Binding Constraints as Instructions of Binding Machines 
Ant6nio Branco 
I)ept. of ll~fi)rmatics, University of Lisbon 
Faculdade de Ciancias de Lisboa 
Campo Grande, 1700 Lisboa, Portugal 
Antonio .Branco@di. fc.ul .pt 
Abstract 
Binding constraints have resisted to be fully 
integrated into the course of grammatical 
processing despite its practical relevance 
and cross-linguistic generality. The ultimate 
root for this is to be found in the exponential 
"overgenerate & filter" procedure of the 
mainstream rationale for their satisfaction. 
In this paper we design an alternative 
approach based on the view that nominals 
are binding machines. 
Introduction 
Binding constraints are an important set of filters 
in the process of anaphor resolution'. As they 
delimit the relative positioning of anaphors and 
their possible antecedents in the grammatical 
geometry, these constraints are of crucial 
importance for restricting the search space for 
antecedent candidates and enhancing the 
performance of resolvers. From an empirical 
perspective, they stem from quite robust 
generalizations and exhibit a universal character. 
given their parameterized validity across natural 
langnages. From a conceptual point of view, in 
turn, the relations anaong binding constraints 
involve non-trivial symmetry, which lends them 
a moduhtr nature. Accordingly, they have 
typically been taken as one of the most 
intriguing and robust gramnaar modules. 
I See Annex for examples and the definition of 
binding constraints. 
Ill contrast to this, however, the formal and 
computational handling of binding constraints 
has presented non-negligible resistance when it 
comes to their integration into the representation 
and processing of grammatical knowledge. 
In its mainstream formulation, the methodology 
for verifying the compliance of grammatical 
representations with binding constraints requires 
a series of extra grammatical parsing steps 
(Chomsky, 81). More recently, prominent 
unification-based frameworks either require 
special purpose extensions of the description 
formalism for a partial handling of these 
constraints (LFG: Dalrymple, 93), or offer no 
integration yet for them into the grammatical 
setup (HPSG: Pollard and Sag, 94.. Backofen et 
al., 96). 
Our primary aim in this paper is to bridge this 
gap between the gram,natical nature of binding 
constraints and their full integration into 
grammar processing. In Section 1, we review 
previous steps towards this goal proposed in the 
literature. Building on these contributions in 
Section 2, we introduce the rationale of a new 
methodology for the verification of binding 
constraints, in Section 3, in the light of this new 
approach, we show how these constraints are 
fully integrated into g,ammar and the drawbacks 
of current methodology are overcome. 
1 The Cohldexation Paradigm 
The specification of binding constraints have 
greatly evolved in the htst three decades. The 
device of coindexation for marking anaphoric 
104 
links has, however, remained quite stable. This 
stems from the fact this device is at the heart of 
the mainstrealn nlethodology for verifying these 
constraints, a methodology whose basics were 
proposed in (Chomsky, 80, 81) and have been 
adopted since then in its different variants. 
L1 Post-grammaticall overgerieratior~ 
and filtering 
This methodology can be outlined as in Fig. 1. 
After the grammatical parsirig of a seriterice 
with n NPs has been completed: 
(i) iteration:repeat (ii)-(iii) uritil all 
possible different assignments of n indices 
(tokens) have been exhausted; 
(ii) indexation:generate a tree by assigning 
indices to its NPs; 
(ill)filtering:store the arniotated tree if the 
indexation of NPs respects binding 
constraints, otherwi'~e dc:letc it. 
Fig. 1 • ('/wm,vk),'.v al:;()i°ithm 
As noted as early as in (Correa, g/'), thi:~ 
approach is grossly inefficient. Later Fong, 90° 
showed that its complexity is of exponential 
order. Moreover, this methodology disregards 
any concern with interfacing grarnmar with 
systems for reference processing. The input for 
such systems will riot l)c a grammatical 
representatiori to lie refined vis4-vis the 
heuristics for anaphor resohition, but a forest of 
differently labeled trees that have to be 
internally searched and compared with each 
other by anaphor resolvers. 
