Binding Machines
Ant´onio Branco
 
University of Lisbon
Binding constraints form one of the most robust modules of grammatical knowledge. Despite their
crosslinguistic generality and practical relevance for anaphor resolution, they have resisted full
integration into grammar processing. The ultimate reason for this is to be found in the original
exhaustive coindexation rationale for their specification and verification. As an alternative, we
propose an approach which, while permitting a unification-based specification of binding con-
straints, allows for a verification methodology that helps to overcome previous drawbacks. This
alternative approach is based on the rationale that anaphoric nominals can be viewed as binding
machines.
1. Introduction
Since the so-called integrative approach to anaphor resolution was developed in the
late 1980s (Carbonell and Brown 1988; Rich and LuperFoy 1988; Asher and Wada
1989), and its practical viability extensively tested (e.g., Lappin and Leass 1994; Mitkov
1997, 1998), it has been common wisdom that factors determining the antecedents
of anaphors divide into filters and preferences. The former exclude impossible an-
tecedents and help to circumscribe the set of antecedent candidates; the latter help to
pick the most likely candidate, which will be proposed as the antecedent.
Binding constraints are a significant subset of such filters. As they delimit the rel-
ative positioning of anaphors and their possible antecedents in grammatical geometry,
these constraints are crucial to restricting the search space for antecedents and enhanc-
ing the performance of anaphor resolvers.
1
From an empirical perspective, they stem
from quite robust generalizations and exhibit a universal character, given their param-
eterized validity across natural languages. From a conceptual point of view, in turn, the
relations among binding constraints involve nontrivial symmetry, which lends them a
modular nature. Accordingly, they have been considered one of the most robust and
intriguing grammar submodules, usually referred to as binding theory. However, in
contrast to this, the formal and computational handling of binding constraints has
presented considerable resistance.
Anaphor resolution typically builds on many sources of information—among them,
information about the grammatical structure of the sentence—so that the different fil-
ters and preferences may be used. Consequently, it must in general be regarded as a
postgrammatical process, in the sense that it is completed after sentences are parsed.
Binding constraints, as a subset of the filters for anaphor resolution, are a special case
 Department of Informatics, Faculdade de Ci^encias de Lisboa, Campo Grande, 1700 Lisboa, Portugal.
E-mail: Antonio.Branco@di.fc.ul.pt.
1 See the Appendix for a specification of binding constraints. We adhere to the following terminological
convention: anaphors divide into reflexives and nonreflexives; reflexives form a class that includes
short-distance (ruled by Constraint A; e.g., himself ) and long-distance reflexives (Constraint Z; e.g.,
Chinese ziji); nonreflexives include pronouns (Constraint B; e.g., he) and nonpronouns (Constraint C;
e.g., the student).
c© 2002 Association for Computational Linguistics
Computational Linguistics Volume 28, Number 1
in this respect. Given that they form a submodule of grammar, they are specified on a
par with other grammatical submodules and constraints, and they are thus expected
to be integrated already into the processing of grammar. Nevertheless, this integration
cannot be considered to have been adequately achieved.
As we will discuss at length, the original methodology for verifying the compliance
of grammatical representations with binding constraints requires extragrammatical
processing steps delivering a forest of indexed trees to anaphor resolvers (Chomsky
1981). More recently, constraint-based grammatical frameworks either require special-
purpose extensions of the description formalism, though ensuring only a partial han-
dling of these constraints, as in Lexical-Functional Grammar (LFG; Dalrymple 1993), or
do not offer a solution yet to integrate them into grammar, as in Head-Driven Phrase
Structure Grammar (HPSG; Pollard and Sag 1994).
2
Our primary goal here is thus to bridge the gap between the grammatical nature
of binding constraints and their full integration into grammar processing. In particular,
we aim at achieving this in such a way that a lean interface between grammar and
reference processing emerges.
In Section 2, we first underline the distinction, seldom taken into account, between
specification and verification of binding constraints. We then review advances pro-
posed in the literature concerning the completion of the verification task. We observe
that three major lines of progress can be identified: packing of anaphoric ambiguity,
packing of nonlocal context, and lexicalization of binding constraints.
Building on these contributions, in Section 3 we argue that the remaining step
forward is to harmonize these different advances. We suggest that a more accurate,
semantics-driven comprehension of the nature of binding constraints is a relevant
move toward this harmonization. On the basis of this revision, we introduce a method-
ology for verifying these constraints, which rests on the new concept of binding ma-
chine, to be defined.
In Section 4, in the light of this new methodology, we show how binding con-
straints can be given a unification-based specification and can be fully integrated into
grammar.
