The Logical Structure of Binding 
Ant6nio Branco 
DFKI and Univ. of Lisbon 
Dep. Inform~itica, Fac. Ci~ncias, Campo Grande, 1700 Lisboa, Portugal 
Antonio.Branco@di. fc.ul .pt 
Abstract 
A log.ical recasting of B.inding Theory is performed as an enhancing step tor the purpose ot its gull and lean 
declarative implementation. A new insight on sentential anaptioric processes is presented which may 
suggestively be c%ptured by the slogan binding conclitions are me effect of phase quantification on the 
universe of discourse referents. 
Introduction 
Due to its central role in natural language and its intriguing propert.ies, reference and anap'hor resolution 
has been a central topic for NLP research. Given the intensive attention devoted to this subject, .it can 
however be said that sentential anaphor orocessmg has been quite overlooked, when compared io the amount 
of research effort put in tackling non sentential anaphoric dependencies. This tends to be so because 
there seems to be a more or less implicit assumption that no substantial difference exists between the two 
~cesses 1. ile this may be arguably true for. the heuristics 
involved in picking out a given antecedent from a list of suitable candidates, a more s.ubtle point asks. itself 
to be made when we focus on the syntactic conditions which sentential anaohoric relations comply with, but 
from which non senfential ones are exempt. In theoretical linguistics these grammatical conditions 
are grouped under the hea.ding of BindingTheory.. In computational linguistics however, tlaoug.n there have 
been a few papers directly concerned with me implementation of this theory, mainstream research 
tends t 9 disregard its conceptual, grammatical or practical modularity. When it comes to define me 
algorithm. .for.setting up the list of suitable candidates from which the antecedent should be chosen, binding 
conditions, holding just at the sentential level, are most otten put on a par with any other kind of 
conditions, morphological, semantic, pragmatic, etc.~ which hold for anaptioric relations at both sentential 
and non sentential level. The interesting p.oint to be made in this connection is 
at, it the modularity ot grammatical knowledge is to be ensured in a sound reference resolution system, 
more attention should be paid to previous attempts of implementing, Binding Theory.. It would then become 
ewdent that mis theory, in its current formulation, appears, as ,a , piece of formalised grammatical 
KnowJe~age wnicn nowever escapes a full and lean declarative implementation. 
In fact, implementation efforts concerning Binding Theory 2 bring to light what tend to be eE!ipsed by. 
mainstream clean theoretical formulations ot it. Behind t.he apparent declarative aspect of its definition under 
the form ot a set of binding principles(plus definitions of associated concepts, e.g. o-command, o-bound, local 
IAs entry points into bibliography vd References in Grosz etal. 
(95) and Botley et al. (96). 
-'Vd. Chomsky(81 ), Correa(88), lngria et al (89), Fong (90), Giorgi 
et al. (90), Pianesi (91). 
domain, etc.), there is a set of procedures which turn out to be an essential p.art ot the theory: after parsing 
being completed, (it in~lexation: assignln.dices to NPs; (ii) filtering: store the indexed tree it the indexation 
respects binding principles, reject otherwise; (iii) recursion: repeat (i)with a new assignment until all 
possible assignments are exhausted. T.his sort of resistance to declarative encompassing is 
also ap.oarent when one considers how Binding Theor Z is hani:lled in grammatical theories developed on top ot 
constraint based formalisms and particularly concerned with computational implementa'bility, lille LFG or 
HPSG. As to HPSG, it has passed quite unnoticed that its 
Binding Theory is the only piece of the grammar fragment not encoded in its own formalism. In the 
Appendix of the foundational book (Pollard and Sag ~9"4)), where the fragment of grammar developed along 
tts 700 pp. is encoded in the adopted formalism, Binding Theory_ escapes such encoding. Bredenkamp 
(96) and Backot'en et al.. (96) subsequent elaboration on this. is.sue jmplied that som. e. ki.'nd pf essential 
limitation ot the tormallsm might have been reacnea and that H PSG. Binding Theory is still waiting to be 
accommpdate~ into HPS.G grammars ...... As tO the UP~ tormulaUon ot t~lndmg lneory, it 
requires the integration of inside-out equations, a sp6cial purpose extension to the general'declarative 
fbrmalism. And even though initial scepticism about their tractabili.ty was dissipated by Kaplan and 
Maxwell \[88), the recent survey, of l~acKoten et al. (96) repo.rts that no implementeH formalism, and no 
implemented grammar, is known to handle LFG Bin.ding Theory.. . ..... 
