Making Sense of Reference to the Unfamiliar 
Helen Seville and Allan Ramsay* 
Centre for Computational Linguistics 
UMIST, PO Box 88, Manchester M60 1QD, England 
heleng/allan@ccl, umist, ac. uk 
Abstract 
C, omi)utational ai)proaches to reference resolu- 
tion, like Centering Theory, are best at resolv- 
ing referring expressions which denote familiar 
reD.rents. We demonstrate how, by t~king a 
proof-theoretic approach to reference resolution 
within a Centering-type framework, we are able 
to make sense of reti;rring expressions tbr un- 
familiar referents. These include, in addition 
to bridging descriptions, definite descripl;ions 
like "the first man" and "the first snowdrops of 
Spring". We claim that the first of these denotes 
a unique subset of a iflural discourse antecedent. 
While the second has no discourse antecedent, 
we similarly treat it as denoting a mfi(lue subset 
of a t'~nniliar referent. 
1. Introduction 
Itow do reti;rring exl)ressions denote? Accord- 
ing to II.ussell, a definite description such as 
%he King of France", denotes a mfique individ- 
ual by virtue of its meaning. But, according to 
Familiarity Theory (Helm, 1.983), reti;rring ex- 
pressions need not denote mfiquely by virtue of 
their meaning as they refer to individuals made 
familiar by the discourse or other context. This 
observation plays a key role in Centering The- 
ory (Grosz and Sidner, 1986; Grosz et al., 1995) 
and other computational al)t)roaches in which 
rethrring expressions are resolved by locating 
their antecedents in the discourse. The refer- 
ence of pronouns like "he", definite descriptions 
like "the woman", and referential tenses like 
"had" clearly has more to do with salience ill 
context thml with uniqueness of meaning. Sim- 
ilarly, while names like "Mary" need not denote 
individuals prominent in the discourse context, 
* \Ve would like to thank the anonymous reviewers for 
their detailed and helpful comments. 
they must nevertheless denote individuals famil- 
iar to conversants if they are successflflly to re- 
fer. However, there is another (:lass of referring 
expressions in relation to which we believe the 
concept of uniqueness of meaning does have an 
essential role to plt~y. These include such def- 
inite descrit)tions as "the first man" and "the 
first snowdrop of Spring", along with such vari- 
ations on these as "the first three men" and "the 
first snowdrops of Spring". 
In implementing a system of retL, renee resolu- 
tion, we have attemt)ted to reconcile the notions 
of familiarity mM uniqueness. This enables us 
to dereli;rence exl)ressions like "the first snow- 
drop of Spring" in a unified framework alongside 
anal)hers ~, pron(mns, retbrential tenses, names, 
and other definite descriptions like "the nlall". 
(1) Two men nrrive(t. 
(2) The .fir.st 'm,a'H, spoke. 
In the case of a referring expression like "the 
first mini", there may be an antecedent of sorts 
in the discourse, trot it is not the individual re- 
ferred to (or indeed ml individual at all). We 
will say that the antecedent "two men" intro- 
duces a set, and that the referring expression 
"the first man" denotes, by virtue of the mean- 
ing of.first, a unique subset of this familiar set. 
(1) Mary saw th, e first snowd,vp of 
Spring. 
In the case of "tile first snowdrop of Spring", 
there need be no explicit antecedent in the dis- 
course. We will s~w that, in the same way 
that "Mary" denotes a familiar individual, "the 
snowdrops of Spring" denotes a t'~nniliar set, or 
>vVe use this term to distinguish reflexives like "her- 
self" from t)ronouns like "he" and "hiln". 
775 
property. Again, by virtue of tile meaning of 
first, "tile first snowdrop of Spring" can be said 
to denote a unique subset of the familiar set. We 
will not claim that it denotes a unique individ- 
ual, but that rather it denotes a unique subset 
of the specified cardinality, i.e., 1. This treat- 
ment has tile advantage that it extends to plural 
referring expressions. 
Below we outline the approach we have de- 
veloped to the representation and resolution of 
referring expressions, betbre discussing in more 
detail its extension to deal with unfamiliar ref- 
erents. 
