Logical Structure and 
Livia Polanyi 
FX Palo Alto Laboratory 
3400 Hillview Ave Bldg 4 
Palo Alto CA 94304 
polanyi@pal, xerox, com 
Discourse Anaphora Resolution* 
Martin van den Berg 
FX Palo Alto Laboratory 
3400 Hillview Ave Bldg 4 
Palo Alto CA 94304 
vdberg@pal, xerox, com 
Abstract 
Working within the Dynamic "Quantifier Logic 
(DQL) framework (van den Berg 1992, 1996a,b), we 
claim in this paper that in every language the trans- 
lation into a logical language will be such that the 
preference ordering of possible discourse referents for 
an anaphor in a sentence can be explained in terms of 
the scopal order of the exp _re~Lslons in the antecedent 
that introduce the discourse referents. Since the 
scope of terms is derived from arguments indepen- 
dent of any discourse theory, our account explal~ 
discour~ anaphora resolution in terms of general 
principles of utterance semantics, from whichthe 
predictions of centering theory follow. When com- 
b'med with the powerful discourse structural frame- 
work of the Linguistic Discourse Model (Polanyi 
(1985, 1986, 1988, 1996) Potanyi and Scha (1984), 
Scha and Polanyi (1988), Prfist, H., tL Scha and 
M. tLvan den Berg, 1994; Po~u~, L. and M. H. 
van den Berg 1996; van den Berg, M. H. 1996b), 
we provide a uni6ed account of di~ourse anaphora 
resolution. 
1 Introduction 
In thl. paper, we use a semantic theory based on Dy- 
namic Quantifier Logic (van den Berg 1992,1998a,b) 
to present an approach to discom~ anaphora resolu- 
tion under the Linguistic DL~ourse Model (Polanyi 
(1985, 1986, 1988, 1996) Pohmyi and Scha (1984), 
Scha and Pclawfi (1988), Prfmt, H., It Scha and 
M. H. van den Berg, 1994; Po~q~ L. and M. IL 
van den Berg 1996; van den Berg, M. H. 1996b). 
Our treatment integrates the imights of the Center- 
~g framework (Jmbi audK,,h- 1979, 1981; Grosz 
et~l. 1983, 1986, 1995; Gundel 1998; Walker et.al. 
1998b) into a -n~Sed theory of discourse level struc- 
tufa/and semantic relations. In our account, dis- 
course level aaaphora resolution effects fall out of 
a general theory of discourse quantification. Scope 
orderinge in the logical representation of the 
antecedent utterance result in d|fferences in 
" The authors dedkate this paper to the memory of Megumi 
Kameyama (1953-1999), a dedicated researcher and a very 
dear friend. 
accessibility for potential referents in a target 
utterance. No additional c~ntering mechanisms are 
required, the centering predictions follow from this 
theory. 
Our treatment is universal: explanations of rela- 
tive coherence do not depend on conventions that 
might differ in different languages. Furthermore, 
we provide a treatment for the resolution of mul- 
tiple anaphors, resulting from a range of possi- 
ble antecedents including plurals and multiple an- 
tecedents. 
The approach to discourse anaph°ra resolution we 
take in this paper integrates a rigorous formal se- 
mantic machinery within a theory Of discourse strtlc- 
ture. Before giving a detailed account of our treat- 
meat of di~murse reference resolution, we would llke 
to address explicitly some of the positions towards 
rdereace resolution and discour~ ~mcture which 
inform our work. 
1.1 Theoretical and Methodological 
Considerations 
To begin with, we should state explicitly that our en- 
terprise is a semantic one~ we are interested in devet- 
oping and implemen "ring a formalization capable of 
._,~'amln~ a con-ect interpretation to each utterance 
in a discourse. In this, we are fully committed to the 
Dynamic Semantics enterprise (Kamp 1981, H~m 
1982, Groenendijk and Stokhof, 1990, 1991, Cider- 
~i. 1992, van den Berg 1991, Kamp and Reyle 1993, 
Asher 1993, van den Berg 1998). Except in so far as 
it is provably necessary, we are not concerned with 
psychological L~sues of how human language users 
pro~ discourse nor with what human beings in- 
tend when they use language to commuIlicate with 
one another. 