In this connection the central aim ot the research to De pres.ented here is to render possible a lean declarative 
implementation of Binding Theory in constraint based formalisms without resorting to specific complex 
mechanisms. This involves two steps. First, as a sort of enhancing step back, a new account, of Binding 
lheory, is set up. Second, by the exhibition ot aft example~ the new shape of the theory is shown to 
support full declarative implementation in basic HPSG formalism. Due to sp.ace constraints, this .paper is 
mostly concerned with the first, while the latter receives just a rough sketch in last section, being 
develope~l in future papers. 
1 Preliminaries 
1.1 The Square of Opposition 
Recent cross linguistic research, e.g. Xue, Pollard and Sag (94) and Branco and Marrafa (97), ILas shown that 
the binding ability of long-distance renexives.is not reducible to recursive concatenation of short distance 
relations, as it has been assumed in GB accounts, but that it is ruled by a fourth binding principle: 
(1) Principle Z 
An o-commanded anaphoric pronoun must be o-bound. 
181 
(2) Z: B: x is bound compatible x is locally free 
.I 
contradictory 1 implies 1 contradictory 
C: contrary A: x is free x is locally bound 
This new perspective on long-distance reflexives had an important impact in the whole shape of Binding 
Theory. Branco and Marrafa noted still that the four principles can be arranged in a classical Aristoteli.an 
s~uare at oppositions, as in (2). This su~zgests that the Binding Theory may have an unsuspec'(td underlying 
q uantificational structure. The present paper aims at snowing that there is such structure and at determining 
its basic lines. 
1.2 Phase Quantification 
Barwise and Cooper (81) seminal work gave rise to a uitful research tradition where Generalised Quantiller 
Theory has been applied to the analysis of natural land e " " =uag q.uant~ficanon. These authors suggested that a 
universal characterisation of NL nominal quantification could be formally given by means of ,formal prop, erties 
defined in that theory. Th.'e property to live on was postulated as being the most prominent one~ 
admittedly constituting the common specific nature at all nominal quantifiers. 
L.ater, Loebner (87)suggested a criterion to ascertain the quantihcat,onal nature at natural language 
expressions in general. That is the property that, for a one place second order operator Q expressed by a given 
exc~ression, there be a corresponding dual operator 
THls'duality-"¢- based perspective on the essence of natural langua,,. ,.~, e quantificauon permitted to extend 
quann~fication su orted 19 the determiners all, some. canon well beyond the classic cases of nominal q PP . . most many, etc., namely ~y covering also the realms 
of tempora'litv and Doss'ibility. Moreover, items like still/ already, , and others (enough~too, scaling 
adjectives, man)/few, etc.) though they do not lend themselves to be straightforwardly analysed in terms of 
set .quantification, they can alsob.~ arranged in asquare of duality. The formalization at the semantics at these 
aspectua\] items by Loebner led tq the enlarging of the notion at quantincation through the introduction at the 
new concept of phase cmantification. He noted that still and alreaclv express duals m2,,d that 
they are corners,of a square of,d, uality. Let P be she is asleep" and -P 'she is awake', durative propositions 
which are the arzuments of the semanuc operators corresponding to aTready and still. Then: 
(3) She is already asleep iff 
it is not the case that she is still awake. 
ALREADY P iff - STILL -P 
Further similar tests can be made in order to show that these aspectual items enter the following square of 
duality: 
(4) inner still negauon .not yet 
/q , 
e OU ~r OUt ~" negauon/ dual | negauon 
no longe) ~'~---~ ~ already inner neganon 
In order to ~et a formalization of (4), Loebner noted that alreac~,.should be taken as convey.in~ the 
information that there is a phase of not-P which has st a(ted before a given reference time tO and might be 
IOllOWeO lay at most one phase P which reaches tall tu. This can be displayed in a time axis by means of the 
diagram in (5). 
(5) tO tO 1 
'"~'"'"'-" ~ t 
P -P ~p P 
still P not yet P 
tO tO 
P -P ~p P 
no longer P already P 
Similar diagrams for the meaning of the other aspectual phase quantitiers at this square of duality are 
easily intemretable. Inner negation results in exchanging the positive and the negative semiphases, 
while outer negati9n c.oncerns the.decision whether the parameter to tails Into the hrst or the second 
semiphase. Phase quantifiers in general (already, scaling a.djectives, 
etc.) . were thus characterised as requiring two ingredients: (i) a property P, which defines a positive 
phase in a sequence of two opposi\[e phases; (ii) a p.arameter point. The four types at quantifiers just 
~liffer in presupposing that either the positive or the negative semiptiase,co.mes first_and in stating that the 
parameter point tm~s rata the tirst or into the second semiphase. . . . . 
