A Binding Rule for Government-binding Parsing 
Nelson CORREA 
IBM Thomas d. Watson Re.search Center 
P. O. Box 704 
Yorktown lteights, NY 10598 
USA 
Abstract 
In this paper I propose a Binding rule for the iden- 
tification of pronoun and anaphor referents in 
phrase-structure trees, assuming the general frame- 
work of lhe Government-binding theory outlined 
by Chom,;ky (1981). The Binding rule, specified by 
means of an attribute grammar, is a particular 
instantiation of the Free Indexing rule and binding 
axioms in Chomsky's Binding theory, with certain 
empirical and practical advantages. The complexi- 
ties of the Binding rule proposed, as well as that 
inherent in Chomsky's Binding theory, are studied, 
and it i~ shown that the new rule is more 
psychologically plausible and cornputationally effi- 
cient than the original theory on wtfich it is based. 
The fragment of the attribute grammar shown here 
is part of an English grammar and parser being 
developed in tile Prolog and PLNLP languages. 
Introduction 
Binding is a component subtheory of Government- 
binding which applies in the derivation of the 
logical form of utterances from their surface rcpre- 
sentation. The area of semantic interpretation dealt 
with by the binding theory is that of anaphora. 
Binding theory defines only syntactic conditions on 
anaphora; the reader is referred to /Hobbs, 1978/ 
for some of the extra-syntactic factors that might be 
involved. Binding assumes an Indexing rule which 
applies to an input S-Structure tree and annotates 
it, assigning to every NP node ha the input tree a 
referential index, which represents the coreferenee 
relation ot the NP with other NPs in the input. 
In this paper research is continued on the use of 
attribute grammars to provide a fully explicit and 
computationally oriented statement of the 
Governmc.nt-binding (GB) theory /Correa, 1987/. 
The Binding rule presented here improves over the 
standard statement of the Binding theory in two 
respects: From an empirical point of view, the new 
rule accounts for crossover binding phenomena 
/Kuno, 1987/ without recourse to reconstruction 
/Chomsky, 1981/; from a practical point of view, 
the new rule is more computationally sensible than 
the generate-and-test approach understood in 
Chomsky's theory, and hence is a plausible candi- 
date for incorporation in natural-language parsers 
that account tot anaphora. Previous literature on 
GB parsing /Wehrli, 1984; Sharp, 1985; Kashket, 
1986; Kuhns, 1986; Abney, 1986/has not addressed 
the issue of implementation of the Binding theory) 
The present paper intends in part to fill this gap. 
In the development below I will assume that the 
reader is thmiliar with attribute grammars and the 
basic concepts and terminology of Government- 
binding, although not necessarily with the Binding 
theory. The reader is referred to Waite and Goos 
(1984) for a concise introduction to attribute gram- 
mars, and Sells (1985) for the basic assumptions of 
Government-binding. 
Chomsky's Binding Theol T 
Binding theory defines the syntactic constraints on 
coreferenee that exist between the noun phrases in 
a sentence. In the course ot" doing this, thE themy 
indirectly determines constraints on the distribution 
of certain kinds of noun phrases. In this section we 
review the standard formulation of the Binding 
theory; tile reader already familiar with it may 
proceed to the next section. 
The ret~rential possibilities of a noun phrase 
depend on the fimetional type of the NP and the 
Binding conditions for that type. Government- 
binding distinguishes three types of overt NP, 
shown in (1). 
I Sharp (1985) checks correclness of binding in traces; we consider lexical NPs here. 
123 
O) a. anaphor (reflexive and reciprocal) 
b. pronominal 
c. referential 
An anaphor is an expression that has no inde- 
pendent reference mad must take its reference from 
some other expression in the sentence in which it 
occurs. English has reflexive and reciprocal 
anaphors, such as 'themselves' and "each other" in 
(2). The NP from which an anaphor or pronom- 
inal takes its reference is called its antecedent, since 
an anaphor must have an antecedent within the 
sentence in which it is used, we obtain the contrast 
between (2.a) and (2.b). If there is no appropriate 
antecedent, the string is ill-formed at the Logical 
Form level. The antecedent of the anaphor must, 
furthermore, c-command the anaphor and be found 
within a certain local domain, notions to be made 
precise below. Thus, in (2.c), although there is a 
potential antecedent for the anaphor, namely 
'Greeks', it is not within the required local domain. 