Our aim is to build machinery applicable to all 
genres and all modes of comm~nLication. Thus we 
can not assume that a discourse is n ec~xlly uco. 
hereat" and that our goal is to provide an account 
of why that is so, nor can we assume that all dis- 
course iswritten or spoken or.occurs in a task con- 
text where the demands or reasonable expectations 
of a~ external activity are available to guide parsing 
and interpretation. 
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Our theory is a formal one, therefore we can rely 
on well-known, rule-driven, parsing methods devel- 
oped for sentences which allows us ~parse discourse 
incrementally as it unfolds. In order to do so, our 
framework formalizes the relationship among con- 
stituent units in the discourse by specifying how ant 
tecedent units provide context for the interpretation 
of later units. In all cases, our method involves 
computing the resulting meaning of the combina- 
tion of the meanings of the combined units, rather 
than identifying appropriate labels under which to 
characterize the relationship obtaining between the 
units. Our units of analysis are welldefined seman- 
tic units. These units are usually encoded as single 
simple sentences or clauses but may also be realized 
by words, phrases or gestures which communicate 
exactly one elementary predication. 
In our view, a formal theory of discourse structure 
should give well defined structures on which infer- 
encing operates and on which world know, ledge ap- 
plies. We strive to limit the role of world knowledge 
in so far as possible to a specific moment in d~;ourse 
processing--namely at the precise moment when a 
choice must be made about how a newly incoming 
unit must be integrated into the unfolding discourse. 
Just as in sentence grammar where world knowledge 
is used to decide between syntacticaUy equivalent al- 
ternatives in the case of pp attachment, for example, 
in discourse grammar the relationshilm between ele- 
ments are purely grammatical, and world knowledge 
is only used to decide between syntactically equally 
reasonable alternatives. 
Similarly, in calculating the structure of discourse, 
we do not rely on the use of cue words suchas so, 
angtway or thcfefor~ because these terms are never 
obligatory. The relationsl~p of one unit to another 
is always calculated on the relationshlp between the 
meanings of the constituent utterances which may 
then be ~in¢orced by the presence of terms which 
specify the nature of the intended relationship. 
In the framework developed below, thea-e is 
a dose relationship I~en discourse rderents 
and discourse structure. We deal both with 
how anaphors are resolved to partienb, r an- 
tecedents using the structure of the discourse, 
and how an antecedent gives me,,nlng to 
an anaphor. The problem of identifying the an- 
tecedent to which an anaphor refe~ is dealt with 
in Centering Theory, discussed in Section 2 below. 
After reviewing Centering, we will discuss Dynamic 
Quantifier Logic (Section 3) and then show how the 
insights of Centering can be integrated into a ben- 
era\] theory of discourse syntactic and semantic struc- 
ture (Section 5.1), We shall point out how our ap- 
proach accounts for multiple anaphors to different 
antecedents as well as ac~tmting for anaphoric ref- 
erence to multiple antecedents, a problem which re- 
main unsolved within that framework (5.2). 
2 Centering Theory 
CenteringTheory first described in detail in Gro~z, 
Joshi and Weinstein (1983, 1986 \[1995\]) is designed 
to provide an assignment of a preference order 
among discourse entities in a sentence for the pur- 
pose of anaphora resolution. Centering Theory, 
which built upon earlier work by Joshi and Kuhn 
(1979) and Joshi and Weinstein (1981, 1998), pro- 
posed that (1) is perceived to be more coherent than 
(2) because in (1) 
(I) (a) JeH helped Dick wash the mr. (b) He. 
washed the windows as Dick washed the car 
(c) Heb soaped a pane.. 
He~ and h~ are both co-referential with .leO', while 
in .(2) 
. (2) (a) Je~ ha~ed Dick wasA the car. (b) //e. 
washed the windows as Dick wazed the car (c) 
Heb b..~ed the hood. =. 
the referent for//~in (c) is D/ck while he, in (b) 
refers to Je~. 
We quote here from the concise description of Cen- 
tering given in (Walker et.al., 1998b): 
The centering model is very simple. Dis- 
courses consist of constituent segments and 
each segment is represented as part of a dis- 
course model. Centers are semantic entiUes • 
that ~re part of the discourse model for each 
utterance in a discourse segment. The set of 
vO~wxao-LOOKma ¢~r~, Cj(vi~v) repre- 
seats discourse entities evoked by an utter- 
ance Ui in a discourse segment D (Webber 
1978; Prince 1981). The \[unique\] BACKWARD- 
WOKmO c~-rza, C,(Ui.D) is a sp~l mem- 
ber of the C:, which represents the discourse 
entity that the utt~ance U most omtrally 
concermL ... The Ct entity links the current 
utterance to the previous discour~ ...(or 
not more thaa one) ... The set of I~01~WARD- 
woxmo cm~m~.s, C:, is ranked according to 
discom~ s~enm. This ranki~ is a part~ 
order. The hi~es~ ranking member of the set 
of forward-looking centers.., represents a pre- 
diction about the CGd the following utlterance. 