Next Loebner showed that the semantics of phase ~oUantifiers sketched in the diagrams above can be 
rmalised in such a way that" a square of duality formed b~, the generalised q.uanti.fiers XX.some'(D,X~/ 
XX.every (D,X) turns out to t~e su.bjacent to the square of duality of already~still. In order to do it, he just 
needed the auxiliary, notion at starting, point at the relevant semiphase. This is rendered as the intimum at 
the set of the closest predecessors of the parameter po.i.nt pt which, forman unint.errt~pted linear sequence 
w~th property P, or ~P (.termed Libl(K,pt) lay Loelaner): 
(6) GSI(R,pt) =df inf{x I x<pt & R(x) & 
Vy(x<y<pt & R(y) --~ Vz(x<z<y ----~ R(z)))} 
The semantics of the four ohase quantifiers above can then. be rendered in the following way, making pt=tO 
tar the parameter point and R=P or R=-P: 
(7) still: XP.every'(X x.(GSI(P,a)<x<t0),P) 
already: XP.some'(X x.(GSI(-P,a)<x<t0),P) 
not yet: XP.no'(Xx.(GSI(-P, a) < x < t0),P) 
nolonger: XP.not every'(Xx.(GSI(P,a)<x<t0),P) 
2 The Logic of Binding 
Taking Loebner's view on quantification, our goal in this section is to make apparent the quantificational 
structureof binding by showing that on a par with the square o! opposition, of (2) binding, principles form a 
,squa4".e of d.dality, we are going tDus to argue .that olnain.g prlnciptes are out the reflex ot the ph.ase 
quantincational nature oI corresponding nominal expressions: reflexives, prg.no.uns, long-distance 
reflexives and R-expressions will be shown to express phase quantiners acting on the grammatical 
oonqueness axis. 
182 
2.1 Phase quantification ingredients 
In order to show that the above referred nominals .express ,phase quantifi.ers t.he relevant .components 
mvoJvea m pnase.quantm.catlon snored t~e. mentmea. lne relevant scale here Is not the continuous nnear 
~.rder of mo.ments of time, as for still~already, but a lscrete partla~ order made oI mscourse rererents (ct. 
DRT) arramzed according to the relative obliqueness of grammatical functions. Note that in multiclausal 
constructions there is the corresponding subordination of different clausal obliqueness hlerarchles (for the salve 
or comparalgility with diagrams (3) involving time arrow, Hasse dm~ams for obliqueness are displayed 
with a turn of 90~right): 
(8) Kim said Lee saw Max. 
O 
k 1 m 
Note also that the relation "less oblique than" may not be linear: 
(9)Kim said Lee, who saw Max, hit Norma. 
O--------O O 
k 1 n 
O O I m 
The sequence of two oEposite semiphases is defined by a,prooerty 1-'. Contrarily to what happens 
with .alread3, wfie.r.e operator (quantifier). and o~rand (auraUve proposmon) are renderecl p.y mtterent 
expressions, m binding p.hase, quantification .me operanu r is also contnbuteO by. the nomlna~ 
expressing the operator, i.e. expressing the binding phase quantiner. 
For a given nominal N P is determined by the relative position of N in the scale . For a discourse referent r 
corresponding to N, semiphase P is a linear stretch containingonly elements that. are less than or equal to 
r in the obliqueness order, that is discourse reterents correspondi.ng to. , nom in.als o-commanding N.. 
Moreover, it semlpnase .r Is. presupposecl to precede semiphase -P, P is such that the last successor m it is 
local wrt to r; and if semiphase -P is presupposed, to precedes semlphase P, P is such .tha.t the first 
predecessor in It is local wrt to r. In both cases tide closest ~ nei~hbour or semiphase -P has to be local 
wrt r, where the notion of locality has the usual sense given in the definition of binding principles: 
(10) P(x) iffdef x < r & Vy\[(-P(y)& 
(x-<y or y-<x))----) x is local wrt r\] 
As to the parameter point, in binding..p.hase quantification, it is the discourse reterent a winch is 
the antecedent of r. 
2.2 Binding phase quantifiers 
We can now formalise phase quantification subjacent to nominals. Let us start with an anaphoric 
expression N like himself 
(11)Kim said Lee thinks Max/hit himself/. 