In Section 5, we present an illustrative example and discuss in detail how binding
constraints and reference-processing systems are coordinated, and how the previously
identified drawbacks are overcome.
2. Advances in the Verification Task
In recent decades, great strides have been made toward an empirically adequate spec-
ification of binding constraints, this being an important research issue in theoretical
linguistics. Many aspects of this issue—a parameterizable definition of local domain,
the existence of a fourth constraint for long-distance reflexives, the possible subject-
orientedness of some anaphors, and the degree of universality of binding constraints,
to name just a few—have come under intense scrutiny.
In contrast, the verification task has been studied much less extensively. Even
though important problems also remain to be solved in this more applied dimension
2 The fragment of grammar developed and extensively discussed in Pollard and Sag (1994) is formally
specified in its Appendix with the HPSG unification-based description language. Binding constraints
escape such encoding. While noting that these constraints have yet to be accommodated in HPSG
grammars, Bredenkamp’s (1996) and Backofen et al.’s (1996) subsequent elaboration of this issue
implies that some kind of essential limitation of the unification-based formalism might have been
reached, a suggestion we seek to contradict here.
2
Branco Binding Machines
of the so-called binding theory, the issue of determining whether a given grammatical
representation complies with binding constraints has not attracted similar attention.
In this section, we briefly review major advances reported in resolving this issue.
2.1 Exhaustive Coindexing for Filtering
The first formulation of a verification procedure, based on exhaustive coindexation,
dates back to Chomsky (1980, Appendix; 1981, Section 3.2.3). The basics of this ap-
proach can be outlined as follows:
After the grammatical parsing of a sentence with n NPs has been completed,
for every parse tree t:
a. Indexation: Generate a new, annotated tree by assigning indices to the NPs
in t.
b. Filtering: Store this annotated tree if the indexation of NPs respects binding
constraints; otherwise, delete it.
c. Iteration: Repeat (a)–(b) until all type-different assignments of n possibly
different indices have been exhausted.
As discussed in Correa (1988), this procedure is grossly inefficient: its complex-
ity was shown in Fong (1990) to be of exponential order. Moreover, this approach
is conceptually awkward, given that a submodule of the grammar, the set of bind-
ing constraints, is not operative during grammatical processing, but functions as an
extragrammatical add-on.
3
This proposal also disregards the need to interface grammar with systems for ref-
erence processing. The input for such systems will not be a grammatical representation
to be refined vis-`a-vis the preferences for anaphor resolution, but a forest of differ-
ently labeled trees that have to be internally searched and compared with each other
by anaphor resolvers.
2.2 Packing Anaphoric Ambiguity
A first proposal for improving the exhaustive coindexation-driven methodology is due
to Correa (1988), whose goal was to enhance the integration of binding constraints into
grammar and obtain a tractable verification procedure.
Simplifying some details, the proposed algorithm can be outlined as follows:
Let t be a constituency tree where every NP has a type-distinct index. Start from
the top node of t with two empty stacks, A and B, where indices will be collected,
respectively local c-commanding
4
indices and nonlocal c-commanding indices,
while descending the tree. When an NP
j
is found:
a. Copy: Leave a copy of A (if NP
j
is a short-distance reflexive) or B (if it is a
pronoun) at the NP
j
.
3 Correa (1988, page 123) observes that although the integration of binding constraints “into rules which
may 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 on this issue
by Merlo (1993).
4 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 (Barker and Pullum 1990).
3
Computational Linguistics Volume 28, Number 1
b. Assign: Take the first index i of the stack copied into the NP
j
node, and
annotate NP
j
with j = i.
c. Collect: Add index j to A in each sister node of NP
j
.
When a local domain border is crossed:
d. Reset: Reset B to A [ B.
This algorithm has been given two different implementations, one by Correa
(1988), the other by Ingria and Stallard (1989). Further elaboration by Giorgi, Pianesi,
and Satta (1990) and Pianesi (1991) offers a variant in terms of formal language tech-
niques, where the stack copied into pronouns contains the antecedent candidates ex-
cluded by Principle B.
The “do-it-while-parsing” approach of Correa’s implementation has the advantage
of discarding a special-purpose postgrammatical module for binding. Nevertheless,
this solution turns out to be dependent on a top-down parsing strategy. On the other
hand, while Ingria and Stallard’s implementation is independent of the parsing strat-
egy adopted, its independence comes at the cost of still requiring a special-purpose
postgrammatical parsing module for binding.