W~ker, Joshi, Prince (1998b) in Walker, Jochi, 
" Prince 1998a henceforth WJP) p. 3. 
From a linguistic perspective (cL papers and ref- 
erences in Walker, Joshi and Prince 1998; Strube 
1998), Centering theor/sts have explained the choice 
of C6 in a sentence in terms of a'large .number of 
potential factors. In particular: the grammatical hi- 
erarchy with subjects ranking higher than objects 
(Grosz, Joshi, Weinstein 1983), topic or empathy 
marking (Kameyama 198,5), surface order position 
111 
(Rainbow, 1993) or grammatical function (Brennan, 
Friedman and Pollard 1987) of the encoding of dis- 
course entities in the immediately preceding seg- 
ment. 
Roberts (1998) argues that C0 is an unordered set- 
of backward-looking centers in terms of classical Dis- 
course Representation Theory notions of familiarity, 
compatibility and logical accessibility (Kamp 1981, 
Helm 1982, Kamp and Reyle 1993, Asher 1993), 
with an additional constraint that the set of dis- 
course referents are attentionally accessible, a notion 
taken from Grosz and Sidner (1986). Under Roberts' 
treatment, the set of preferred centers, takes the 
place of the original C6. Walker (1998) also replaces 
a unique Ct with a set of possible backward look- 
ing centers computed from a set of possible forward 
looking centers using agreement features, selection 
constraints of the verb and contra-indexing condi- 
tions. 
The choice of segment also remains contested 
ground in Centering, with mint linguists choosing 
for the sentence or clause while Walker (1998), ar- 
gues for integrating Centering with a more global 
model of discourse focus. Within computational 
linguistics, several Centering Algorithms have been 
proposed, most notably by Brennan, S, M. ~ied- 
man and C. Pollard (1987), Walker, Iida and Cote 
(1990, 1994) and, more recently, by Strube and Hahn 
(1996), Strube (1998), and Walker (1998) which re- 
flect these various perspectives. 
Although the several variants of Centering can be 
argued to be better suited to one or another task 
or to account for phenomena in one or another lan- 
guage, they all fail to account for the interpretation 
of common examples SUch as (3) s. 
(3) (a) Joan s went to ~ork at e~hZ. (b) B//g ar- 
t/veal at n/he. (c) Th~+a met in the ¢on/erence 
rOOl~ 
In (3), no entity in a single target clause or sentence 
resolves the plural pronoun in (3c). Thqa+a refers 
to a complex semantic entity created by combining 
entities in (3a) and (3b). 
In the reformulation of Centering in terms of Dy- 
namic Quantifier Logic presented in Section 3, be- 
low, we show how multiple anaphoric elements can 
be handled and each assigned its preferred resolu-. 
tion. DQL allows us to calculate a preference order- 
ing on the discourse referents that can be used to 
account for multiple anaphors refering to different 
antecedents. When paired withthe LDM, we also 
provide a means for one anaphor to refer back to 
multiple antecedents. 
s Notational Convention: Introduced Indices are written as supe~pts; indices that are old (refer back) amwritten as 
subscript& 
• 3 - Dynamic Quantifier Logic. 
DQL combines Generalized ~uantifier Theory 
(GQT) (Barwise and Cooper 1991) and Plural 
Quantifier Logic (Scha 1981; van der Does 1992) 
with Dynamic Semantics. DQL was designed to han- 
dle phenomena such as plurals and complex relations 
between discourse referents often left unaddressed by 
other formal semantic frameworks (see van de Berg 
1992,1996a,b). 
Dynamic Quantifier Logic is based on the observa- 
tion that NPs are generally anaphoric, quantifl- 
cationa\] and can be the antecedent of further 
anaphora, as illustrated by (4): 
(4) (a) The children I arrived at the natural history 
museum early in the morning. (b) Threes boys 2 
disappeared in the girl shop. (c) The~ had a 
great time touching almost evert~ing. 