*Kim said Lee/thinks Max hit himself/. 
QA: XP.some'(Xx.(GSI(-P,a)<x<a),P) 
.a P 
o ! 
k .... 0 X 
C 
X 
N can thus be inte.rpreted as presupposing that a semiDhase -P precedes a semipfiase P and requiring 
that the p.arameter point occurs, in the. !atter~ ttiat is, the antecedent a ~s to be round in .s.em~pn~e r among 
the discourse referents corresponding to Uae local o- commanders of r, the disc referent correspgnd.ing tq N 3. 
This is captured by_ the definition oI tide pna:s.e .quantifier QA. Sanstaction. of QA(P) obtains iH 
between the bottom ot tide uninterrupted linear sequence -t-' most close to me parameter 
p.omt/antecedent a and a inclusive there is at'least one ~liscourse referent in P. Given -P.P, this amounts to 
requiring that a be in P, and that a be a local o- commander of 
r. 3 Next, it is then easy to see how the phase 
quantificational force or a pronominal expression N should be formalised: 
(12) *Kim said Lee thinks Max/hit him/. 
Kim said Lee/thinks Max hit him/. 
QB:XP.no'(Xx.(GSI(~P, a) < x < a),P) 
_p ~a ~:~ p 
Here the parameter point a occurs in semiphase -P, which amounts to the antecedent being picked 9utside 
t,n.e set of loc~ o-commanders. QB(P). Is satisnea itt no discourse reterent between the bottom ot me 
uninterrupted, linear sequence -P re.ore c.lose to the oarameter i~olnt/antecedent a and a Inclusive Is In r'. 
Given.-P.P, this.amount.s to requiring that a be ,in semiplmse ~1 ~, and mat a be not a local o-commanoer 
of r. Like in diagram of (11), ~P is taken here as the 
complement set oIP. All discourse reterents which are not "local o-commanders of r are in it, either o- 
commanding r or not. Notice that set -P includes also discourse referents Xl.vX n introduced by previous 
sentences or the extra-linguistic context, which in constructions similar to (l'2)b. accounts for possible 
aeictic readings of the pronoun. Below, when studying .R.-expressions~we,wlll see why. the possible non 
linearity ot me ot~li.qu.eness orizler will led. us. to consider that -1: is sljglatly more complex than just 
me complement se_t ot r'._ Coming now to long-distance reflexives, ruled 
by. the fourth binding principle in (1), we get the following formalisation: 
(13)\[O amigo de Kim\]i disse que ele pr6prioi acha que Lee wu Max. (Portuguese) 
\[Kim's friend\]/saidLDRi thinks Lee saw Max. 
*\[O amigo de Kimi\] disse que ele pr6prioi acha que Lee viu Max. 
\[Kim'si friend\] said LDRi thinks Lee saw Max. 
Qz:XP.every'(X x.(GSI(P, a)<x_<a),P) 
~a P _p 
O I xn k 
3For the sake of simplicity, agreement requirements between N 
and its antecedent are overlooked here. 
183 
Here, like for short-distance reflexives in (11), a is required to occur in P though the presupposition now 
is .t.13at semiphase P is fpIlowe.d by~ ~m.ipnase ?,r'. laKmg.mto account the de/m.mon oI t- m t~u), me 
antecedent of N is thus required to Dean o-comma3a.ger Qocal or n.ot) of N. Thesemantics PL P.13ase quantiner 
~Z ~s such tpat, tor QZ(r') to .De saUsned, between me bottom oI the uninterrupted linear sequence V more 
close to the parameter point/antecei\[lent a and a inclusive every ..discourse referent is in P. This 
amounts to requmng that a be in semiphase P, and that a be an o-commander or r. 
Finally R-expressions call to be formalised as the fourth phase quantifier of (7): 
(14) \[Kim'si friend\] said Kimi thinks Lee saw Max. 
*\[Kim's friend\]/said Kimi thinks Lee saw Max. 