2 A Framework for Reference 
Resolution 
Our framework for reference resolution has been 
implemented in the system of  under- 
standing described in (Ramsay, 1999). The 
starting point tbr reference resolution is the log- 
ical tbrm we obtain fl'om parsing. For example, 
the tbllowing is the logical tbrm we get for the 
utterance "Mary slept." 
~A : { A is interval $~ 
f o,'e(,'e f ( aB (  V ech,_ti e( B , 1))), A ) } 
3C : {aspect(simple, A, C)} 
0 (C, agen.t, ref (,kD (,,.amed(D, Mary) 
g card(D, 1)))) 
sleep(C) 
C is event 
We use tile inference engine described in 
(Ramsay and Seville, 2000) to update the dis- 
course model with a new discourse state con- 
taining the intbrmation explicitly represented in 
tile logical tbrm together with any further infer- 
ences which are licensed given the existing dis- 
course model. Reference resolution, which in- 
volves carrying out a proof that a retbrring ex- 
pression denotes, is implemented as part of the 
update step. We anchor a referring expression 
like ref()~D(named(D, Marg)&card(D, 1))) in 
tile discourse model by proving the existence of 
an entity in the model which satisfies the prop- 
erties specified by the referring expression, in 
this case aD(na,~ed(D, Mary)~ea,'d(D, 1)) 2. 
2Strictly speaking, it is a set which is denoted. For 
readability, our referring expressions conflate tim prop- 
erties of sets and their members. In this case, the car- 
dinality is a property of the set denoted, but the nmne 
Mary is a property of its member. 
Given that many referring expressions do not in 
themselves denote uniquely, however, we need 
a theory of reference resolution to enable us 
to obtain the appropriate (i.e., intended) ret- 
erent for any referring expression. We incorpo- 
rate our theory of reference resolution into the 
actual representation of referring expressions; 
for example, we label anaphors with the prop- 
erty "salient" and pronouns (and also referential 
tenses) with the property "centred"3: 
"himself" 
re f ( AX (salient ( X, re f ( AD ( eds (D)))$~m (X))) 
"she ~, 
ref (),X (ee..tred(X, reZ (),D(e&(D) ) )~Z(X) ) ) 
Retbrence resolntion relies on maintaining, as 
in Centering Theory, a list of tbrward-looking 
centres for each discourse state (corresponding 
to an utterance) in the discourse. Furthermore, 
for the purposes of reference resolution, the dis- 
course states themselves are organized into a 
discourse tree, which is constructed automati- 
cally based on referential cues 4, as described in 
(Seville, 1999). 
0 I 
1 /\ 
2 3 
/1\ 
456 
(1) a mani diedj in a park/~. 
(2) hei hadj been sleeping ther%. 
(3) a womanl lovedm him/. 
(4) shez had,~ hated him/. 
(5) he/ hadm hated himself/. 
(6) he~: hadm loved herl. 
The nodes in such a tree correspond to dis- 
course states. Those oll tile right-hand frontier 
are open, which essentially means that tile enti- 
ties mentioned in them are available to pronom- 
inal reference. 
The process of reference resolution for tile 
various referring expressions can be briefly de- 
scribed as tbllows. Anaphors, characterised as 
salient, are resolved to a less oblique argument 
of the same verb (Pollard and Sag, 1994) within 
the current discourse state, which is constructed 
aHere rcf(AD(cds(D)) is a reference to the current 
discourse state and the properties m and f refer to male 
and female gender respectively. 
4The tree illustrated was constructed using pronomi- 
nal cues. Each discourse state was attached as a daugh- 
ter of the highest node in the discourse tree to which all 
pronouns and referential tenses (like had) mentioned in 
it could be anchored. 
776 
incrementally. We also st;art our sere'oh tbr the 
referents of prononns and other centred enti- 
ties in the current disconrse state, which is nec- 
essary if we are to resolw; such referring ex- 
pressions as "her" in "Mary took John with 
her." However, referring expressions contain- 
ing the property centred are prevented front 
1)eing dereferenced to salient entities, thus en- 
suring that the constraint of disjoint reference 
is met. If we fail to tind the centred en- 
tity in the current discourse state, we search 
the previous open node and, if necessary, fllr- 
ther open nodes in the discourse tree, in order 
to deal with long-distance pronominalisation. 