In (4b), thr~ boys is anaphoric: its domain of 
quantification is given by The chi/dre~ ,Within this 
domain, it is quantificatiunal:, there are exactly three 
boys that disappeared in the gi~ shop. Finally, it is 
an antecedent: it introduces a referent picked up by 
Theyl in (4c) to refer back to the three/w~. 
DQL, designed to explaia examples like (4), was 
d~ned to preserve as far as possible the prediction of 
its precursors while inheriting most of the/r results. 
Under DQL well known, solid results and established 
procedures remain tmehanL, ed. As. an illustration of 
a DQL representation of a sentence, take the simpli- 
fied representation of (5b) below 
(5) (a) Some childrerf were playing in the back- 
yar~ (b) Every= g/rP ~ wear/ng a hat,. 
(c) ~ had put ~ on belore ~ le# the 
house.. 
(5'b) Vg C z (girl(y), ~ C_ • (hat(z), wear(y, z))) 
Formula (50o) states that/or ever g eat/ry that is a 
g/d, taken from the doma/n Siren by the d/scourse 
ngereat z', it is the case that there is a hat such 
tha~ she wmws iL This expremion is vew similar to 
clamcal umslatious into logic of Co). The only dif- 
fe~mco in the form of the expression is the explicit 
mention d the context set that sets the domain of 
. qumstiflcation. These context sets are given by dis- 
Course referents. The universal quantification Eve~ 
girl takes its range from the discourse referent =, and 
introduces a subset y, the indefinite a ha£ takes its 
domain from an as yet unspecified domain (-). 
3.1 Quantification and Reference 
Resolution 
In DQL, all di~ourse anaphoric effects take 
place through discourse referents functioning 
as context sets to quantifiers. Variables that 
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are quantified over 2 are introduced as dis- 
course referents to function as :context sets 
in subsequent sentences. 
Although (Sb) introduces both referents y for the 
girls and z for the hats, the referents do not have 
equivalent status. This is caused by the quantifica- 
tionaI structure. The set of girls is given as a simple 
subset of the set of children, and as such is readily 
available. The set of hats, on the other hand, is only 
introduced relative to the set of girls. The hats are 
not introduced independently, but rather are intro- 
duced indirectly as belonging to the girls. Referring 
back to the set of hats is much more computation- 
ally expensive than referring back to the set of girls; 
to refer to the hats we must implicitly refer to the 
girls relative to which the set of hats is defined. 
A consequence of the fact that the hats are intro- 
duced relative to the g/r/s, is that there is an implied 
ordering of the discourse referents that we use in re- 
letting back to these sets. The discourse referent 
corresponding to the ~ is much easier to pick up 
from the conti~ than the discourse referent refer- 
ring back to the hats s. Everything else being equal, 
the discourse referent referring to 'the g/r/a will be 
preferred over the discourse referent referring to the 
hats because accessing it requires less computation. 
• This preference order corresponds closely to the 
forward-lcoking centers C 1. However, there is noth- 
ing in the construction of the preference ordering 
based on complexity of retrieval sketched above that 
would lead us to believe that there is at most one 
backward-looking center. In fact, our treatment 
gives the same predictions as Centering for the first 
pronoun resolved, but results in different predictions 
for embedded auaphors. The foliowing diagram rep- 
resenting the scopes of (b) and (c) illustrates th!~: ==~vts/mts 
ol y \[ (6) ~. ~, = y ("t,'~") \] 
I I w II 
3.2 Anaphera Resolution Preference Order 
It follows from the argument we have laid out above, 
• that the referent I/in (e), is preferred for anapherie 
However, once the girk are available as a set 
:in(c) via u, the hats are ako available, via discourse 
referent z, to ser~ as an antecedent. The set of 
girls, being already available no longer adds to the 
computational burden of calculating the set of hats. 
Within the scope of they, the referent z is much more 
accessible than outside that scope. 
We can push this line of reasoning further. Con- 
sider example (Ta). In this example, the subject, 
2Like y and z in (5'b). 
SThk is related to the discussion in Jmhi and Weinstein 
1998, whi¢.h motivates Centering from the perspective of com- 
plexity of inference in discourse. 
Every amman, has scope over the object, a car. As 
(7-8) shows, the preferred center of the C! corre- 
sponding to this is the set of women because the 
cars are introduced as a function of the women. To 
refer correctly to the set of cars, we must also refer 
indirectly to the set of women since we are interested 
in retrieving only the cars owned by the women, not 
cars owned by men. On the other hand, to refer to 
the women, we need no information about their cars. 