Qc:hP.not every'(Xx.(GSI(P,a)<x< a),P) 
P -P 
o m 
0 I xn k 
a) 
The parameter point a is required to occur in -P, which means that a cannot be an o-commander (local or not) 
of r. This renders the same condition as expressed by Principle C, that R-expressions be free, though it also 
encodes an uncommon assumption agout the referential autonomy of R-expressions. Here, like for 
other more obvious dependent reference• nominals, the interpretation .of l,~-expressions is. taken as being 
dependent on the interpretation ot other expressions or on the salience of discourse referents made available by 
the communicative context. Taking an extreme example in order to support the plausibility of. this 
view and awkwardly, ab'6reviate a deep philosophical discussion, one should notice that even a proper name 
is not a unique label of a given individual~ once knowing who is the person called John (out ot those 
we know that are named John) depends on the context. Note that like in previous diagrams, -P is taken in 
(14) just as the complement set of P. However, QC asks finally for a serious ponderation o) this and a 
more accurate definition of -P for phase quantincation in non linear orders, where it is possible that not all 
elements are comparable.. ..... Por t~c(P ) to be satisfied, between the t~ottom o\[ i- 
and the parameter point/ antecedent a inclusive not every discourse referent is in P. Since we have here the 
p.resupposition P.-P, andgiven P is an uninterru.pted linear sequence, this would-amount to requiring that a 
be in -P. It is wortb noting then that i.f we keep -P simply as 
the complemen.t set of r', the interpretation o! ~- expressions is however not adequately predicted by 
~c(P). 
(15) John said Kimj thinks Lee saw Max. 
P -P 
a-...~l o n 
P -P 
~: ......... m 
Let D be Ix: GSI(P,a)<x<. a}~t.he domain of .Qc. Taking (15)b., it is easy to check that in constructiops 
like (.IS)a, D is always empty. In fact, it is not the case that G S.I(P,a)<a as a=xl- is not comparab.le to any 
element ot 1-', andafortiori it is not comparable to the bottom.of P. Consequently, every'(D,P) is trivially 
true whatever discourse referent xn we take as antecedent for r, and not every'(D,P) is trivially false. 
The interpretation of.(1.5)a, sketched in (15)b. would thus be incorrectly ruled out. 
What these considerations seem then to suggest is that, when ph.ase quantification opera.tes o.n non linear 
orders, negatmn ot the ooerand r' ~s slightly more complex ttian sim_ple Boplean negation rendering the 
complement se.t.W..e are thus.taugm tla.at negation qf.P involves also the lilting ot the comolement set o~ L', 
P_L, with _1_ equal to r, the top of P, when P.-P . It is easy to check with diagra..m (15)c. that this 
specification of-P makes it possible to satisfy Qc(P) in exactly the correct constructions. 
2.3 The Binding Square of Duality 
Fol!owing Loebner's claim that logical duality is the cardinal property to recognise the quant~hcational 
character 9f nat.ural language expressions, we are thus led to the vmw that the interpretaUon or pon 
quantincational dennite nominals ~s...ruled by their phase quantincational Iorce over the obliqueness order. 
Since ~he defining formulas of binding quantiners result from .(7) just by assigning P the ~lefinition .in 
(10) and taking the .p.arameter point, pt to be toe antecedent a, ~t is w~th no su.rpnse that we get the 
following square of duality for binding quantitmrs: 
(16) ~ inner ,-, x/Z negatmn ~/ 
~~~ ~outer outer - / dual / ne~atmn negauon/ _ _ / 
q -- C inner Q A 
negation 
3 Consequences 
This new conception of binding seems to have important consequences not only in terms of the 
understandimz of dependent reference mechanisms captured by Binding Theory but also in terms of our 
conception o.f generalised quantification in natura\] language, of the twofold semantic capacity, ot nominal 
expressmns, referential and quantificational, and maybe even of the.nature of grammar devices. Here we cannot 
do but to limit ourselves to hint how a lew central i.ss.ues usual\]y assgciated to binding are handled, u.nder 
this new viewpoint, bet~e we proceed to bnetly~ consider its consequences tor the implementation ot 
Binding Theory in constraint based grammars. 
3.1 Further insights into binding... 
Parameterization It is well known that though binding principles are assumed to hold universally m 
all languages, final "grammatical geometry" between 
184 
nominals and their antecedents may be different from lanRuage to language.. .... 
Da\[ry mple (9.3) pointed out that this is.oue .to l.anguage specific cqndit!ons i.mpinging ~),on the eligibimy or 
t.ne anteceoe.nt (wnemer it is a ~ubiect. or not) and ~l~) the range 9t the local domain (whether it ~s nnite, 
tensed, .etc.). As to (i), Branco and Marrafa (97) showed that it ~s a conseqgence of a lexical property of the 
precticates, whose ot~liqueness.hierarchy may be either linear or non linear. Es to (ii), t0is variation may 
accommogated in the definiuon ,ot property P in 00.), in particular in the de.finitiqn of loca~ w.rt tq r., to 
proyl(Je for each partlcu!ar language. ~oth splu.hons are oertectly contluent w~th. the uLi standpomt .that 
binding v.aria.tions across language are the result ot parameterlzatlon. 