In (2.d), there is a potential antecedent "donkey', 
but it does not c-command the anaphor. Hence 
:i~e string is also ill-formed. 
(2) a. Greeks like themselves/each other. 
b. * Each other/Themselves like Greeks. 
c. * Greeks i think that each otheq/themselves i 
are smart. 
d. * Every man who owns a donkey i beats 
itself. 
A pronominal is a pronoun in any of its inflected 
forms (e.g., as due to agreement and Case- 
marking), as in (3). Pronominals exhibit a distrib- 
ution in phrase structure trees nearly 
complementary to that of anaphors. A pronominal 
need not pick its reference from some other NP in 
the sentence, but rather may have independent 
(deictie) interpretation, as in the first reading of 
(3.a). The pronominal may also be read 
anaphorically, having its reference determined by 
some other NP in the sentence (3.a-b). In tlfis 
case, though, the antecedent must either be outside 
the local domain of the pronominal, or not 
c-command it. Hence, the assigned coreference in 
(3.a-b) is possible, while that in (3.c) is not. 
Within a local domain, where an anaphor must 
have an antecedent, a pronominal cannot. 
(3) a. Brigitte i said that Shell i is tired. 
b. Every man who owns a donkey i beats it i. 
c. * Sibylle i loves her i. 
Lexical or fully referential expressions are names 
like "John" and "the man" in (4); the class inchldes 
all nominals headed by a common or proper noun. 
A referential expression defines its reference inde- 
pendently and must be free in every domain, in the 
sense that it may not have a c-commanding 
antecedent. Tiros the interpretations in (4.a-b) are 
unwarranted. Coreference between referential NPs 
is possible only if the first NP does not c-command 
the second (4.c-d); the result, though, may be 
awkward or place emphasis on the anaphoric noun 
phrase. 
(4) a. * John i likes John i. 
b. * .lohn i wants that John i leaves. 
c. The man who hired John i likes .lohn i. 
d. John i came and .lohn i left. 
The most difficult area of the Binding theory is the 
tbrmulation of the notion local domain referred to 
above. This notion is defined such that it is iden- 
tical for anaphors and pronouns. We note in 
advance, however, that while the notion is nearly 
identical for both, it should not be defined the 
same, as sentences (5.a-b) show (Chomsky, 1986). 
In this paper we shall not be concerned with the 
solution of this still open problem. 
(~ a. The children i like each other'sipictures. 
b. The children i like theiq pictures. 
Chomsky's axiomatic statement of the Binding 
theory is as tollows. Chomsky (1981) assumes a 
Free Indexing rule which appfies at LF and assigns 
(randomly) a referential index to every NP in tim 
input structure. Two NPs are said to be 
coreferential if they bear the same referential index. 
The indexhlg rule massively overgenerates logical 
forms, and indiscriminately assigns unwarranted 
coreference relations. The annotated structttres 
produced by the rule are subject to a number of 
well-formedness conditions, which are constraints 
on the assigned coreference relations. 
The most elementary condition is the agreement 
conditkm (6). The main component of the theory 
is given by the Binding axioms (7), where tim 
notions of binding and local domain are as in (8) 
and (9), respectively. Notice that the definition (9) 
of local domain does not distinguish between 
anaphors and pronominals, and thus is problem- 
atic, as the examples (5) indicate. We assume this 
definition, though, for the development below. 
The notion of c-command used in (8) is given in 
(10), 
124 
(6) Agreement Condition 
If NP l and NP2 are coindexed, then their 
agreement features A GR = < Person, Gender, 
Number> agree. 
(7) Binding Axioms 
(8) 
(9) 
A. An anapkor must be bound within its 
local domain. 
