tVIodeling syntactic constraints on anaphoric binding 
Mary Dalrymple 
SRI International 
and 
Stanford University 
John Maxwell 
Xerox-PARC 
Annie Zaenen 
Xerox-PARC 
and 
CSLI, Stanford University 
Abstract 
Syntactic constraints on antecedent-anaphor re- 
lations can be stated within the theory of Lexical 
Functional Grammar (henceforth LFG) through 
the use of functional uncertainty (Kaplan and 
Maxwell 1988; Halvorsen and Kaplan 1988; Ks- 
plan and Zaenen 1989). In the following, we 
summarize the general characteristics of syn- 
tactic constraints on anaphoric binding. Next, 
we describe a variation of functional uncer- 
tainty called inside-out functional uncertainty 
and show how it can be used to model ana- 
phoric binding. Finally, we discuss some bind- 
ing constraints claimed to hold in natural lan- 
guage to exemplify the mechanism. We limit our 
attention throughout to coreference possibilities 
between definite antecedents and anaphoric el- 
ements and ignore interactions with quantifiers. 
We also limit our discussion to intrasententiM 
relations. 
1 General characteristics of syntactic 
constraints on anaphoric binding 
The relation between an anaphor and its an- 
tecedent is semantic in nature. In the simple 
cases that we limit our attention to here, the 
two are coreferent. 1 This semantic relation is 
subject to syntactic constraints, however, and 
it is the statement of these constraints that we 
focus on. 
In the LFG approach to these constraints 
proposed in Bresnan et al. (1985), 2 bind- 
ing conditions are stated as conditions on f- 
structure configurations rather than conditions 
on c-structures. Two kinds of syntactic fac- 
1This is of course not always the case. Reciprocals 
and binding by quantified NP's are two well-known cases 
in which the semantic relation is more complicated. 
2For a summary of the views in Bresnan et al. (1985), 
see Sells (1985). 
tots are shown to influence anaphoric binding 
possibilities: the grammatical function of the 
potential antecedent (in particular whether or 
not it is a subject) and the characteristics of 
the syntactic domain in which the potential an- 
tecedent and the anaphor are found (for exam- 
ple, whether that domain is tensed or whether 
it has a subject). In Bresnan et al. (1985), 
anaphors are consequently annotated for both 
domain and antecedent constraints. 
Some constraints are stated in positive terms: 
the antecedent must be tbund within a partic- 
ular domain or have a particular function. In 
other cases the constraints are negative: the an- 
tecedent and the anaphor cannot both be part 
of a particular domain, or the antecedent cannot 
bear a particular grammatical function. Under 
such negative conditions, the a naphor is disjoint 
in reference from its antecedent. 
2 Modeling binding constraints with 
functional uncertainty 
F-structure relations are in some cases not char- 
acterizable as a finite disjunction over paths: 
for example, dependencies between ~fillers' and 
'gaps' in, for example, relative clauses and wh- 
questions. Functional uncertainty was devel- 
oped for the analysis of such dependencies. 
Kaplan and Maxwell (1988) and Kaplan and 
Zaenen (1989) develop a formal specification of 
relations involving disjunction over paths by al- 
lowing the argument position of functionM equa- 
tions to denote a set of strings. Suppose (t is a 
(possibly infinite) set of symbol strings; then 
(1) (fa) = v holds if and only if 
a. f = vande 6 a, or 
b. ((f s) Surf(s,a)) = v for some sym- 
bol s, where Surf(s, a) is the set of suffix 
strings y such that sy 6 a. 
72 1 
An equation with a string-set argument holds if 
and only if it holds for some string in that set. 
This kind of equation is trivially unsatisfiable if 
.c, denotes the empty set. If a is a finite set, this 
\[brmula is equivalent to a finite disjunction of 
equations over the strings in a. Passing from fi- 
nite disjunction to existential quantification en- 
ables us to capture the intuition of unbounded 
uncertainty as an underspecification of exactly 
which choice of strings in a will be compatible 
with the functional information carried by the 
~;urrounding surface environment. 
Kaplan and Zaenen (1989) require that a be 
drawn from the class of regular languages. The 
characterization of uncertainty in a particular 
grammatical equation can then be stated as a 
regular expression over the vocabulary of gram- 
matical fllnction names. 
Functional uncertainty can also be used in the 
case of negative constraining equations. In that 
situation, the requirement is that there be no 
path picked out by the regular expression that 
makes the equation true. That is, the negation 
of an expression involving functional uncertainty 
has the effect of negating an existentially quan- 
tified expression. 
Kaplan and Zaenen (1989) consider only ex- 
pressions of the form 
(f 
where a is a. regular expression. In expressions 
such as tihese, a represents a path through the 
f-structure f. We refer to paths of this type 
as PathIn, and to functional uncertainty of this 
type as outside-in functional uncertainty. 
In IIalvorsen and Kaplan (1988), expressions 
of the form 
(a f) 
are introduced. We will refer to the path in ex- 
pressions of this form as PathOut, and to func- 
tionM uncertainty of this type as inside-out func- 
tional uncertainty. Expressions involving inside- 
out functional uncertainty are interpreted as de- 
noting f-structures fi'om which f is reachable 
over some path in a. 
More formally: 
(2) (a f) = g e {hi 3s e a\[(hs) --~ f\]} 
(a f) denotes some f-structure g through which 
Lhere is a path in the set of strings a leading to 