Besides incorporating binding theory into grammar, Correa’s development inside
the coindexation-driven methodology presents other significant improvements. If one
disregards step (b)—a disguised recency preference mixed with binding constraints—
and considers the result of verifying these constraints to be the assignment to an NP
of the set of indices of its grammatically admissible antecedents, then it is possible
to discard the proliferation of indexed trees as a way to express anaphoric ambigu-
ity. Moreover, this packing of anaphoric ambiguity provides for a neat interface with
anaphor resolvers, whose preferences will then pick the most likely antecedent candi-
date from the relevant stack of indices.
These advances permit a verification procedure of tractable complexity (Correa
1988, page 127; Giorgi, Pianesi, and Satta 1990, page 5). This results crucially from
the move toward the lexicalization of the constraining effect of binding principles, a
solution also adopted in subsequent proposals by other authors, as we will discuss
below. The binding constraint of each anaphor is now enforced independently of how
the surrounding anaphors happen to be resolved. This implies that there is no need
to anticipate all the different resolutions for every relevant anaphor with a process of
exhaustive coindexation. It also implies that cases of undesired transitive anaphoricity
are handled by other filters during the anaphor resolution process.
5
However, these positive results regarding the verification task seem to be obtained
at the cost of some negative consequences regarding the specification task and em-
pirical adequacy. The above algorithm is acknowledged not to be able to cope with
5 Consider the sentence John said that he shaved him. Ignoring how other anaphors are resolved, in the light
of Binding Constraint B, he can take John as its antecedent, as empirically replicated in other minimally
different examples such as John
i
said that he shaved Peter; likewise, him can take John as its antecedent. A
point worth noting is that, if he actually ends up resolved against John, the latter cannot be the
antecedent of him, and vice versa. This specific resolution of he and him, out of the many possible
resolutions, blocks two anaphoric links that would otherwise have been admissible. It induces a
contingent violation of binding constraint B due to an accidental, transitive anaphoric relationship
between he and him.
This issue is not discussed in Correa (1988), since this paper is strictly focused on syntax and
binding. See footnote 13 below for a suggestion on how this issue may be handled in a grammatical
framework integrating syntactic and semantic representations.
4
Branco Binding Machines
constraints involving nonlocal dependencies. It does not account for Principle C, and
it only partially accommodates the anaphoric potential of anaphors complying with
Principle B. As Stack B only contains indices of the nonlocal c-commanders—rather
than all indices except those of the local c-commanders—the algorithm does not cor-
rectly account for the constraining effect of Principle B. Also this approach does not
account for backward anaphora or crossover cases (Correa 1988, page 127; Ingria and
Stallard 1989, page 268).
6
2.3 Packing Nonlocality
Other improvements in the task of verifying binding constraints are due to Dalrymple
(1993) and Johnson (1995). Instead of being concerned with packing ambiguity, they
are concerned with packing nonlocality.
2.3.1 Trees in Nodes of Trees. Johnson’s (1995) algorithm is embodied in Prolog code.
Abstracting away from details associated with that format, it can be outlined as fol-
lows:
Let t be a constituency tree where every NP has a type-distinct index. For
every NP
i
in t, traverse the tree from NP
i
upward until the top node is reached.
When a locally c-commanding NP
j
is found:
a. Annotate NP
i
with i = j if NP
i
is a short-distance reflexive.
b. Annotate NP
i
with i6= j if NP
i
is a nonreflexive.
When a nonlocally c-commanding NP
j
is found:
c. Annotate NP
i
with i6= j if NP
i
is a nonpronoun.
Although this outline renders the algorithm in a bottom-up fashion, Johnson inge-
niously develops an implementation of it that is independent of the parsing strategy by
resorting to delaying mechanisms. Consequently, despite its postgrammatical flavor,
this implementation does not require postgrammatical processing, thus incorporating
the task of binding constraint verification into grammar processing.
These results are obtained with some auxiliary devices. Each node in the tree is
“conceptualized as a pair consisting of a tree and a vertex in that tree” (Johnson 1995,
page 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 makes the verification of binding constraints more efficient because
it does not resort to exhaustive indexation. However, it does so at the cost of highly
complicating the grammatical representation, since the tree is replicated at each one
of its nodes.
While avoiding exhaustive indexation, this approach does not fully eliminate the
proliferation of trees. For a given ambiguous reflexive, with more than one admissible
6 See the Appendix for the notion of locality and local domain and other auxiliary notions in the
definition of binding constraints.
Backward anaphora occurs in cases where the anaphor is resolved against an antecedent that
occurs linearly after the anaphor, as in If he
i
is around, Peter
i
will do it.
An example of so-called crossover cases is the ungrammatical construction *Who
i
did Peter think she
i
saw?or*Peter
i
,he
i
said you like, where the fronted phrase is meant to be the antecedent of some pronoun
c-commanding the position from which this phrase is displaced.