B. A pronomb,al must be free within its local 
domain. 
C. A referential expression must be free in 
every domain. 
For nodes a and fl, a binds \[1 if (i) a is 
coindexed with fl, and (ii) a c-commands ft. 
A node a is free (within a given domain) if it 
is not bound (within that domain). 
The local domain of a node a is the subtree 
dominated by MGC(a), where 
MGC(~), the minimal governing category of 
a, denotes the maximal projection # nearest 
to ¢z such that 
/~ dominates a, and 
/~ has an accessible Subject, and 
/L dominates a governor ~ of a 
(to) For nodes a and \[1, a e-commands \[I if the 
firsi; branching node dominating a also domi- 
nates ft. 
It is a straightforward task to verify that the 
Binding axioms in (7) explain the grammaticality 
judgements and interpretation possibilities of the 
examples presented thus far, except those in (5). 
The theory is explanatorily adequate, in the sense 
that it applies to a wide range of natural languages. 
Procedt~ral Binding 
The Binding theory just outlined follows the style 
of most recent work within the Government- 
binding framework. Extremely general rules, such 
as the Free Indexing rule, are assumed for the gen- 
eration and annotation of syntactic structure; the 
bulk of the grammar then consists of well- 
formedness conditions or axioms that must be sat- 
isfied by the generated structures. This approach: 
due to it:; extreme inefficiency, is problematic as a 
model of linguistic performance or natural language 
parsing. It seems more appropriate to view the 
general rules and axioms that constrain them as 
Ifigh-level specifications of certain grammatical 
processes, rather than as models of how the proc- 
esses are actually carried out. 
The refinement of the general rules and axioms 
associated with them into procedural rules which 
may be used to derive structure that already satis- 
fies the axioms is not a straightforward task, and 
has only recently begun to be addressed /Abney 
and Cole, 1986; Barton, 1984/. The incorporation 
of axioms into the rules leads to grammars which 
are more sensitive to psychological issues/linguistic 
processing, rather than mere linguistic description. 
It seems clear that only these new rules may be 
used in practical natural language parsers. Further- 
more, the formulation of procedural mechanisms 
provides a new way of looking at linguistic phe- 
nomena, which may in turn lead to insights for the 
solution of outstanding problems. I offer the fol- 
lowing Binding rule as an illustration. 
The Binding rule is defined by means of attribution 
rules associated with productions in the base. It 
applies at S-Structure and assigns to each NP node 
in the structure a referential index, in such way that 
the Binding axioms are satisfied by the assignment. 
The generate-and-test method implicit in 
Chomsky's account is avoided. In those 
S-Structures for which there is no possible correct 
assignment, tile rule blocks, and the structures are 
marked ill-formed, due to some violation of the 
13inding theory. The rule applies after the time- 
tional type of every NP has been determined, 
according to lexical features of the head nominal 
and principles of the Government and Case theo- 
ries. Functional classification of an NP consists of 
determining the values of its attributes anapkoric 
and pronominal /van Riemsdijk and Williams, 
1986/. The first approximation to the rule is 
limited to cases of backward reference only; assign- 
ment of forward eoreference, as in (IlL will not be 
covered by the rule. Also, we ignore cases where 
referential expresskms may be used anaphorically, 
as in (4.c-d). 
(i I) Men who met her i saw how kind Mary i was. 
The formulation of the rule relies crucially on the 
following hypothesis: For every NP node in an 
S-Structure, it is possible to define two sets of 
nominal expressions AAS and PAS, which contain, 
respectively, potential anaphoric and pronominal 
antecedents. Given a mechanism to compute the 
two sets noted, an antecedent for the current node 
may be selected from the appropriate set, according 
to the current node's functional type, as in (12). 