This does not mean that we cannot refer to the cara 
in a subsequent sentence, as (gb) shows... 
(7) (a) Every waman in this town has a car. 
(b) They park them in their garages. 
Where the set of women is referred to with Theg, 
the cars can be.referred to directly. There is then no 
longer a hidden cost of retrieving the set of women 
in addition to the cars, since cars are already given 
in the sentence. 
But now consider (8) and (9): 
(8) (a) Every woman in this town has a car.. 
(b) They use it to drive to work. 
(9) (a) Every t~oman in this town has a car. 
~o) They are l~u'ked in their garages. 
Note that (7-9) are decreasin" g in acceptability. 
(8) is more problematic than (7), because in (7) only 
the set of cars need be retaieved, while in (8) also the 
actual dependence of the carsonthe women that own 
them is invoked by the use of the singular ~. (9) is 
much less acceptable than either (7) or (8), because 
in (9) They refers to the cars without the help of an 
explicitly given set of women. 
The fact that once we have used a discourse ref- 
erent, we can use other discourse referents that de- 
pend on it has important consequences as soon as 
we consider anaphora more complex than pronouns. 
Consider exmnple (I0).. 
(10) (a) Seventeen people 1 in our lab have their own 
cmnputer~. (b) Three o~f themt are silly and 
them~ oD ~ n~L 
h (10a), a discourse referent d~ to aset of seven- 
teen people is introduced, and as well as a discourse 
referent d~ to a the set of computers they own, which 
depends on ds. In (10b), Three o! them quantifies 
over the domain given by all, and states that within 
dh there are exactly three people who switch their 
4For some people (8) is totally impmsible, becamm they 
demand a plural here as in (7), seemingly preferring semantic 
number agreement over syntactic number agreement. How- 
ever, syntactic agreement does occur, as the following example illustrates: 
~ sotd/er/, neqmu/bte lot ~ own gun. He haJ to dean 
it and will be reln'imandd i\] anll dirt is found on it. 
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:!°" 
own computers off every night. If the discourse refer- 
ent introduced by their own computers would sim- 
ply refer to the set of computers owned by people 
in the company, and not be dependent on the peo- 
ple, them2 would refer to this set, rather than only 
to the set of computers owned by the three people. 
The meaning of (10b) would then be that these three 
people switch off all computers in the company, not 
just their own. This, of course, in not the correct 
reading. 
4 Quantifier Scope and Anaphora 
R~-solution 
Under our analysis, the preferred antecedent for a 
pronoun is based on computational complexity aris- 
ing from universal facts of scope ordering in the log- 
ical representation of the antecedent utterance. Dif- 
ferent approaches to centering will be better or worse 
at predicting ordering relations depending on the 
match between the ordering scheme decided upon 
and the underlying scopal ordering. 
We argue as follows. 
If the discourse referent A is introduced by a term 
that has scope over a term introducing discourse 
refe~.nt B, and discourse zefe~ent B is introduced 
by a term that has scope over discourse referent C, 
A will be preferred over B and B will be preferred. 
over C. Since this explanation is not dependent on 
conventions that might be different in different lan- 
guages our treatment is universal. This is not the 
case for explanations based on linear ordexing of syn- 
tactic constituents or arguments based on gemnmat- 
ical function, for example. Because in .Engli~ the 
subject has scope over the objects, and the objects 
have scope over more deeply embedded terms, the 
ordering of discourse rderents familiar to us from 
the literature will result in the well known C! pre- 
dictions. 
Rejecting a preferred ordering for a less preferred 
ordering is a computationally complex operation. 
First the preferred order is computed, then this anal- 
is rejected ---perha~ on pragmatic grounds. 
The calculations must then be re-done and the re- 
sulting less preferred ordering checked to see if it fits 
• the pragmatic facts of the situation described in the 
target utterance. Differences ha computational com- 
plexity arising from rejecting more prderred inter- 
pretations for less preferred thus result in the judg- 
ments of relative coherence which have been noted 
in the literature. Our account thns explains how 
Centering effects originate and why some anaphoric 
choices may involve more attention to the referent 
retrieval process than others s. 