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Computational Linguistics Volume 28, Number 1
antecedent, each antecedent candidate corresponds to a different coindexation and,
consequently, to a different tree. That is what generally happens with long-distance
reflexives, whose antecedents can be found in any of the binding domains induced
by the local or by the upward predicators, but it may also happen with short-distance
ones, as in (2) below.
As to the interface with reference processing, problems arise with reflexives and
nonreflexives, though of different nature. Reflexives, if ambiguous, give rise to prolif-
eration of trees, thus requiring comparison between trees during subsequent anaphor
resolution.
As to nonreflexives—pronouns and nonpronouns—their analysis does not give
rise to proliferation of trees, but the representation of their ambiguity is not fully
made explicit in the grammatical representation of the sentence being parsed. This
is so because they end up associated with negative information, that is, information
about what NPs cannot be their antecedents. The index of a pronoun is made unequal
with the indices of its local c-commanders; it is not made equal with the indices
of its grammatically admissible antecedents. The same holds for nonpronouns with
respect to their c-commanders. Consequently, in this case, the task of determining
the antecedent candidates that satisfy the relevant binding constraint of nonreflexives
remains to be completed after grammatical processing is finished. This will involve
some postgrammatical rescanning of the parse tree generated for extracting the indices
that do not enter in the inequalities obtained during the parsing.
Finally, like Correa’s approach, Johnson’s does not account for backward anaphora,
as only surface c-commanders are visible to the tree-climbing procedure.
2.3.2 Equations with Regular Expressions. The basic LFG account of binding, set
forth by Dalrymple (1993), adopts a different approach to generalize over the possible
nonlocality of intrasentential anaphoric dependencies. This approach makes crucial
use of a special-purpose extension of the LFG description formalism, the so-called
binding equations, which are lexically associated with anaphors. Building on Kaplan
and Maxwell’s (1988) proposal concerning functional uncertainty, binding equations
are designed to encode the uncertainty concerning the long-distance path between the
positions of the anaphor and its permissible antecedent in the grammatical structure.
7
Given that uncertainty concerning long-distance dependencies involves a (possibly
infinite) disjunction of possibilities, the basic idea is to encode such a disjunction in
finite terms by the use of regular expressions over feature structures. An example of
a binding equation encoding functional uncertainty is given in (1), preceded by an
example with the corresponding long-distance subject-oriented reflexive, Chinese ziji.
(1) Zhangsan
i
yiwei [Lisi
j
yiwei [:::ziji
i=j=:::
:::]].
Zhangsan
i
thought [Lisi
j
thought [:::him
i=j=:::
:::]]
ziji: ((COMP* OBJ ") SUBJ)
 
= "
 
The right-hand side of the equation stands for the semantic representation (“ ”) of the
anaphor (“"”), while the left-hand side stands for the semantic representation of the
antecedent. The description of the antecedent indicates that the long-distance reflexive
is an object and that this object is constrained to be part of a feature structure where
7 Koenig (1999) introduces a device in HPSG description language for stating inside-out constraints. This
would help in developing an HPSG emulation of the LFG approach for the verification of binding
constraints.
6
Branco Binding Machines
its antecedent may be one of the possibly many upward subjects. The Kleene operator
“*” allows abbreviation of the set of paths consisting of zero or more occurrences
of COMP—corresponding to possible successive clausal embeddings—followed by one
occurrence of OBJ.
While regular expressions may be used in binding equations, such expressions are
not necessary if the grammatical relation between the anaphor and its admissible an-
tecedents does not involve a long-distance dependency. That is the case in (2), which
displays the binding equation for the short-distance reflexive himself. Given that both
the subject and the object are admissible antecedents for the reflexive, in the binding
equation the use of the attribute GF, which stands for any grammatical function, un-
derspecifies the grammatical functions of the admissible antecedents (Dalrymple 1993,
Section 4.4.2).
(2) John
i
described Bill
j
to himself
i=j
.
himself: ((OBL
Goal
") GF)
 
="
 
Binding equations may also express negative constraints, as in (3), where the se-
mantic representation of the pronoun is constrained to be different from that of its
local coarguments.
(3)
 
John
i
described Bill
j
to him
i=j
.
him: ((OBL
Goal
") GF)
 
6="
 
As noted in Dalrymple (1993, Section 3.3), a few aspects of this approach for bind-
ing need to be fully worked out. For instance, the positive equations for reflexives
do not require identity of indices of anaphorically related expressions, but instead
impose identity of semantic representations. Without further elaboration, this will in-
correctly enforce any type of anaphoric link (coreference, bound, bridging, e-type, etc.)
to the sole mode of coreference. Another important issue is the account of nonlexical
anaphoric NPs: it is not clear how this type of NP (e.g., anaphoric definite descriptions,
ruled by Principle C) may be assigned the corresponding binding equation.