Besides the efficiency issue, this methodology 
implies the conceptual awkwardne.,;s of having a 
<2 tnodnle of ~rammar that is not made operative 
~,ranallaatical processing, but as an during the <2 
extra-grammatical add-on. Correa, 88, p.123~ 
observed that although the integration of binding 
constraints "into rules which rnay be used to 
derive structure that already satisfies the 
\[constraints\] is not a straightforward task", that 
should be the path to follow, a point also 
strongly stressed in subsequent elaboration o11 
this isstie by Merle, 93. 
1.2 Packaginganaphoric ambiguity 
A first proposal for enhancing integration of 
binding cosntraints into grammar is due to 
Correa, 88. Simplifying some details, the 
proposed algorithm can be outlined as in Fig.2. 
Start fl'om the top of the tree with two empty 
stacks A and B where indices will be 
collected, respectively local c-commanding 
indices and non-local c-commanding indices. 
While walking down a tree where every NP 
l-ias a distinct index (type): 
When an NP is found: 
(i) copy:leave a copy of A (if it is an 
anaphor) or B (if it is a pronoun) at the NP 
node; 
(ii) a,vsign:take the first index i of the stack 
copied into the NP node., take the NP iridex j, 
and annotate the NP with j=i; 
(iii) collect:add NP index j to A. 
When a local domain border is crossed: 
(iv) reset:reset B to A m:B. 
t,'i,g-. 2 -, Cor/ea's a&orithm 
This algorithm was given two different 
implementations, one by Correa, 88, the other by 
Ingria and Stallard, 89. Further elaboration by 
Giorgi et al., 90, and Pianesi, 91, led to a 
restatement of this algorithm using formal 
 techniques. 
The do-it-while-parsing approach of Correa's 
implelnenlation has the advantage of discarding 
)OSW a special-purpose \[ .' erammatical module for 
binding. That iml~lementation, however, tulns 
out to be del)cndent on a top-down parsing 
strategy. On the other hand, lngria and Stallard's 
implementation has the advantage of being 
indelmridenl of the parsing strategy adopted. 
105 
This was done however at the cost of still 
requiring a special purpose postgrammatical 
parsing module for binding. 
Besides the issue of bringing binding into 
grammar, it is worth noticing that this evolution 
inside the coindexation paradigm presented a 
significant improvement and yet a clear 
drawback. On the one hand, if one disregards 
step (ii) (a disguised recency heuristic spuriously 
mixed with binding constraints) and considers 
the result of verifying binding constraints to be 
the assignment to an NP of the set of indices of 
its antecedent candidates, then it is possible to 
discard the proliferation of indexed trees as a 
way to express anaphoric ambiguity. 
On the other hand, the algorithm is 
acknowledged not to be able to cope with 
constraints possibly involving non-local 
anaphoric links. Principle C, backwards 
anaphora or cross-over cases were not accounted 
for (Correa, 88, p.127, Ingria and Stallard, 89, 
p.268). Moreover, as stack B only contains 
indices of the non-local c-commanders 2, but not 
all indices in the tree except those of the local 
c-commanders, Principle B is also not correctly 
accounted for. 
1.3 Packaging non-locality 
Other contributions to improve the coindexation 
method are due to Dalrymple, 93 and 
Johnson, 95. Instead of being directed to 
packaging ambiguity as the one above, they 
have in common being concerned with 
packaging non-locality. 
1.3.1 Nodes as mirrors of trees 
Johnson's algorithm is embodied in Prolog code. 
Abstracting away from details associated to that 
format, it gets the outline in Fig.3. 
2 C-command is a configurational version of the 
command relation where x c-commands y iff the first 
branching node that dominates x dominates y. 
Although this outline renders the algorithm in a 
bottom up fashion, Johnson ingeniously 
developed an implementation that is independent 
of the parsing strategy resorting to delaying 
mechanisms. Crucially, in spite of its post 
grammatical flavor, likewise Correa's 
implementation, this algorithm does not require 
postgrammatical processing. 
These results were obtained with some 
(i) Repeat (ii) until all NP~ (l<_i_<n) in the 
tree have been used as starting points; 
(ii) Walk up the tree from NPi and 
repeat (iii) until the top node of the tree is 
reached; 
(iii.i) When other locally c-commanding 
NPj is found: 
(iii.i.i) if NPi is a short-distance 
reflexive, annotate NPi with i=j; 
(iii.i.ii) if NPi is a non-reflexive, 
annotate NP~ with i:~j; 
(iii.ii) When other non-locally 
c-commanding NP 3 is found: if NP~ is a 
non-pronoun, annotate NP~ with i~j. 