SThe DQL formalism has been explicitly designed to look 
as similar as peasible to weIl-lmown, standard logiel. "1"o argue 
about issum of acceesibility of the referents, a logical system 
that is le88 natural, but externalizes the dependencies between 
4.1 Acceptability Predictions 
To return then to examples (1) and (2), reproduced 
here as (11) and (12) 
(11) (a) Jeff helped Dick wash the car. (b) Hea 
washed the windows as Dick washed the car 
(c) He6 soaped a pane. 
(12) (a) 3e~ helped Dick wash the car. (b) Hee 
washed the windows as Dick waxed the car 
(c) Heb bused the hood 
Since the d iscom-se referent Jell is introduced bY a 
term that has scope over a term introducing dis- 
course referent D/ck, Je~ will be preferred over 
D/ok The difference in perceived coherence between 
(1/11) and (2/12) falls out of the more general fact 
that wide scope quantifiers are preferred over narrow 
scope quaatifiers. 
We will now turn to discussing how discourse 
structure and Anaphora Resolution interact to pro- 
duce different acceptability predictions for different 
structures of discourse. 
5 Discourse Structure and Anaphora 
Resolution 
Although Centering Theory is associated with the 
Discourse Structurm Theory of Gr~z and Sidner 
(1986) which considers speaker intention and hearer 
attention as the critical dimensions to be modeled in 
discourse understanding, there are alternative mod- 
els for understanding the relations among utterances 
in a discourse which are based on other principles. In 
particular, Dynamic Quantifier Logic, the anaphora 
resolution mechanism based on quantifier scope we 
are working with here, has been designed to provide 
the semantic machinery for the Linguistic Discourse 
Model (LDM). The LDM provides an account for 
discourse interpretation in terms of structural and 
semantic relations among the linguistic constituents 
making up a discourse e. 
5.1 The Linguistic Discourse Model 
The LDM is designed as a discourse ~ designed 
to construct a meaning representation of the in- 
put discourse icrementally. The LDM treats a dis- 
course as a sequence of basic discourse units (evue) 
ranges of values for ~ might be more suitable, such as 
liar to DO~ we thank eae mmaymous revumer mr pomung 
out the work of Ranta (1991), who's use of Marthz-16Ps type 
theory, m~ atso be suttsble ts a~ anal3~t8 tool 
ela Prfmt, Scha and van den Berg 1991, • resolution mech- 
anJmn for unification based discourse grammar for verb phrase 
anaphom is defined, in terms of the Linguistic Discourse 
Model (LDM; PolanyJ and Scha 1984;. Polanyi 1987, i988. 
1996), which takes semantic representations as input. This 
treatment was later extended to a unification based discourse 
grammar actinf~ on dynamic quantifier logic in Polanyi 1996, 
van den Berg and Polanyl 1996. The current paper extends 
that work. 
,qp 
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each of which encodes formal semantic, syntactic 
and phonological properties of either an elementary 
predication or a discourse function. Using rules of 
discourse wellformedness whiCh specify how to com- 
pute the relationship between a BDO and the pre- 
vious discourse, the LDM constructs a parse tree 
by successively attaching the SVUs to a node at the 
fight of edge of the emerging tree. The nodes of the 
tree are called Discourse Constituent Umts (VCUS) 7. 
DCUs encode formal semantic, syntactic and phono- 
logical properties that are calculated by following 
construction rules corresponding to the relationship 
computed as a result of the attachment process. 
The discourse parse tree represents the structural 
relations obtaining ~Lmong the DCUs. There are three 
basic types of relations among DCUs: Coordination, 
Subordination and Binary Re!A_tion. Corresponding 
to these relations, a DCU can be attached at a node 
on the right edge of a tree in one of three waysS: 
1. The input DCU will be Coordinated with a node 
present o n the fight-edge of the tree if it contin- 
• ues a discourse activity (such as topic Chaining 
or narrating) underway at that node. 
2. The input DCU win be Subordl,a~ted to a node 
on the right-edge of the tree if it elaborates on 
material expressed at that node or if it inter- 
rupts the flow of the discourse completely. 
3. The input DCU will be Binary-attached to a 
node if it is related to that node in a logical, 
rhetorical or interactional pattern specified ex- 
plicitly by the grammar. 
The LDM is a compesitional framework. Simnltane- 
oas with the incremental construction of the struco 
tural representation ofthe discourse by attaching in- 
coming DCUS, a semantic representation of the mean- 
ink of the discourse is constructed by incorporating 
the interpretation of an incomi-~ ~ in the ~man- 
tie representation on the discourse. 