However these difficulties turn out to be resolved, the LFG approach for binding,
though building on a different strategy for handling nonlocality, presents the same
sort of problems as Johnson’s proposal.
The interfacing of grammar with reference-processing systems is problematic since
the proliferation of representations is not avoided. Constructions with reflexives, if
these are ambiguous, end up associated with several grammatical representations.
In the case of long-distance reflexives, as exemplified in (1), these representations
result from the possibly many solutions for the functional uncertainty encoded by the
regular expression in the binding equation. In the case of short-distance reflexives, as
exemplified in (2), they result from the different solutions for the unification of the
different grammatical functions of the admissible antecedents with the attribute GF in
the binding equation.
Likewise, the anaphoric capacity of pronouns and nonpronouns, typically ambigu-
ous, is not explicitly captured in the final grammatical representation. These anaphors
are lexically associated with negative equations, and for this type of equation there
is only one possible solution, namely, the grammatical structure where the semantic
representation of the anaphor is not identical to the semantic representations of any
of the phrases complying with the description of the antecedent in the left-hand side
7
Computational Linguistics Volume 28, Number 1
of the equation (Dalrymple 1993, Section 4.1.5). Therefore, for these anaphors the fi-
nal grammatical representation provides no information about what their admissible
antecedents are according to the relevant binding constraints.
3. A Semantics-Driven Approach
The contributions assessed above share a common point of departure with regard
to the verification algorithm first proposed by Chomsky (1981), each addressing and
solving some of its more significant drawbacks. The common move toward the lexical-
ization of binding constraints represents an important shift in the verification strategy:
verifying binding constraints is not a matter of inspecting final grammatical represen-
tations, but instead a matter of some local operation triggered by information lexically
associated with anaphors about their anaphoric class. This move has allowed bind-
ing constraint verification to be incorporated into grammar processing and permitted
tractable verification procedures.
From the discussion in the previous section, it follows also that these contribu-
tions have been partially successful in overcoming other problems of the verification
methodology based on exhaustive coindexation. Though partially successful, they have
brought to the fore important dimensions of binding that have to be concomitantly
accounted for. Accordingly, an alternative method for the verification of binding con-
straints has to find a way to harmonize all those different dimensions—lexicalization,
anaphoric ambiguity packing, and nonlocal context packing—while providing ade-
quate empirical coverage and neatly interfacing grammar with reference processing.
Against this background, a breakthrough depends, in our view, on reconsidering
some primitives underlying the conception of binding constraints. In the previous
section, we made a clear distinction between specification and verification of binding
constraints, so that the latter task could be isolated and better assessed. We will argue
now that further progress on the verification task depends on bridging this distinction
and possibly changing the way the specification of binding constraints is understood.
3.1 Patterns in the Semantics of Anaphors
Binding constraints have generally been viewed as well-formedness conditions on
syntactic representations, thus belonging to the realm of syntax. In line with Gawron
and Peters (1990), however, we think these constraints should rather be understood as
conditions on semantic representations, since they primarily delimit (nonlocal) aspects
of semantic composition, rather than aspects of syntactic composition.
8
Like other types of constraints on semantic composition, binding constraints im-
pose conditions on the interpretation of certain expressions—anaphors, in the present
case—based on syntactic geometry. However, this cannot be viewed as implying that
they express grammaticality requirements. By replacing a pronoun with a reflexive
in a given sentence, for instance, we do not turn a grammatical construction into an
ungrammatical one, even if we assign to the reflexive the antecedent appropriately se-
8 As implied by the title of this section, and as will become clear in the following discussion, this does
not mean that we are claiming that binding theory can be built without any reference to syntactic
constructs.
In the argument in the following paragraphs, we are assuming a notion of semantic composition
not in its strict sense, as used for example in Montague Grammar, but in the broader sense that the
intermediate semantic representations of the expressions are composed from other representations, as
used in Discourse Representation Theory (DRT). Note that reformulations of frameworks like DRT can
be worked out that result in a semantic system adhering to strict compositionality; see Janssen (1997,
Section 4.4) for references and a thorough discussion of this issue.
8
Branco Binding Machines
lected for the pronoun. In that case, we are simply asking the hearer to try to assign to
that sentence a meaning it cannot express—just as if we were to ask whether someone
could interpret The red book is on the white table as describing a situation where a white
book is on a red table.