Attribution rule (12) is associated with every pro- 
duetion for NP and defines the value of the NP's 
referential index. The function se&ct-from takes an 
ordered set as argument and selects (arbitrarily) the 
125 
first element that morphologically agrees with the 
NP2 
(J2) Binding Rule: 
NP.Reflndex ,- 
if NP.anaphoric then 
if N P .pronominal then / * Control* / 
else select-from( AA S) 
else if NP.pronominal 
then seleet-from(PAS) 
else NP.node 
The main component of the Binding rule consists 
of the attribution rules that define the values of the 
AAS and PAS sets at each node. I now proceed to 
describe the types of the attributes involved in the 
computation and the manner in which these values 
are defined. 
Binding attributes and their types 
Assume integer-valued attributes node and 
Re/Index. The attribute node is associated with 
every node in an S-Structure tree, enumerating 
them in preorder. Thus the node number of an NP 
may be used to identify the NP. Reflndex repres- 
ents the referential index of the NP with which it is 
associated. This attribute is synthesized by rule 
(12) and its value is equal to the referential index of 
the first NP with which the current NP corefers 
(assuming a preorder enumeration of tree nodes). 
When NP.RefIndex = NP.node, for some NP, we 
say the NP has independent reference. 
The attribute AAS contains, for a given NP, the 
sequence of c-commanding NPs found within the 
local domain of the current node. Thus, any NP in 
this set is a potential antecedent for the current 
node, if that node is anaphoric. Each element in 
the AAS is a pair of the form < NP.Reflndex, 
NP.AGR >, for some NP to the left of the current 
node. NPs are ordered in the AAS in such way that 
the most recently found NP is ranked first (AAS is 
a stack, or ordered set). The attribute IMS is 
similar to the AAS, except that each element in it 
either does not c-command the current node, or is 
outside its local domain. Thus, each NP in the 
PAS is a potential antecedent for the current node, 
if that node is pronominal. 
An important difference between the AAS and PAS 
is that, if the current node is an NP, say NPi, the 
pair < NPi.node, NPi.AGR > is a member of PAS, 
but not AAS. Because of this, a pronominal's ref- 
erential index may be set to its own node number 
(i.e., may be interpreted deictically), while an 
anaphor's may not. This difference between the 
AAS and PAS need not be stipulated as a special 
case, but rather follows naturally if we assume the 
c-command relation is irreflexive. 
The distribution of values tor the AAS and PAS 
attributes in an SoStructure may be illustrated hy 
means of example (13), ill which the subscripts are 
NP node numbers; we ignore their actual values. 
(13) John h told \[his i parents\]j about himself k. 
The values that result for the AAS and PAS are 
shown in (14); the reader may verify their correct- 
hess with the aid of .examples (15). For the tirst 
NP, "John', there is no potential anaphoric 
antecedent (15.a), so the AAS is empty (14.a). 
Ilowever, at that position it is possible to have a 
free pronoun, so the PAS contains a single erthy, 
the pair <h, AGRh>. For the second NP, "his', 
the values of AAS and PAS are as in (14.b). Thus 
the AAS is empty and no anaphor is permissible at 
the position (15.b), while a pronoun is, in which 
case it may be interpreted deictically or 
anaphorically, referring back to "John'. The values 
of the AAS and PAS attributes associated with NP i 
and NP k are as shown in (14.c-d). 
(14) a.. NPh.AAS = { } 
NPh.PAS = { < h,AGR h > } 
b. NPi.AAS = { } 
NPi.PAS = { < i,AGRj >, < h,AGR~ > } 
c. NPi.AAS = { <h,AGRh> } 
NPj.PAS = { <.\],AGRj > ) 
d. NPk.AAS = { <j,AGRi> , <h,AGRh> } 
NPk.PAS = ( <k,AGR k>, <i,AGR i >} 
(1~ a. * Himself/ He i told his parents about 
himself. 
b. Jolm i told \[*himself s~ hisj/i pa.rents\] ahout 
himself. 
c. John i told himself/ *him i to stop smoking. 
t c. John i told \[Mary: s parents\]k about 
himself/each otherk/ tler~/i 
2' No theoretical significance is attached to the order of' the elements in the AAS and PAS. Psycholinguistic 
evidence, however, suggests that gaps "reactivate" their antecedents, which hears on the order of the sets. 