The dereferencing of other referring expressions 
like ref(AD(named(D, Mary)gcard(D, 1))) is 
similar but less constrained in that we con- 
sider entities mentioned in all nodes mentioned 
in the discourse, tree, whether open or closed, 
in order of recency. This means that, essen- 
tially, names and definite descriptions are deref- 
created to the most recently mentioned refer- 
ent which is appropriate. Unlike in the case of 
pronouns, we also consider Discourse State 0, 
which doesn't correspond to an utterance but, 
rather, contains the background knowledge as- 
stoned in the model. This is how we are able 
to deal with the first mention of a familiar 
referent like Mary (assmning that the proper- 
ties kD(na, m(:d( D, Mary)gcard( D , 1)) sumce 
to distinguish a particular entity in Discourse, 
State 0 from all the others). 
Our approach extends naturally to cases like 
%he first snowdrop of Spring" because it; is 
proof-theoretic and so able to exploit back- 
ground knowledge in reference resolution. This 
can be illustrated, in the first instance., by exam- 
thing the backgrmmd knowledge which is used 
in updating the utterance "Mary slept." The 
update step for this utterance yields Discourse 
State 1, contailfing (amongst others) the tbllow- 
ing facts: 
Discourse State 1 
,s/eep(#134) 
0(#134, agent, #94) 
ends_before(#4(1), #133) aspect(simple, 
#13a, #134) 
We were able to prove named(#94, Mary) 
and card(#94, 1) and so dereference 
rcf(,\D(namcd(D, Mary)&card(D, 1))) as 
the tbllowing were amongst the t~cts contained 
in Discourse State 0: 
Discourse State 0 
female(#94) 
named(#94, Mary) woman(#94) 
f(#.94) 
card(#94, 1) 
adult(#94) 
These were generated from the lexical memfing 
1)ostulates we stipulated for "Mary", "woman", 
and "folnale" : 
3X (namcd( X, Mary)&woman( X)&card( X, 1)) 
VX(woman(X) 
VX(.fcmalc(X) -4 f(X)) 
3 Unfamiliar Referents 
In this section we show how, within the frame- 
work above, we are able to make sense of a vari- 
ety of referring expressions denoting unfamiliar 
referents. The most straighttbrward of these are 
bridging descriptions, so we start with these. 
3.1 Bridging Descriptions 
(1) Mary loves her" moth, or. 
In this first case, "her mother", contains a refer- 
ring expression nested within it;. Having deref- 
erenced this, the knowledge that moth, er of is a 
fllnction enables us to obtain a unique reli;renl;. 
Our representation of the referring expression 
to be derelbrenced is as follows: 
"her mother" 
ref(AB(of(B, 
,.e f ( a, 1) 
$~ f(G)))) ca .d( B, 1))) 
Tile first step involves anchoring tile referring 
expression by dereferencing its nested rethrring 
expression for "her ''5. 
'SThe referent for this is characterised as salient_or_centred 
as we allow I)ossessivc pronouns 
to be dereferenced as anal)hers or, failing that, as 
pronouns. 
777 
Current Model 
ends_at_or_after(#4(1), #135) 
aspect(simple, #135, #136) 
0(#136, agent, #94) Zove(#la6) 
Tile partially constructed current discourse 
state we have when we do our dereferencing is as 
shown. "Mary" has already been dereferenced 
to #94 and this has been entered into the list 
of forward-looking centres fbr the current utter- 
ance. We are able to prove both salient(#94) 
and f(#94), and so our nested referring expres- 
sion is dereibrenced to this entity. 
ref(kB(of(B, , F(,,,other( F) ), 
#94) card(m1))) 
It is then a straighttbrward matter to derefer- 
ence the anchored referring expression, given 
the tbllowing facts in Discourse State 0: 
Discourse State 0 
mother (#60 (#94)) 
of(#60(#94), ;~A(moth.cr(A)), #94) 
f (#60(#94)) 
card(#60(#94), 1) 
These derive from our nmaning postulates fbr 
"mother ''6 and "of": 
VX((X is a,~i.,o,O~card(X , 1) --~ 
~Y (o.f (Y, kZ (rnother( Z) ), X) 
&card(Y, l)&f(Y))) 
VXVYVZ(of(X, Y, Z) -+ Y.X) 
Dealing with other bridging descrit)tions is 
more complicated: 
(1) Mary saw a house. 
(2) She tbund the door. 