In this example, given how they happen to be syntactically related, the semantic
values of red and table cannot be composed in such a way that the sentence could be
used to describe a situation concerning a red table, rather than a white table. Likewise,
in the sentence John thinks Peter shaved him, given how they happen to be syntactically
related, the semantic values of Peter and him cannot be composed in such a way that
this sentence could be used to describe a situation where John thinks that Peter shaved
himself (i.e., Peter), rather than a situation where John thinks that Peter shaved other
people (e.g., Paul, Bill, or John himself). The difference between these two cases is that
in the former, the composition of the semantic contributions of white and table (for the
interpretation of the NP white table) is constrained by local syntactic geometry, while
in the latter, the composition of the semantic contributions of John and him (for the
interpretation of the NP him) is constrained by nonlocal syntactic geometry.
This discussion leads us to consider that, semantically, an anaphor should be spec-
ified in the lexicon as a function whose argument is a suitable representation of the
context—providing a semantic representation of the NPs available in the discourse
vicinity—and its value is the set of the grammatically admissible antecedents for that
anaphor. This rationale is in line with other approaches to the meaning of anaphors
that, building in other sorts of arguments or research concerns, understand it also as
a projection from some relevant representation of contexts to entities.
9
But given the
specific focus of the present study, what should be noted is that, all in all, there will
be four such functions available to be lexically associated with anaphors, each corre-
sponding to one of the four different classes of anaphors, in accordance with the four
binding constraints A, B, C, and Z.
10
3.2 Binding Machines
Given these considerations, we can show that this conceptual shift to a semantics-
driven approach for the verification of binding constraints provides an adequate basis
for harmonizing the advances put forward in the literature and discussed above.
To make this alternative rationale for binding perspicuous, we suggest envisioning
an anaphoric NP as a binding machine, which operates by receiving an input, changing
its internal state, and returning an output. More specifically, an anaphoric NP can be
9 See, among others, Gawron and Peters (1990), Lappin and Francez (1994), and the discussion in
Jacobson (1999).
Adopting L¨obner’s (1987) duality criterion for quantification in natural language, and the formal
tools he developed for the analysis of phase quantification, we showed in Branco (2000) that the four
binding constraints can be seen as the effect of four binding quantifiers. These phase quantifiers can be
viewed as being expressed by the nominals of the four binding classes, and they quantify over the
reference markers organized in the obliqueness order.
A full-fledged account of the empirical support and justification for these results, and of their
implications, is beyond the scope of this article. For an abridged presentation of the core argument, see
Branco (1998).
10 As there are different grammatical frameworks, binding constraints have been specified under different
versions. Some differences between versions are due just to this fact that binding constraints are
supposed to be accommodated into different grammatical frameworks; some other differences,
however, are real differences of specification in the sense that different variants may not have the same
empirical coverage or be aimed at predicting the same (un)grammatical constructions. In the
Appendix, we present a common and fairly well empirically tested version of binding theory given the
current state of the art in this area, a version presently adopted in the HPSG framework. For an
alternative, see for example Reinhart and Reuland (1993).
9
Computational Linguistics Volume 28, Number 1
viewed as a binding machine that (1) takes a representation of its context; (2) updates
its own semantic value in response both to its context and to its intrinsic anaphoric
potential (i.e., in accordance with its binding constraint); and (3) contributes to the
makeup of the context, which the other binding machines read as input (i.e., against
which the other anaphoric NPs are interpreted).
11
The output of an anaphoric nominal n viewed as a binding machine is simply the
incrementing of the context with a copy of its reference marker.
12
The internal state of the machine after its operation is a representation of the con-
textualized anaphoric capacity of n under the form of the set of reference markers
of the grammatically admissible antecedents of n. This internal state results when the
binding constraint associated with n is applied to the input, and it is the interface point
between grammar and reference processing. This set of reference markers collects the
antecedent candidates, and its elements are submitted to other filters and preferences
by the anaphor resolvers so that one of them ends up being chosen as the antecedent.
The input, in turn, is a representation of the aspects of the context relevant to
help circumscribe the anaphoric potential of nominal anaphors. It is coded under the
form of three lists of reference markers, A, Z, and U. In list A, the reference markers
of the local o-commanders of n are ordered according to their relative grammatical
obliqueness; Z includes the o-commanders of n, possibly observing a multiclausal
obliqueness hierarchy; and U is the list of all reference markers in the discourse context,
including those not linguistically introduced.