126 
The attribution rulcx i.ii;tt dcihw, i.liC v~t!O,'::~ ~+{ \[i+< 
."J'/.~,q ai<t,.i \]J/J,('>' ~(;l;S arc y~ivcn h~ d~., /\7::,<,~;i~{\[; 
(hdy tb.~:;~,, afica :::;sociatt;d w.i.i~ ti., ,';ai :l~/;)i :'t ',i, ': : 
).,!, au<! W u'od projectiou:., x.c p)v<:, 5i:+ :,~;+iU~u/ 
" ' <' + used iu lilt <, c,:>~+~0ui:c+./.io,:, + J :+ 4 ,+ ,:+.ti ;ibu i+ ~ d~:., i:: " d,,: 
\]:','7,<,+; is sy,th~:'.<&'::,l au,+; ;~<l<i~; t<~ \]:'/!/( ~,li i,,~+c ...< 
(;7~)1(.:;~;71)11:; uo+~iuiu(.d hi the p\]#i:m" {,c::+i: i:i;, 
'i'!~o l:ic~dil~{!,; ~lli~', prcscili.¢;d i.hlls \[i:,:+ doe;; tl'~! 
~l.f;(;Otiil\[ ~7)\[i' C?'03,YOI, d/= (*,3,~;C,S t-;ilC}) <:!'<', (i('Q \]JI \[\]1{; 
c;:a.mplc, "NPj ha,'.; "tllid(;i'l~on(: Wh-:ill()vollit,il\[ \[\]\)1iI 
;lf; \]) ?~i~ ~,::!.~il(: l)(),'gitlorl C,: u) 11{i ~4t!iliB;G positio~ ii~ 
the mairix t;~l:\[!lp\]oliicii~iT,(: G ctOSS\]i|}; OVt',f i\]i~ 
subjc+:i; ',/oh:/, ti. i:~ i,ossii,i,: iu \]ti\[cr!:,rci "\]iTni.y¢:O" 
l(;\['t:J:litll{ \[0 "ff()hH', Th(. I~htdiiil~ i,;l\[(; in(,'SC, li\[(:d 
~ix:;ociate:~ all cnipty AAS with 'hires@", a\[ld f;hus 
fa.ils to accouI~t for tMs coi'oloroilcc possibility. 
(t6) \[Which picture of himse(/i\] j does .~oh~ h iilo,~ % 
/,;xample (16) is also problematic ibr the axioui~;tic 
Biitdinl, ';:hcoiy defined t.,y (6)-(i0) sluice, accor(lhlg 
io definition (g), the. ~li/:l\[/\]i()i" IS li(>l, l)ouild ~>y ii.:+ 
• qiifc(:(;(IOlli, alld \[hi?is ;:i~.@Dlll A Of" lh(~ IlIC()))/ IF, V}() 
laicd, ()hotil,<liL7 (19{",J) iJl'(qi():/i;:; ~I ,'i!\],.', (){ \]7.'.to<sit 
.~nl,<:,"l,n,, whh:t, :,!>i,iic;:+ :il !,t ~ piioi i:j a~q;Ii;',;~:;<i, 
of lhc. Biu.'ihi4 axi~),~: ~ Hiltl ii'i:, /!;t: {:!i~:4;i. (Ji" "KC~t )11 
':trm:finl:" 7!!.',: :+i%'./t:ti {?:i:';::;:.~ ;5i )it: 7.,"'-7;{il+::it!i(: I,.:);;J 
don, xo :it;l!; t~. XT'IIO\[i~/C :;imiia.r i~ (iV) l:; obi::~i~it+d+ 
'\]",~ ILl:-; ~i{7~(:i.il:c~! '~ • ;I~; ;i )~.it ) ~ \] Jill )" I i <~\]\[,}/ i!t )~fl .; P '~} )l'/ i() 
yicid ibc coi icx:i +~su/i:s 
(i'/) !\[ ':,:',': .> a ;,g~;i,,~:t; ,k,~; ;,:,i,:j ill<(" 1~ <>7 
i,i.,.~, i!\]' I. 