Fig. 3 - .lohnson's algorithm 
accessory devices: Each node in the tree is 
"conceptualized as a pair consisting of a tree and 
a vertex in that tree" (p.62). Consequently, the 
whole tree where a given NP appears is locally 
accessible to be "walked up" since its replica is 
present at the pair (Category, Tree), which is the 
NP node itself. 
This algorithm improves the coindexation 
methodology in terms of efficiency as it does not 
resort to free indexation. Note, however, that the 
anaphoric ambiguity of pronouns and 
nonprououns is not captured (Principles B and 
C) since grammatical coindexation of pronouns 
or nonpronouns with their possible antecedents 
is dismissed. Only reflexives and their 
antecedents end up coindexed, while the index 
of a pronoun is only made "unequal" with the 
106 
indices of its (non-grammatical) locally 
c-commanding antecedents. Nevertheless, even 
dispensing with free indexation and restricting 
the representation of anaphoric ambiguity to 
reflexives, this approach does not get rid of the 
proliferation of trees: For a given reflexive, each 
corresponding tree/coindexation represents a 
different antecedent candidate. 
1.3.2 Equations with regular expressions 
The I_,FG/I)alrymple, 93, account of binding 
resorts to a different approach to generalize over 
the eventual non-locality of anaphoric links. It 
uses lexical "inside-.out equations", a 
special-purpose extension of the description 
formalism which may include regular' 
expressions (as in (3) below for long-distance 
reflexives): 
(1) John/introduced Billj to himself//)-. 
kimse(\[! ((()Bi-c;<,,,i "1" ) SUB J) o. = 1"c~ or 
((()13L(;<,~u "1" ) ()B\])c ~ = ~'o 
(2) *John introduced Bill/to hirrli. 
him: ((()BI<<,:,I I" ) ()BJ)o. ~ "i" o. 
(3) Zhangsani yiwei \[LMi yiwei\[...z_~i_i/j/k/...\]...\] 
Zkangsani thouglu \[Li.v(i tlumgkt ft.. kimi/j,d../...J 
z(ji: ((OBJ * J" ) S\[JBJ)<, = 1" o 
The right-hand side of the equation stands for 
the sernantic representation (c~) of tile 
functional-strncture ('\]') of the anaphor. The left 
hand side stands for the semantics of the 
antecedent: In (3) the Chinese long-distance 
reflexive is an Object in a functional--structure 
where one of the upstairs Subjects may be the 
antecedent. 
Although initial scepticism about the tractability 
of these equations was dissipated by Kaphm and 
Maxwell, 88, the survey by Backofen et al., 96, 
reports that no iml~lemented I,FG grammar was 
known to handle binding. To a significant extent 
this bears on tile fact that many different 
equations have to be defined for every anaphor: 
Each equation specify concrete grammatical 
functions for the anaphor and its potential 
antecedent, but either the anaphor or the 
antecedents may occur with one of a range of 
several grammatical functions (see a n-finimal 
ex,'lnlple ill (1)). Moreover, it is not defined how 
non-lexical NPs (e.g. anaphoric definite 
descriptions, ruled by Principle C) may be 
assigned the respective equation. 
However these difficulties turn out to be solved, 
the LFG variant of the coindexation 
methodology presents the same type of problems 
of Johnson's approach. The proliferation of 
representations is not avoided: The ambiguity of 
reflexives may end up represented by several 
different grammatical representations. These 
representations correspond to the satisfaction of 
the different equations involving different 
grammatical functions, as in (1), and possibly 
result also from the several existential 
interpretations of functional tmcertainty in the 
case of long-distance reflexives, as in (3). 
Likewise, the ambiguity of pronouns is omitted 
in the single functional-structure resulting from 
the universal interpretation of negative equations 
associated with these anaphoric expressions. 
Moreover, the positive equations for reflexives 
do not require identity of indices between 
anaphorically related expressions, but instead 
impose identity of semantic representations, this 
way incorrectly enforcing any type of anaphora 
(bound, bridging, e-type, "donkey", etc.) to the 
sole modality of coreference. 
