
texts drawn from MUC newspaper texts, the
Wall Street Journal corpus, and the Brown
Corpus, reliable agreement among annotators is
consistently obtained for discourse segmentation
and assignment of nuclear-satellite status, while
agreement on rhetorical labeling was less
reliable (statistically significant for only the
MUC texts). This means that even when there
exist differences in rhetorical labeling, vein
expressions can be computed and used to
determine DRAs.
VT also has ramifications for evaluating the
viability of different structural representations
for a given text, at least for the purposes of
reference resolution. Like syntactic parsing,
discourse parsing typically yields several
interpretations, and one of the a priori tasks for
further analysis of the parsed texts is to choose
one from among potentially several alternative
structures. Marcu (1996) showed that using only
rhetorical relations, as many as five different
structures can be identified for some texts.
Considering intention-based relations can yield
even more alternatives. For anaphora resolution,
the choice of one structure over another may
have significant impact. For example, an RST
tree for (6) using rhetorical relations is given in
Figure 8; Figure 9 shows another RST tree for
the same text, using intention-based relations. If
we compute the vein expressions for both
representations, we see that the vein for segment
C6 in the intentional representation is <A6 B6
C6>, whereas in the rhetorical representation, the
vein is <(B6), C6>. That is, under the constraints
imposed by VT, John is not available as a
referent for he in C6 in the rhetorical version,
although John is clearly the appropriate
antecedent. Interestingly, the intention-based
analysis is skewed to the right and thus is a
"better" representation according to the criteria
outlined in (Marcu, 1996); it also eliminates the
left-satellite that was shown to pose problems for
stack-based approaches. It is therefore likely that
the intention-based analysis is "better" for the
purposes of anaphora resolution.
(6) A6.  Tell John to bring the car home by 5.
B6. That way I can get to the store before it
closes.
C6. Then he can finish the bookshelves tonight.
Figure 8: RST tree for text (6), using rhetorical
relations
Figure 9: RST tree for text (6), using intention-based
relations
Conclusion
Veins Theory is based on established notions of
discourse structure: hierarchical organization, as
in the stack-based model and RST's tree
structures, and dominance or nuclear/satellite
motivation
B6-C6
motivation
B6
C6
A6
A6-B6
condition
condition
A6 B6
C6
relations between discourse segments. As such,
VT captures and formalizes intuitions about
discourse structure that run through the current
literature. VT also explicitly recognizes the
special status of the left satellite for discourse
structure, which has not been adequately
addressed in previous work.
In this paper we have shown how VT addresses
the left satellite problem, and how VT can be
used to address various issues of structural
ambiguity. VT predicts that references not
resolved in the DRA of the unit in which it
appears are more difficult to process, both
computationally and cognitively; by looking at
cases where VT fails we determine that this
claim is justified. By comparing the types of
referring expressions for which VT and the
stack-based model fail, we also show that VT
provides a better model for determining DRAs.
Acknowledgements
We thank Daniel Marcu for providing us with
the RST annotated MUC corpus, and Valentin
Tablan for developing part of the software that
enabled us to process the data.
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