Given this setup, the contribution of binding constraints in circumscribing the an-
aphoric potential of nominals is explicitly acknowledged. The particular contextualized
instantiation of that potential and the verification of binding constraints coincide and
consist of a few simple steps. If n is a short-distance reflexive, its internal state is set
up as A
0
, where A
0
contains the reference markers of the o-commanders of n in A.
If n is a long-distance reflexive, its semantic representation includes Z
0
, such that Z
0
contains the o-commanders of n in Z.Ifn is a pronoun, B = Un(A
0
[[r-mark
n
]) is
encoded into its representation, where r-mark
n
is the reference marker of n. Finally, if
n is a nonpronoun, its updated semantics keeps a copy of C = Un(Z
0
[[r-mark
n
]).
Besides adhering to an empirically grounded conception of binding constraints,
this approach embodies, and harmonizes, the crucial contributions of previous pro-
posals concerning the verification of these constraints. It assumes the lexicalization
of binding constraints. Concomitantly, it builds on specific strategies for the packing
of anaphoric ambiguity (viz., list of reference markers) and nonlocal context (viz., set
of lists of reference markers). Moreover, it achieves this while avoiding the above-
mentioned problems related to the proliferation of grammatical representations and
to the interfacing of grammar with reference processing, as well as the problems of
ensuring complete empirical coverage.
What remains to be discussed is whether, given this new format for the verifica-
tion of binding constraints, they can still be specified and integrated into grammar
processing with currently affordable formal and computational tools.
4. A Unification-Based Specification Exercise
This new approach to binding constraints can be integrated into grammar easily and
in a principled manner. In what follows, we outline how these constraints can be
specified and handled in a unification-based grammatical framework such as HPSG.
11 This rationale is in line with the insights of Johnson and Klein (1990) concerning the processing of the
semantics of nominals.
12 See Kamp and Reyle (1993) for the notion of reference marker.
10
Branco Binding Machines
As a proposal for that integration, we designed an extension to the Underspecified
Discourse Representation Theory (UDRT) semantics component for HPSG developed
by Frank and Reyle (1995). This component is encoded as the value of the feature
CONT(ENT), which is now extended with the feature ANAPH(ORA); see (4). This new fea-
ture keeps information about the anaphoric potential of the corresponding nominal n:
its subfeature ANTEC(EDENTS) keeps a record of how that potential is updated when the
anaphor enters a grammatical construction; and its subfeature R(EFERENCE)-MARK(ER)
indicates the reference marker of n, to be contributed to the context.
Similarly, and still assuming Pollard and Sag’s (1994) feature geometry as a starting
point, the NONLOC value is also extended with a new feature, BIND(ING), with subfea-
tures LIST-A, LIST-Z, and LIST-U. These lists provide a specification of the relevant context
and correspond to the lists A, Z, and U above. Subfeature LIST-LU is a fourth, auxiliary
list for encoding the contribution of local context to the global, nonlocal context.
The SYNSEM value of a pronoun, for instance, can now be designed as shown in (4).
(4)
2
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
4
locjcont
2
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
4
ls
"
l-max 1
l-min 1
#
subord fg
conds
8
<
:
"
label 1
arg-r 2
#
9
=
;
anaph
2
4
r-mark 2
antec 5 principleB
 
4 , 3 , 2
 
3
5
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
5
nonlocjbind
2
6
6
6
4
list-a 3
list-z list
list-u 4
list-lu 2
3
7
7
7
5
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
5
Given this feature structure, the binding constraint associated with pronouns is
specified as the relational constraint principleB. This relational constraint returns list
B as the value of ANTEC. It is defined to take (in the first argument) all markers in
the discourse context, given in LIST-U value, and remove from them both the local
o-commanders of the pronoun (included in the second argument) and the marker
corresponding to the pronoun (in the third argument).
The SYNSEMs of other anaphors, ruled by Principles A, C, and Z, are similar to the
one above.
13
The only difference lies in the relational constraint in the ANTEC value,
which encodes the appropriate binding constraint and returns the updated anaphoric
potential under the form of list A
0
, C,orZ
0
, respectively, as discussed in the previous
section.
Turning to the specification of the context (i.e., the values of LIST-A, LIST-Z, LIST-U,
and LIST-LU), this is handled by means of a new HPSG principle, which can be termed
the Binding Domains Principle. This principle consists of three clauses constraining
13 Binding constraints for nonlexical anaphoric nominals are lexically stated in the corresponding
determiners.
A constraint for pronominal anaphoric transitivity may also be introduced at the lexical
representation of pronouns, by including in the CONDS value in (4) Discourse Representation
Structure conditions expressing that
8r
a
, r
b
(( 2 =
anaph
r
a
^ r
b
=
anaph
r
a
) ) ([r
b
] [ 5 = 5 )).