2 The Concept of Binding Machine 
Being partially successful in overcoming 
problems of tile original post-gramnmtical 
"overgenerate & filter" methodology, each of tile 
contributions mentioned above brought to tile 
fore essential dimensions of binding that have to 
be concomitantly acconnted for. Accordingly, an 
alternative methodology for binding constraints 
107 
verification should find a way to harmonize all 
these dimensions: lexicalization, anaphoric 
ambiguity, packaging and non-local context 
packaging. 
Given these hints, a breakthrough depends now 
on changing some entrenched primitives 
underlying the conception of binding 
constraints. These constraints have been 
basically taken as syntactic well 
conditions: "\[they\] capture the distribution of 
pronouns and reflexives" (Reinhart and 
Reuland, 93, p.657). In line with Gawron and 
Peters, 90, however, we take them as conditions 
on semantic interpretation, as they delimit 
non-local aspects of meaning composition. 
In what follows, we set up a semantics-driven 
methodology for verifying binding constraints, 
organized under the rationale that an NP is a 
binding machine: (i) it reads a representation of 
the context; (ii) updates its own semantics given 
this context and its own anaphoric potential (in 
accordance with its binding constraint, if it is a 
non-quantificational NP); (iii) and makes a 
contribution to the context, against which other 
NPs are interpreted. This rationale is in line with 
the insights of Johnson and Klein,90 concerning 
the processing of the semantics of nominals, and 
also the spirit (but by no means the letter) of the 
dynamic semantics framework (Chierchia, 95). 
The output of a nominal n as a binding machine 
is simply the incrementing of the context with a 
copy of its reference marker (Kamp and 
Reyle, 93). The internal state of the machine 
after its operation is a compacted representation 
of the anaphoric potential of n, if any, under the 
form of the set of the reference markers of the 
grammatically admissible antecedents of n -- 
this internal state results fiom the binding 
constraint, lexically associated to n, being 
applied to the input. The input is a representation 
of the relevant aspects of the context under the 
form of a set of three lists of reference markers, 
A, Z and U, from which the internal 
state/semantics of anaphors can be computed. 
Taking n and its subcategorizing predicator p, A 
is the list with the reference markers of the 
complements of p ordered according to their 
relative obliqueness; Z includes the elements of 
A plus the reference markers of the upstairs 
predicators directly or indirectly selecting the 
domaiu of p, observing the multiclausal 
obliqueness hierarchy; and U is the list of all 
reference markers in the discourse context. 
Given this setup, the verification of binding 
constraints consists in a few simple steps. If n is 
a short-distance reflexive, A' is associated to its 
semantic representation, where A' contains the 
reference markers of the o-commanders of n in 
A. If n is a long-distance reflexive, its semantic 
representation includes Z', such that Z' contains 
the o-commanders of n in Z. If n is a pronoun, 
the set B=U\(A'u{refin,,}) is coded into its 
representation. Finally if n is a nonpronoun, its 
semantics keeps a copy of C=US(Z'u{ refin,,}). 
3 An HPSG exercise 
This methodology can be easily accommodated 
in a unification-based framework such as HPSG. 
We designed an extension to the UDRT 
component for HPSG of Frank and Reyle, 95. 
This component is encoded as the CONT(ENT) 
value, which is enhanced now with feature 
ANAPH(ORA). On a par with this extension, also 
the NONLOC(AL) value is extended with the new 
feature BIND(ING), with subfeatures LIST-A, 
LIST-Z, LIST-U and LIST-protoU. 
The SYNSEM value of a pronoun is as follows: 
p, MAX LS LI,-MIN ~V~\] 
SU.ORD { } 
J\[l ,ABEl, LOC\[CONT / C°NDs \[LARG-R ~\]} 
\[.A.NAPIt \[-REFM \[JJ \[ANTEC 
non - Ioc- ocom(lW\], VVI,~j-) 
-LIST- A 
NLOC I BIND LIST- Z IJST- U 
LIST- protoU (\[~\])j 
108 
The relational constraint ~on-loc-ocomm takes 
(in first argnnlent) all markers in the context. 