f. The equation =~ is a constraining equation 
checking for the existence of such an f-structure. 
Relations between anaphors and their an- 
tecedents are also in some cases not char- 
acterizable as a finite disjunction of paths 
within f-structures; for this reason, the use 
of functional uncertainty in characterizing the 
anaphor-antecedent relation seems appropriate. 
In our view, modeling anaphoric binding con- 
straints consists of specifying a set of f-structure 
paths relating anaphors with elements that are 
either possible or disallowed antecedents. We 
use inside-out functional uncertainty to charac- 
terize the relation between an anaphor and these 
elements. 
To illustrate, the antecedent of the Norwe- 
gian anaphor seg must be a subject outside of 
the minimal complete clause nucleus 3 in which 
seg appears; this antecedent can be at an indefi- 
nite distance away from the anaphor, as long as 
only the highest nucleus in the domain contains 
a tense marker (tIellan 1988; p. 73): 
(3) Jon bad oss forsoke i f£ deg til 
Jon/asked us to try to get you to 
£ snakke pent om seg 
talk nicely about himi 
Under an LFG analysis, the path between the 
antecedent and the anaphor in (3) contains three 
XCOMPs, as diagrammed in Figure 1. Assume 
that TA denotes the f-structure for seg, the struc- 
ture labeled 9 in :Figure 1. The set of nested 
f-structures containing 9 is characterized by the 
regular expression 
(4) (XCOMP* OBJ TA) 
In Figure 1, this set consists of the structures 
labeled 1, 2, 3, and 4. The expression in (5) 
designates the subjects of these four f-structures, 
those labeled 5, 6, 7 and 8: 
(5) ((XCOMP* o.J svBJ) 
F-structures 5, 6, and 7 are the f-structures of 
the possible antecedents of seg: the subjects out- 
side of the minimal clause nucleus in which seg 
appears. F-structure 8 is not a possible an- 
tecedent for seg, since it appears in the same 
minimal clause nucleus as seg; f-structure 8 will 
3A clause nucleus is formed by any predicate (regard- 
less of its syntactic category) and its dependents. A com- 
plete clause nucleus is a clause nucleus with a subject 
dependent. 
2 73 
1: 
suBJ 5:\[\] 
XCOMP 2: 
s,BJ 6:\[\] 
XCOMP 3: XCOMP 4: \[OBJ 9:\[(anaphor)i 
Figure 1: F-structurefor sentence (3) 
be excluded from the set of possible antecedents 
for seg by a negative constraint. 
More schematically, the set of possible an- 
tecedents of an anaphoric phrase can be char- 
acterized by an expression of the form in (6): 
(6) ((PathOut TA) Pathln) 
(PathOut TA) picks out the set of f-structures 
which contain the anaphor and in which the an- 
tecedent must be located. PathIn characterizes 
the functional role of the antecedent. It is a gen- 
eral constraint on antecedent-anaphor relations 
that the the antecedent must f-command 4 the 
anaphor; for this reason, the PathIn is always of 
length one. The PathIn, then, consists of (and 
constrains) the grammatical function borne by 
the antecedent. 
Conditions on the binding domain are formal- 
izable as conditions on the PathOut, since the 
PathOut characterizes the domain in which both 
the anaphor and its antecedent are found. ~Ve 
will look in detail at one such constraint; be- 
fore doing so, however, we make a simplifying 
assumption about the semantics of the anaphor- 
antecedent relation. 
In the simple cases we are considering here, 
the relation is be represented as identity be- 
tween the semantic content of the anaphor and 
its antecedent. Elaboration of this represen- 
tation would require us to introduce the LFG 
mechanism of projections (HMvorsen and Ka- 
plan 1988), which is beyond the scope of this 
paper. 
Here we will use the informal notation in (7): 
(7) < cr > ((PathOut \]'A) PathIn)=< a >TA 
4Bresnan (1982) defines f-command as follows: for any 
functions GF1, GF2 in an f-structure, GF1 f-commands 
GF2 iff GF1 does not contain GF2 and every f-structure 
that contains GF1 contains GF2. 
to indicate that the semantics of the anaphor, 
< a > TA, is to be identified with the semantics 
of its antecedent. The material in angle brackets 
stands for the mapping (not further specified) 
between the syntax and the semantics. 
To prevent the anaphoric element from be- 
ing contained in its antecedent, we formulate the 
constraint in (8), where TANT stands for the f- 
structure of the antecedent: 
(8) -1 \[(TANT GF +) = ~'A\] 
The effect of this constraint is very similar to 
the i-within-i condition in Government-Binding 
Theory (Chomsky 1981). It has been argued 
that this constraint should be relaxed (see e.g. 
Hellan (1988)) but the correct analysis of pu- 
tative counterexamples is not clear. We will 
assume here that the constraint can be main- 
tained. 
We now describe how to model a domain 
constraint that holds of some anaphors: some 
anaphors must be bound within the minimal 
complete nucleus -- the minimal nucleus con- 
taining a subject. 
Let F1 designate an f-structure containing the 
anaphor. We can characterize F1 in the follow- 
ing way: 
(9) F1 = (GF + TA) 
where GF denotes the set of grammatical 
function labels. 
For F1 to be a valid binding domain for 
anaphors subject to this constraint, it; must not 
contain any smaller f-structure that properly 
contains the anaphor and a subject. That is, 
FI must be the smallest complete nucleus. We 
will define DPF ('domain path f-structure') as 
any of the f-structures that contain the anaphor 
and are properly contained in FI: 
74 3 
(i0) (DPF, GF +) =~ TA 
DPF1 ==¢ (F1 GF +) 
It is these intermediate f-structures that must 
n.ot contain a subject: 
(1\]) -~(DPF1 SUB J) 
The constraint that an anaphor must be 
bound within the minimal complete nucleus can, 