l'h,! itd~.: <,i rccoit,'ii:ructi(m+ JJi addilJo,.~ /.o it~tVi\[li! it:-i 
\].')Wit ~IC;\[ ')\[ problcmrs/vau l<:icmxdijlc ai~c! Wiili'<uW,, 
1986/, +'+'+.'(:~t+'; tJli(lc,'iii+ablc in ihc !9"a~illIi<ii', t~iilt;(', it 
complicak~:x, tile ~;c3tmnar spccit\]cai!y i}>r the ptli '~ 
posc~; ~Ji fi~c Ui~:ding theory. 'Kh~ \[luici:ioii of !.iu; 
r'ilc, mi,l:)ht!5 the pr~:vhms apT~I{c:~tio~< <>i a t:~:umfb~'. 
J ii"tti<>~t, {<; tuU: w;;ty U?pcalini,,: 
I)rt)ccdc+c,ll i}iudi~g rid{: lflay be w.tTuc;l (.(J ;..tcco/lil\[ 
{'01 (\]6) bVi\[ilOI!\[ \]'CC()ItJ):;I:, \[+) r'.;c:oslstruct.ion, t:l{i.t':~:-; 
<)bservc~ that the mll:(w, odolli; (3\[ ;u~ ail3p\]i;ios l:flllS\[ 
C'COYllIit~VO.,'-( a~t(~ i)(: wil.hill it/(: lu<:ai d()lJlaiii Of 
ci!hcr i.Jw +mai>}~or , of orJc. of l:iic i;laces o\[ the 
/,lt\[{~<;~:;O i>'L '¢V\[~'Ii#\['.}I i\[!-tC ~Nl~tsi..)t\](')~{' i~; ernlw.dctcd. Thi,~; 
}oprl::;i.::iit:-; .-+l 5i~.ti:tii;ic:+ilti; Icg)lJCl.tl~\];i.i.iOt~. ,:)J' ih.c; biudiu/,~ 
:lxkmts, to. h~c:lu:!, rcii:svucc it; iV. lkw t:lv;i:;x, The 
.>fi:f.l'ibtti:i(;ll t'ulcx i:{i:-ii. (h:;Jhlc lhc v~:lue:~ 'd du'. AAS' 
<iild \[>/>{,+)+ sc{<s Ii!.37 {'~t: modified I:o lake intu ~-tCCOUII\[ 
!Piis obsetvati(+;~. The; chuuK,: ;c<tuh+x\] L<; ++) ({e~liitt: 
i7~+; V{l\]\[lJ(:,c; 31 ill(; lO()t \[)l' ilJC HIOVtJf\] phJ'~l+;c c;.s i.hc 
a+,.+iOll o( t}tc valu~ dciinc.d by the t;l!rrc++t i+uic, phu; 
!i., ,!~c.:; d,~iincd ;;t i:hc traces in tim chain headed 
.,. ~} +: i: ll.~.<+:. 'Ftui~, in (16) NP. AdS arid e tlA5 + 
: ~<:,ti,~: u,c c..~:;u~c!:,¢. -<:i, A(,\],~i> , aild the attri- 
i,tlti(m iO!t:S dc,~ciJilX,.!J hi the previous section make 
i!~i; V~i.iUC au..C,<;<;i1<)iO i:O i.hc armphor him,s'eU: 
~'t.; cx:,.:i r,ibi,iulati<.m_ of the attribution rules for 
.i,'i,? u,l P,C;' iu~O~ bc dent iu diltbronl ways, (hm 
;iN,.:~+~-~iivc b; io cm~q:,utc th,'; extended AAS and 
/'d,<; :~:!a b~ two p:-,_sscs through the tree, with the, 
.'.;('.colld Vx,:+:~ used to compute the IlIliOll<'; not0d. A 
sccoi~i xpvmac\].,, dclay:~ anaphora, resolution for 
~ucprv.~:.;io~i>; inside an m.~teccdcnt (cliaitl head) tmtil 
ih~. i~u;! !~a~:c: ;d' the chain i<<~ fotntd. At this lime 
+h,: ,4,1/7 mid P./IS a;t.s o\[ tbc antecedent nlay l>C 
cvalt++iic(t, baviitg access {() tl!:: c;OIiOS\])Ott(\]il/+~ SOtS 
iU the tim-cs. 't'his sc'.coud ai~pioach seems more 
'+.iJ~;ibic, :.;into; it !,ctmita ;~lhqicalicni of t\[t?, l\]indhig 
i,tl<: i,i oJ,c Iov.<.IcJwu, i(.:i\]r'\[O " right pass through the 
ii'CO. We do iiot; i)tlt:n\]c the &:tails of the revised 
ru!c here. 