Lexical gaps 4 It is also well known th.at although. t~e tour binding principles, are claimed to be universal 
mere are. languages wnicn nave not all the corresponding tour type of nominals. For instance, 
English is not known fo have long-distance reflexives. Ine answer Ior this oecomes now quite simple: like 
what happens in other squares of duality, it is possible that no\[ ever)/, corner of the. square IS le~calized. 
9oeoner t~s/) qlscusses at.length t.ne Issue. m ~ngusn, ~or instance, it is noted mat the square or ouauty 
concerning deontic possibility involvingright h.appens nave only two le_xic_alized .corners, right and duty. , 
r~xe.mption, and Iogophoricity AlSO worm considering here is the borderline case where the 
maximum shrink of semiphase P occurs, i.e. when P is the singl.eton whose sole ele .ment is r, the .discourse 
r.eterent whose interpretation ~s to De anchored Dy nnolng an antecedent tor ~t. _ . 
Oiven the definition of binding phase quantitlers~, me maximum shripk .of P into a. singl.eton attects 
significantly only the quantifiers wlaere the parameter polnU antecedent a is to be found in P, namely QA and 
QZ. In these cases, for a to be in P an~l-me quantincation to 0e satisfied, a can only be r, r being 
thus its own antecedent. Consequently.~, although the Quantification is satisfied, a '.meaningftil a.nc.hor.mg of 
the discourse referent r is still to be accomplished since by the sole effect of.quantification satisfaction r is iust 
anchored to itself. Admittedly, an overarching inte~retability requirement imposes that the 
significant anchoring of nominals be consummated, which, i.nduces in present case an exceptional 
logopnorlc ettect: tor me anap.nor (snort or Io.ng- distance), tq t)e lnterpreted,.and given t.nat satls.t.act.lon 
ot its t)lnding constramt is ensured, It should thus freely . find an antecedent outside any specific 
restriction. This constitutes th.usan explanation for the exemption 
restrictions in the definitions oI rrinciples. A and Land so called logophoric effects associated .to exempt 
anaphor.s. Restrictions. which appeared until no.w to ,~ .mere.stlp.ulations recewe in this approach a pnnciplea 
jusnttcatlon. 
3.2 ... for a lean implementation 
The new conception of. Binding Theory presented in is paper is currently being inte~ated" in an HPSG 
grammar implemented in ProFI.T 1.54.. Space lim.its restrict us here to a very. prier rauonme ot .mat 
implementation, which wall be fully presented in tuture tpapers. 
T.he in}erestingpqint t 9 note in t.his connectip.n.is .th.at me new insight !nto oinmng phenomena elicited t~y 
the discovery of. t0eir qua ntin.cationa\] nature seems, to constitute a breakthrough tot t.ne desideratum or giving 
Binding Theory a lean declarative implementation. Adopting a pnnciple based semantics in fine with 
Frank and Reyle (95), the central goal is not anymore 
4 Though it is empirically not necessary, for the sake of uniformity, 
when -P.P, the order-theoretic dual of this specification of -P can 
be assumed. 
9o filter coindex.ations between NPs in post-processing ut rather to identi.ty the relevant sets oldiscourse 
reterents against which satistation ot the binding phase fluantitlc.atlon expresse.d by .NPs is check.ed. .. . 
in practical term.s that myolves first._ collecting discourse reterents into set values ot 
specific teatures, requiring a minor extension to "HPSG feature 
declaration. S.econd, giyen the possible .non local nature ot the elements ot a given set, in order to avoid 
termina.tion problems" some. mechanism of delaying constrmnt satlstactlon has to be ensured. 
Conclusions 
fThoe research .reported here present a cogent ,argument r the quantmcatlonal nature ot sententlal dependent 
reference relations among nominals. This radically new conception of binding appears as a decisive step. 
~w~fls a full lean decIara.tive, encompassi_ng or .~inaing lneory i.n constrain.t based g.ram.mars. It may 
have also opened .new intriguing directions 3or the research on natural language generalised quantitl.cation~ 
on the. apEarent twolold semantic .capacity .ot nominals, reterential and quantillcational, or on the 
nature of grammar devices. 
Acknowledgements 
lSfsecial thanks are due to Palmira Marrafa and Hans zkoreit for their advice and discussion and to 
Berthold Crysmann for his detailed comments. 

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