then, be stated as follows: 
(\].2) a. < o" > (F1 GF) =< cr >TA 
b. -~CDPF1 SUBJ) 
These two equations ensure identity between the 
semantic content of the anaphor and its an- 
tecedent, where the an.tecedent is the value of 
some GF of an f-structure F1 that contains the 
anaphor. There may not be a f-structure DPF1 
that is properly contained in F1 which has a sub- 
ject. 
% Examples of anaphoric binding 
We now illustrate the use of these binding con- 
straints with some of the conditions that have 
been proposed for English, Marathi, and Scan- 
d inavian pronouns and reflexives, s 
The English retlexive pronoun was described 
in Bresnan et al. (1985) as having to be bound 
in the minimal complete nucleus, as illustrated 
by the following contras t: 
(11.3) a. Hei told us about himself/. 
b. We told himi about himselfi. 
c.*Hei asked us to tell Mary about himself/. 
As discussed in Section 2, this pattern of gram- 
maticality judgments can be modeled by the 
constraints given in (9) through (12). 
The an.tecedent of the Marathi reflexive 
,~:wataah must be a subject, but may be at an 
iadefinite distance from the anaphor, so long as 
the antecedent and the anaphor appear in the 
same minimal tensed domain. Th.is req,irement 
can be translated into the following path speci- 
fication. 
(~14) a. < o >(F~ SUBJ) = < cs >TA 
SData are from Bresna.n et al. (1985), ttellan (1988), 
and D~flrymple (in prep.). 
b. -~(DPF1 TENSE) = + 
where F1 and DPF1 are as defined above 
According to these equations, the antecedent 
of the anaphor must be contained in an f- 
structure F1; further, there must not be an f- 
structure DPF1 properly contained in F 1 that 
has a TENSE attribute with value +. 
A more interesting ease arises when a bind- 
ing relation is subject to both a negative and a 
positive constraint. An example is the Swedish 
anaphor honorn sjiilv. Its antecedent must ap- 
pear in its minimal complete clause nucleus, but 
it must be disjoint from subjects. This anaphor 
occurs Micitously within the following sentence: 
(15) Martin bad oss bergtta fhr honom 
Martini asked us to talk to him/ 
om honom sjglv 
about himself/ 
Conditions on honom sjiilv do not prohibit Mar- 
tin and honom sjiilv from being interpreted as 
coreferent, though Martin bears the grammat- 
ical function suBJ. This is because Martin ap- 
pears outside the binding domain of honom sfiilv 
and is thus not considered when either positive 
or negative binding constraints are applied. 
In our framework, two constraints are re- 
quired for honom sjiilv. One, (16)a, states 
the positive constraint: the domain in which 
the antecedent of honom sjfilv must be found. 
The other, (16)b, states the negative constraint: 
honom sjhlv must be disjoint from the subject 
in that domain. 
(\]6) a. \[F 1 = ((J'F + TA) A 
< ~r >(F1 GF) = < cr >\]A A 
-~(DPF1 SUB J)\] 
b. ~ \[V: = (aF + ~A) A 
< a > (F2 SUBJ) =< ~ >TA 
-~(DPF2 SUB J)\] 
The negative constraint rules out coreference 
only between the anaphor and the subject of 
the minimal complete clause nucleus; it does not 
prevent coreference between the anaphor honom 
zjiilv and a subject Martin outside the binding 
domain. In general, negative binding constraints 
do not hold in a larger domain than is specified 
by the positive equation. 
4 75 
For the Norwegian anaphoric form hans, the 
only specifications are negative (Hellan(1988), 
Bresnan et al. (1985)); it must be disjoint from 
the immediately higher subject. We can encode 
this requirement as: 
(17) -1 \[F1 =(GF + ~A) A 
< ~ 2> (F1SUBJ) =< cT > TA A 
~(DPF1 SUB J)\] 
This is the same negative requirement as was 
illustrated above, in example (16). As no posi- 
tive requirement is given, no antecedent relation 
is imposed. It is assumed that another module, 
presumably the discourse component, will sup- 
ply a referent for the pronoun. 
4 Conclusion 
We have sketched a way to use inside-out func- 
tional uncertMnty to constrain the relation be- 
tween an anaphor and an antecedent. A formal 
theory of anaphoric binding will involve a spec- 
ification of a universal inventory of anaphoric 
binding possibilities and possible dependencies 
between them. 
A general discussion of such a theory is be- 
yond the scope of this paper, but we conclude by 
indicating how our approach captures a few of 
the cross-linguistic properties of anaphoric bind- 
ing. 
If the domMn and the antecedent binding re- 
quirements for an anaphor are both positive or 
both negative, the requirements must be satis- 
fied by the same element. This is enforced by re- 
quiring that only one positive and one negative 
equation can be associated with each a naphor. 
Additionally, only elements that are superior 
to the element should be considered in apply- 
ing the constraints. GF1 is superior to GF2 if 
(1) GF1 asymmetrically f-commands GF2, or 
(2) GF1 and GF2 f-command each other, and 
GF1 is higher on the hierarchy of grammatical 
functions given in (18): 
(18) SUBJ > OBJ > OBJ2 > OBL > ADJ 
As noted above, the f-command requirement is 
enforced by the requirement that the Path Out 
be non-null and the PathIn be of length one. 
The modelling of the functional hierarchy given 
in (18) within onr framework is, however, a task 
that remains to be done. 
A finM observation is that inside-out fllnc- 
tional uncertainty can interact with outside-in 
functional uncertainty as used in the analysis of 
dependencies between 'fillers' and 'gaps', as in 
the following: 
(19) a.*Bill said that Sue likes himself. 
b. ttimself, Bill said that Sue likes. 
Preliminary research indicates that no special 
machinery is needed to model the right interac- 
tions in these cases. 