l,'h',,;t wu consldcr Ch<~m,<d~y's Bindin/, theory. The 
combilmtion ol" ih(: !"~ee l+~dr.xiug lute aud Bin(iini4 
,xiom:.~ d,:\[h;{:s , gcncrai~>-aNd4cs~t ~d::o~iihm 
~ ;i,/~:~i as::,.mKl>li:~n.:+ o' tbc X' i!icury, thc nun~bcr of 
!-4P,<; il~ uit i,li,lu <iirhU~ ia ilur:ariy related to th+~ 
!cnp, ih o\[" ihc xt.i~!!;. ~h:uce \[br ,s(m~e fixed and 
:+ul;,ll \]g ~br a xcu.ic~,x"; o\[" lcn:gth n i.lacre will ix; n/# 
Ni" ~.:~><h;.~. ~u~.<;umhuy a slight mcxtificaticm of the 
iudcxing ride. (which improves it), accordil~g to 
which ii..<;clcci.s imcgcrs in the range l ..... n/k to 
:,:;silSJt ,.'ts potential rd?',rcnt.ial in:ticc.s to dt~: VII'.,: 
i~+vo!vcd, iJw.rc will bc (n/k)n/k caudidatc i,i" 
,:;:;iBnmuuts tr~ be. checked again.<;t the Bimlhig 
axioms (7). Assuming that thu 13indhlg axion!a 
~,Jay t)< chcck,.:d hL constant time, thc, rt nnim! tiiuc 
iLr the ;ligorithm is exponentially related to i}lc 
Icugt.Jt '" '~ ,:~I um input ,~tring. 
I~or the procedural Binding rule iommlatcd hero, 
iilc tiinc needed to coinpui:c the synth0<'dzcd AA/7 
and I>,4S aitributcs at each node \]?om the attrihules 
at that node on which AdS a,d t'AS direct(y 
depel~d may bc assumcd to be constant; the oper- 
ations inwflved are assignment, push, and pop 
ouly. Asamling f'urthel ~ tlmt the number o\[ empty 
catc+>~orics hlsc'rted between tcmdnal clement.<; is 
proportional to the k;rigth of t|lc hiput string, the 
mmcib~:r of nodes iri the dc, rivation trees generated is 
proportional to ttl~: input length. Since (:lie AAS 
and PAS attribuk'.s arc computed at me, st once ai 
each node, iu the tree, the l~roce, ssing time for the. 
nc.w Binding rule i.<~ linear -+ a siguificant improve- 
Hicut over qm abstract specification (6)-(10). 
\] 2}' 
2onclusions 
n this paper an attribute-grammar specification of 
Binding rule for the identification of pronoun and 
naphor referents has been proposed. The rule 
~rovides a correct account of backward reference of 
qPs, and also of forward reference due to move- 
nent, without recourse to reconstruction. The rule 
~resents a model of Binding in which sets of poten- 
ial anaphoric and pronominal antecedents are 
ncrementally defined at each node in a tree. 
;torage use may be optimized by use of global 
'.torage cells, as described by/Sonnenschein, 1985/. 
n more general terms, tiffs rule presents a trend 
:omplementary to that of recent linguistic theory. 
Fhe rule formulation indicates how conditions on 
'eprescntations may be incorporated into the rules 
s, hich generate the representations in the first place. 