The LDM a~m~ts for both structural and se- 
mantic aspects of discounse parsing using logical and 
structural notions analogous to units and p~ 
constituting lower levels of the linguistic hierarchy. 
It is an ideal framework for tmdenmmding the re- 
latioas between sentential syntax and semantics, on 
the one hand, and on the other hand, the texts and 
~teractious that are constructed using sentential lin- 
guistic structures. 
?BDU8 once attached to the tree are DCU8. 
-8Baside8 these three basic composition relations between 
ncus, a complex ncu can also he constructed by an operator 
having a ncu as an argdment and within mmtences, a ncu can 
occur embedded in another DcU. These two cases wiU not be d~umed here. 
5.2 Reference Resolution in the Linguistic 
Discourse Model 
Let us now look at several short example of the inter- 
action of anaphora resolution with discourse struc- 
ture using the Dynamic Quantifier Logic framework 
above. 
(13) (a) Susan came home late yesterday. (b) Doris 
hod held her up at work. (c) She needed help 
with the copier. 
In (13) the relationship between vco (13a) and 
Dco (13b) is a Subordination relation because (13b) 
supplies more detailed information about why Susan 
came home late. As is shown in (13a), the S node in- 
herits all information about the dominating VCO. In 
this case (a). A representation of Susan is therefore 
available at this constructed node. (13e) gives more 
explanation about what went on when Doris held 
Susan up at work and is therefore Subordinated to 
(b). Susan and Doris available for reference at that 
node. In (14) the situation is different. 
(14) (a) Susan came home late yesterda3l. (b) Doris 
had held her up at worl~ (e) She didn't ~oen 
have time \]or dinner. (13') ~-~ (14')~.~., 
Although the relationship between DCU (14a) and 
DCU (14b) is a Subordination relation, as shown in 
(14a), as the di~ourse continues with (14c), the 
state of the discourse POPS from the embedded ex- 
planation to continue describing the state of affairs 
of Sasan's evening. (14c) is therefor~ in a Coordi- 
nation relation with (14a) as shown. Only Susan is 
now available as a potential referent in the current 
context. 
In fact, the antecedent of an anaphora need not 
be one specific earlier utterance, but may be a con- 
structed higher node in the parse tree as in (15): 
(15) (a) J~m went to um'k at dght (b) ,8///art/red 
a¢ n/,w~ (e) They met in the ~/e,m~eroom. 
Qt+I(ARRIVE(AT-TIME)) and Theys+=(meet-in-C) 
Qs+=(ARRIVE(AT-~~~heyx (meet-in-Ci 
JoanX(got-to-w~rk(at eight)) Bmt (arrive(at eight)) 
In this case, the antecedent of (15c) is not (15a) 
or (15b), but the discourse node that constitutes 
115 
the list (15a+b). In this higher node, there is a 
constructed schematicrepresentation of what (lSa) 
and (15b) share, and They is resolved to this. Very 
schematically, it amounts to resolving the anaphor 
X to the outer quantifier of its antecedent, Ql+2. 
6 Conclusions 
• Within our unified framework we are able to provide 
a detailed account of how anaphora resolution works 
across stretches of discourse, Because the LDM re- 
quires specific calculation of the information avail- 
able at intermediary nodes. Computationally, dur- 
ing parsing, a rich data structure is created rep- 
resenting the meaning of the discourse. This, we 
would argue, is a distinct advantage of Dynamic 
Semantic approaches such as the LDM/DQL sys- 
tem over current computational alternatives such 
as Discourse Structures Theory (Gro.~ and Sidner 
1989) and Rhetorical Structure Theory (Mann and 
Thompson 1987) which rely upon inferring the at- 
- tentional and intentional states of language users, 
in one case, and on labe!ing the coherence relations 
among clauses, in the other. Looking towards formal 
discourse syst~m-__q, we believe that while it would be 
possible to integrate the insights of DQL into a DRT 
approach such as that t~ by Asher (1993), the ap- 
pr.~ taken here is computationally more tractable 
than more standard implementation of DRT for dis- 
course parsing. The increased tractability results 
from the separation of discourse syntax and seman- 
tics which our approach imposes, taken together 
with the restriction of appeals to inference and world 
knowledge to specific moments in interpretation. In 
the case of the LDM, appeals to external knowledge 
are made only at the moment of DCU attachment. 
to the parse.tree. 

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