In order to give an analogous treatment to the 
referring expression "the door", we have to treat 
it as elliptical tbr an exl)ression containing a 
nested referring expression, i.e., "the door of the 
house". In the same way that we have a mean- 
ing postulate for the relation mother of, we have 
one for the relation door of: 
aSkolemization preserves dm dependency of Y on X, 
i.e., #94 is present in #60(#94). 
vx((ho,, e(x) v car(X)) 
qY (of (Y, AZ(door( Z) ), X)~eard(Y, 1))) 
This means that, having used utterance (1) 
above to update the discourse model, we have 
the fbllowing amongst the facts in Discourse 
State 1: 
Discourse State 1 
seel(#138) 
0(#138, agent, #94) 
0(#138, object, #139) 
card(#139, 1) 
house( #139) 
ends_be for'e(#4(1), #sat) 
door(#46(#139)) 
entrance( # 46( #139 ) ) 
of(#46(#139), ~d(door'(A)), #139) 
card(#46(#139), 1) 
aspect(simple, #137, #138) 
In updating utterance (2), the bridging descrip- 
tion which needs to be dereDrenced has the tbl- 
lowing representation: 
ref(AE(door(E) g~ card(E, 1))) 
Since we caimot guarantee that there will only 
be a single entity in our model satisfying the 
t)roperties kE(door(E) & card(E, 1)), we want 
to ensure that the referent we obtain is either 
the most recently mentioned or that with the 
most recently mentioned antecedent, i.e., in this 
case, the house #139. Our ret>rence resolu- 
tion t)rocedure exploits the fact that the house, 
#139, is explicitly represented in the forward 
looking centres of Discourse State 1 and that 
the intended referent, #46(#139), is clearly a 
flmction of this (its dependency having been 
preserved by Skolemization). In considering the 
potential refbrents for our referring expression ill 
order of recency, we attempt to prove, not sim- 
ply, ibr each referent, X, whether door(X) and 
car'd(X, 1), but door(V) and card(Z, 1) where 
Y is a function of X. Since #46(#139) is 
a function of the antecedent #139, we obtain 
the appropriate referent in this case by proving 
door(#46(#139)) and card(#46(#139), 1). 
3.2 Superlatives 
We are now in a I)osition to describe our treat- 
ment of the superlatives discussed in the intro- 
duction. First, we consider a case in which there 
is a discourse antecedent of sorts: 
778 
(1) Two men arrived. 
(2) The first man spoke. 
Discom:se State 1 contains the tbllowing facts: 
Discourse State 1 
arrive( #107) 
0(#107, agent, #1.08) 
card(#108, 2) 
man(#108) 
male(#108) .~(#108) 
adult(#108) 
~n&_b<l'o,'d #4(1), #106) 
a.s'pect(.simplc, #106, #107) 
Our representation of the referring exi)ression 
"the first man" is as follows: 
rcf(k\]3('mo,st(B, 
~C(early( C, AD(man(D)))), 
,.~f (~E(,,,o,,,,(~)))) x~ ,-..,.d(u. 1)))) 
The nested referring expression 
ref(AE('m,a,'n.(E)))) ('m~ be straightforwardly 
dereferenced in this case to give the anchored 
refi;rring exl)ression: 
rcf(A\]3(mo,st(B, 
ac(,.~,,+.,j( c, .xu(,..,.~(J))))), 
#108) 
g ,..,,,,,.d(J3, ~)))) 
Dereferencing this then involves our meaning 
postulate fi)r superlatives: 
VXVZVC(,-,,,,.d(Z, C)~(Z - X)~(~C = 1),~ 
V NV P (-wnosl.( X, P, _) -+ 
~Y (mosl,(Y, P, X)&card(Y, N)))) 
This siml)ly says that tbr any severalton set X, 
any property 1 ) and any N, there is some set Y 
containing the N "most P" members of X. This 
meaning postulate does not translate into any 
facts in Discourse State 0, lint remains as a rule. 
When we have a particular referring expression 
to derefhrence, this rule enables us to prove that: 
most(#81(kA(early(A,...)), 1, 2, #108, #108), 
,x ( c ( ~,~,.ly( c, ~D ( .,,,,,.,( D ) ) ) ), 
#108) 
card(#81 (AA(c'arly (A,...)), 1, 2, @ 108, @ 108), 
1) 
In this way, we prove that the referring ex- 
pression makes sense, i.e., denotes. However, 
unlike in the previous cases, we do not deret- 
erence to a familiar referent. There are no 
existing facts in the database about the ref- 
erent #81(AA(early(A,...)), 1, 2, @108, #108). 