~iven in LISI'-U wflue, and remove l'rom them 
both the local o-commanders (included in 
second argunrent) of tlie t)ronoun and the 
pronoun itself (in third argument). 
Under the conception of nominals as binding 
machines, LISTSA, LIST-Z and LIST-U stand for 
the input, ANTEC(EDFNTS) encodes the internal 
state, and REF(ERENCE)M(ARKF.R) encodes the 
output. The SYNSEM of other anaphors, ruled by 
Principles A, C or Z, art quite similar to the one 
above. The major difference lies in the relational 
constraints in ANTEC value, which encode the 
corresponding binding constraint 3. 
Turning now to the lists with reference markers, 
we handle them by means of a new HPSG 
principle, the Binding I)omains Principle. This 
principle consists of three clauses constraining 
signs and their values with respect to these lists. 
I)ue to space limitations a, we illustrate this 
Principle with its ('lause 1, for LIST-U and 
LIST-protoU: 
Binding Domain~ Principle, Clause I 
(i) in every sign, LlST-protoW value is identical 
to the concatenation of LlST-protoU values of its 
daughters; 
(ii) in a sign of sort discourse, I,IST-protoU 
and LIST-U wflues are token-identical; 
(iii) in a non-NP sign, LIST-U wflue is 
token-identical to each LIST-U value of its 
daughters; 
(iv) in an NP sign k: 
(iv.i) in Spec-daughter, LIST-U value is the 
result of removing the elements of LIST-e\ value 
of Head-daughter from the I,IST-U value ot' k; 
3 Binding constraints fin non-lexical nominals are 
lexically stated in their determiners. 
4 Binding constraints are fttlly integrated in a 
computational lIPS(; gramma,, documented in 
(Branco, 99). 
(iv.ii) in Head-daughter, LIST-U value is the 
result of removing the value of REFM of 
Spec-daughter from the IJST-U value of k. 
The HPSG ontology was extended with the sort 
discourse corresponding to sequences of 
sentential signs. Subclause (iv) above is meant 
to avoid what is known as i-within-i effect. 
Conclusion 
In this paper we designed an alternative to the 
mainstream postgrammatical "overgenerate & 
filter" methodology for the verification of 
binding constraints. Our semantics-driven 
methodology is based on the conception of NPs 
as binding machines. We showed how this 
innovation helped to integrate binding 
constraints into grammar representation and 
processing and to avoid the intractability implied 
by the mainstream methodology. 
Acknowledgements 
I am grateful to Hans Uszkoreit for patient 
advice and criticism. My thanks go also to Mark 
Johnson for helpful discussion. 
Annex 
Recent results (Xue et al., 94, Branco and 
Marrafa, 98) indicate that there are four binding 
constraints: 
Principle A.' 
A locally o-commanded short-distance reflexive 
must be locally o-bound. 
Lee i thinks \[Ma.~ i saw himselj,i/j/. 
Principle Z: 
An o-commanded long-distance rellexive must 
be o-bound. 
Zhang.valq zhidao /Lis'{/ remvei \[gqH~gwttk 
:ui .vihmm z!/i/.//kl/ 
Zhangsan know \[Lisi think \[Wangwu most like sell'I\] 
Zhangsani knows that Lis!/ thinks that \Vangwu k likes 
himi,j/lmnself k most (Xue et al., 94) 
1 09 
Principle B: 
A pronoun must be locally o-free. 
Leei thinl~v \[Ma.x). saw himi/*j\]\]. 
Principle C: 
A nonpronoun must be o-free. 
\[Kimi'sJJ'iend \]j tkinks \[Lee saw Kimi/*j\]. 
These constraints are defined on the basis of 
some auxiliary notions. The notion of local 
domain involves the partition of sentences and 
associated grammatical geometry into two zones 
of greater or less structural proximity with 
respect to the anaphor. O-command is a partial 
order under which, in a clause, Subjects 
o-command Direct Objects, Direct Objects 
o-command Indirect Objects, and so on, 
following the usual obliqueness hierarchy of 
grammatical functions, being that in a 
multiclausal sentence, the upstairs arguments 
o-command the embedded arguments, etc. The 
notion of o-binding is such that x o-binds y iff x 
o..commands y and x and 3' are coindexed, where 
coindexation is meant to represent anaphoric 
links. 

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