References 

Bresnan, J. 1982. Control and complementa- 
tion. In J. Bresnan (Ed.), The Mental Repre- 
sentation of Grammatical Relations, 282-390. 
Cambridge, Mass.: MIT Press. 

Bresnan, J., P.-K. Halvorsen, and J. Ma.ling. 
1985. Logophoricity and bound anaphors. 
Ms, Stantbrd University. 

Chomsky, N. 1981. Lectures on Government and 
Binding. Dordrecht: Foris Publications. 

Dalrymple, M. in prep. Syntactic CoT~straints 
on Anaphoric Binding. PhD thesis, Stanford 
University. 

ttalvorsen, P.-K., and R. M. Kaplan. 1988. Pro- 
jections and semantic description in Lexical- 
Functional Grammar. In Proceedings of the 
International Co@fence on Fifth Generation 
Computer Systems, 1116-1122, Tokyo, Japan. 
Institute for New Generation Systems. 

ttellan, L. 1988. Anaphora in Norwegian and the 
Theory of Grammar. Dordrecht: Foris Publi- 
cations. 

Kaplau, R. M., and J. Maxwell. 1988. An algo- 
rithm for functional uncertainty, in Proceed- 
ings of COLING 88. 

Kaplan, R. M., and A. Zaenen. 1989. Long- 
distance dependencies, constituent structure, 
and flmctional uncertainty. In M. Baltin and 
A. Kroch (Eds.), Alternative Conceptions of 
Phrase Structure. Chicago University Press. 

Sells, P. 1985. Lectures on Contemporary 
Syntactic Theories. Stanford University: 
CSLI/University of Chicago Press. CSM Lec- 
ture Notes, Number 3. 