Instead, in this case, we have to add to Dis- 
course State 2 the facts we have proved. 
Discourse state 2 
° .__ 
spcalv( #112) 
th, cta( #112, agent, 
#81(AA(early(A,...)), 1, 2, #108, #108)) 
end.s_before(#4(2), #11.1) 
.spcech, A.imc( #4(2), 2) 
aspcct(.simplc, #111, #112) 
mo.st(#81(AA(early(A,...)), 1, 2, #108, #108), 
~ c ( ~o,,.z..,j( c, ~ D (,~o,,4 D ) ) ) ), 
#108) 
~,,~.d(#Sl(~A(~o,,@(A,...)), 1, 2, #108, #108), 1) 
~,,@(#81(~A(eo,,@(A,...)), 1, 2, #108, #108), 
:~c(,,,a,~( c) ) ) 
,,,,,,,,,(#81(~A(,,,,,,.ly(A, . . .)), 1, 2, #108, #*O8)) 
mah'(#Sl(AA(early(A,...)), 1, 2, #108, #108)) 
m(#Sl(AA(early(A,...)), 1, 2, #108, #108)) 
,,d,,,U,(#Sl(~A(~,,@(A,...)), 1, 2, #108, #108)) 
The fln:ther facts we. prove, about our refe.rent 
being e~rly, male, etc., are required if we are to 
be aMe to subsequently retb.r to it using referring 
expressions such as "he". The.se are generated 
from a set of associated memfing postulates: 
VXVYVP((ordered(P)~most(Y, P, X)) -+ P.Y) 
V A ( ordered( AB (early( B, A)))) 
vxvP(,.~o,,.1,,(x, 1,) -~ p.x) 
VX ('m, an( X) 
(X is h, uman)~male(X)&adult(X)) 
vx(mde(x) -~ re(x)) 
In addition to these, we have two further mean- 
ing postulates for superlatives: 
vxvYvevcvz(,,.o~t(Y, 1; X),~a,.d(Y, C) 
g,,,os~,(Z, P, X)*~a,.d(Z, C) -~z=Y) 
VXVI'VYVNVC(most( X, P, Z)& 
card(X, N)~card(V, C) 
-~ ~,~o,.~( N, C) ) 
779 
The first of these, the uniqueness meaning pos- 
tulate, states that if there are two subsets of of 
a set which share the same cardinality mid the 
same superlative property, such as first, then 
they must be regarded as identical 7. The sec- 
ond simply ensures that any mffamiliar ret5r- 
ent which we obtain via our meaning postu- 
lates can sensibly regarded as a proper subset 
of its antecedent; that is, it prevents us regard- 
ing "two men" as a potential antecedent of "the 
first men": 
(1) Two meni arrived. 
(2) The first men,f(i) spoke. 
Our treatment of superlatives without dis- 
course antecedents is similar to that above. 
(1) Mary saw th, c first snow&vps of 
Spring. 
There is just one major difference. 
r' I( E 
AF(carly(F, 
: a(of(a, 
,\It(snowdrop(It)), 
re f ( ),I(named( I, 
@ri..o) g  rd(Z, 1))))))), 
ref(),J(of(J, ( s o.odrop( K) ), 
re f ( kL(named( L, Spring) 
&card(L, 1))))))) E, VO ) ) ) 
The representation we obtain for the referring 
expression "the first snowdrops of Spring" is 
shown above. Like that for "the first man", this 
contains a nested referring expression: 
ref(),g(of(J, 
AK ( snowdrop( K) ), 
~card(L, 1))))))) 
The difference is that, in this case, there is 
no discourse antecedent for the nested refer- 
ring expression. This means that, in order to 
7practicaUy, this meaning postulate seems to be re- 
dundant. Our meaning postulates generate for us only 
one such subset and it is impossible for another to be 
introduced through the discourse as "a first man" is un- 
grammatical. 
anchor our referring expression by dereferenc- 
ing the referring expression nested within it, we 
need to introduce a meaning postulate for the 
nested referent (and one for its nested referent, 
Spring): 
3X ( X, rd( X, 1)) 
qX(of(X, 
) ) ) 
&card(X, pl) ) 
These meaning postulates simply introduce into 
Discourse State 0 the fact that there are snow- 
drops of Spring, in the same way that the mean- 
ing postulate for "Mary" introduced the fact 
that there is a singleton set containing an in- 
dividual so named. 