I'his leads to grammars more geared to linguistic 
~rocessing, and to which a higher degree of "psy- 
:hological reality" may be ascribed. The rule is a 
ikely candidate for incorporation in natural lan- 
guage parsers. 
Acknowledgements 
I would like to thank my dissertation advisors 
Susumu Kuno and .laklin Komfilt for discussion of 
Binding, George Ileidorn and Karen .lensen, who 
read an earlier version of tiffs paper, and Dr. 
Edward Stabler at Syracuse University for long 
thne support of my dissertation project. Prof. 
Kuno provided the initial reference to the manu- 
script by Barss, and kindly made it available. 
May be obtained on request from the author. 
128 
Appe~dix: The Binding rul~e 
(Rules ~%r AdS and PAS computation) 
Ch~sc ~nd sentencc ~'ules: 
a. Z-~ CP 
a.ttributi~n: 
C~,.AAS +- \[ \] 
b. CP-, (NIP) CB 
attribution: 
CB.AAS ~- if CP.tense = + then \[ \] else CI'.AAS 
CB.PAS ~- if CP.tense = + 
then CP.AAS U CP.PAS else CP.PAS 
CP.PAS~; ~-. set-diff(CB.PAS s, CP.AAS) 
c. CB--> C IP 
attribution: 
~(P.AAS +- CB.AAS 
\]P,PAS ,- CB.PAS 
CB,PAS'~: ~. IP.PAS s 
d. IP '-~> NP 1B 
attribution: 
NP,dAS +- ~ltLAAS 
N P.PAS ,- \[ <NP.node, NP.AGR>\[IP.PAS\] 
HLdAS ,- \[ < NP.ReJlndex, NP.AGR > \[ IP.AAS\] 
~KPAS ~,- NP.PAS s 
lI!fLP.dS,,; <--- 
\[ < NILReflndex, NP.AGR > \[ IB.PASs\] 
attfibutioa: 
VPMAS ~ ~B.AAS 
VP.PAS ",. ~B.PAS 
)I~3oPAS s ~ VP.PAS s 
~Ve~,b-ph~o~se ~ouUes: 
a~ VP-~... VB ... 
Vi~. A,d S '~ V P.A A S 
V~:LPAS '~-- VP.PAS 
'V)?.PA S s +.~ VB.PA S s 
b. VB -~ V 
attribution: 
VB.PAS s ¢-- VB.PAS 
c. VB ~ V XP, forXP = NP, CP 
attribution: 
XP.AAS ~. VB.AAS 
XP.PAS ,-VB.PAS 
VB.PAS s +-- if XP = NP 
ther/\[ < NP.RefIndex, NP.A GR > \] 
else XP.PAS s 
d. VB--* V NP XP, forXP = PP, CP 
attribution: 
NP.AAS *- VB.AAS 
NP.PAS *- VB.PAS 
XP.AAS *- 
\[ < NP.Reflndex, NP.AGR > \[ VB.AA~ 
XP.PAS ,- NP.PAS s 
VB.PAS s ,- XP.PAS s 
Noun-phrase rules: 
a. NP-~ (Det) NB 
attribution: 
NB.AAS *-- NP.AAS 
NB.PAS ,- ta'tl(NP.PAS) 
NP.PAS s ,- NB.PAS s 
b. NP 1 -~ NP 2 NB 
attribution: 
NP2.AAS ,- NP1.AAS 
NI'2.PAS ,-- 
\[ < NP2.node, NP2.AGI? > I tail(NPt.PAS)\] 
NB.AAS ~ \[ \] 
NB.PAS *- NP2.PAS s 
NPI.PAS s ,- 
\[ < NP2.Reflndex, NP2.AGR > I NP2.PASs\] 
e. NB ~ N 
attribution: 
NB.PAS s ,-- NB.I'AS 
d. NB~N XP, forXP = PPorCP 
attribution: 
XP,AAS ,- NB.AAS 
XP,PAS *- NB.PAS 
NB.PAS s ~ XP.PAS s 
129 

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