Discourse state 0 
season(#98) 
named(#98, Spring) 
card(#98, 1) 
extended(#98) 
snowdrop(#101) 
of(#101, A(A, snowdrop(A)), #98) 
..(#101) 
card(#101, pl) 
Given the above facts in Discom'se State O, an- 
choring our referring expression is straighttbr- 
ward. 
f (  E(. ost( E, 
1F(early(F, 
 C(of(a, 
Mt (.snowdrop( H) ), 
#98)))), 
#101) 
* car'd(E, P0))) 
From this point onwards, the proof that this 
referring expression denotes proeeeeds in the 
same way as in the previous example. Given 
the meaning postulates for superlatives, we are 
able to prove: 
most(#81(),A(early(A,...)),pl,pl, #101, #101), 
~D(early(D, 
)~E ( o f ( E, )~F ( snowdroI,( F) ) , #98)))), 
#101) 
card(#81(~A(ear'ly(A,...)),pl,pl, #101, #101), 
pl) 
780 
Again, as in the example above, the facts we 
have proved concern an nut~miliar referent, and 
so have to 1)e added to the current discourse 
state. 
Discourse state 1 
.seel(#107) 
theta(#107, agent, #94) 
tit, eta(# 107, 
object, 
#81(),(A,...), #98)))),pl,p/, #101, #101)) 
ends_before(#4(1), #106) 
aspect(simple, #106, #107) 
most(#81(AA(...), #98)))),pl,pl, #101, #101), 
AD(early(D, 
AE(o f ( E, AF(.snow&'op( F) ), #98)))), 
#1Ol) 
card( #Sl(AA(. . .), #98) ) ) ),pl,pl, #101, #101), pl) 
carly(#S1(AA(...), #g8)))),pl,pl, #101, #101), 
D ( o f ( D , z ( op ( Z ) ) , #gs))) 
oI(#81(AA(...), #98)))),pl,pl, #101, #-101), 
)~O( ~',,,ow&'op( D ) ), #9s) 
snowdrop(#S1(kA(...), #98)))),...)) 
n(#81(kA(...), #-98)))),pl,pl, #101~ #-101)) 
4 Conclusion 
We have shown how, l)y taking a t)root:theoretie 
approach to reference resolution, we can extend 
a Centering-tyt)e framework to make sense of 
tel!erring expressions for a w~riety of unfamiliar 
referents. Having made sense of such referring 
ext)ressions, we add their referents to our dis- 
course model. This is how we would normally 
deal with indefinites rather than definites. How- 
ever, this al)t)roach makes t)erfect sense, given 
our treatment of su('h referring exl)ressions as 
denoting unfamiliar subsets of familiar referents 
(regarded as sets). We claim that we are able 
to use definite descriptions to refer to the ref- 
erents in question, despite their unfamiliarity, 
SO long as we Call prove that, by virtue of their 
meaning, they denote uniqnely. 
Having imt)lemented our approach in a sys- 
tem of  understanding which already 
deals with a wide variety of referring expres- 
sions, we have demonstrated its practicality. 
It also has interesting theoretical implications, 
since it suggests a way in which pragmatic theo- 
ries of reference resolution, like Familiarity The- 
ory, and semantic theories, like Russell's, may 
be reconciled. However, it is fair to say that 
the success of the approach is not yet proven. 
This is because we have yet to show that we 
can deal with a set of related referring expres- 
sions within a single fi'amework. The following 
example illustrates the kinds of cases we have 
in mind: 
(1) Three meni ate. 
(2) Two menj slept. 
(3) The first meni died. 
Here, "first" in "the first men" is clearly per- 
tbrming a dit\[erent, discourse-related flmction 
from that it plws in the cases we have been 
considering. We have yet to tackle such difficult 
cases but, since they seem to require reasoning 
about sets, we believe that our inference-based 
approach to reference resolution is a good place 
to start. 

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