11
Computational Linguistics Volume 28, Number 1
signs and their values with respect to these lists of reference markers. Due to space
limitations, we illustrate this principle simply by stating Clause I, which constrains
LIST-U and LIST-LU.
14
(5) Binding Domains Principle, Clause I
a. In every sign, the LIST-LU value is identical to the concatenation
of the LIST-LU values of its daughters.
b. In a sign of sort discourse, the LIST-LU and LIST-U values are token
identical.
c. In a non-NP sign, the LIST-U value is token identical to each
LIST-U value of its daughters.
d. In an NP sign k,
i. In Spec-daughter, the LIST-U value is the result of
removing the elements of the LIST-A value of
Head-daughter from the LIST-U value of k;
ii. In Head-daughter, the LIST-U value is the result of
removing the value of R-MARK of Spec-daughter from the
LIST-U value of k.
LIST-LU collects, up to the outermost sign of sort discourse, all the markers contributed
by the different NPs for the context. At this sign, they are passed to LIST-U, by means
of which they are propagated to every NP. The HPSG ontology was extended with the
sort discourse, which corresponds to sequences of sentential signs and at whose signs
reference markers from the nonlinguistic context may be introduced in the semantic
representation.
15
Subclause (d) is meant to avoid what is known in the literature as
the i-within-i effect.
5. Example and Discussion
The above unification-based specification of binding constraints, while ensuring their
integration into grammar, allows the binding module to be suitably hooked up
with systems of reference processing. Feature ANTEC is the interface point between
them.
14 Clauses II and III constrain LIST-A and LIST-Z, respectively. Roughly, Clause II ensures that the LIST-A
value is passed from the lexical head to its successive projections, and also from the head-daughters to
their arguments. Note that exemption occurs when principleA(
1 , 2 )
is the empty list, in which case the
reflexive should find its antecedent outside any binding constraint (Pollard and Sag 1994,
Chapter 6).
Clause III ensures that, at the top node of the grammatical representation, LIST-Z is set up as the
LIST-A value of that node, and that LIST-Z is successively incremented at the suitable downstairs nodes
by appending its value with the LIST-A value of those nodes.
At the lexical entry of a predicator, LIST-A is defined as the concatenation of the R-MARK values of
its subcategorized arguments specified in the ARG-S value.
For a detailed specification of the Binding Domains Principle, see Branco (2000).
15 Reference markers can be introduced linguistically, by the utterance of the corresponding expressions,
or nonlinguistically, by means of their cognitive availability in the context of the discourse. Theories of
natural language semantics can be used to represent these two types of reference markers.
Nevertheless, only a global theory encompassing natural language and cognition seems to be able to
pursue the ambitious goal of providing an integrated account of how both types of markers, and not
only those linguistically evoked, are introduced into semantic representation.
12
Branco Binding Machines
We are following a distinction between the notions of anaphor resolution and ref-
erence processing commonly assumed in the literature. Anaphor resolution is seen as
being concerned with the task of identifying the antecedents of anaphors. It is there-
fore part of a reference-processing system, whose overall goal, in turn, is to determine
the interpretation of the anaphors. This involves determining the appropriate semantic
type of the anaphoric link between an anaphor and its antecedent (coreference, bridg-
ing, e-type, bound anaphora, etc.) and providing a suitable semantic representation
for this link.
Being the interface point between grammatical representation and reference pro-
cessing, the list value of the feature ANTEC has just to be reduced by anaphor resolvers,
given the relevant preferences and filters other than binding constraints, until the most
likely antecedent is isolated. It is thus a process concerning selection in a list, rather
than search in a set of indexed trees.
As to reference processing in general, the specification suggested in the previous
section provides a suitable framework for the correct representation of the semantically
different types of anaphoric links, the range of options not being restricted to corefer-
ence only. After the anaphor has been resolved, the reference marker of the anaphor
and the reference marker selected as the antecedent can be related in accordance with
the mode of anaphora determined by the reference-processing system.
This semantic relation between anaphorically related reference markers can be
represented simply as another DRS condition in the CONDS value. This makes possible
a mainstream DRT representation for the resolved anaphoric link, thus building on
the substantial number of already worked out solutions available in the literature for
DRT-based semantic representation of anaphora.
16
This specification of binding theory for HPSG was tested with a computational
implementation using ProFIT (Erbach 1995). In this implementation, the relational
constraints corresponding to binding principles were straightforwardly encoded by
means of Prolog predicates associated to the lexical clauses of anaphoric expressions,
and defined in terms of simple auxiliary predicates ensuring the component operations
of list appending, list difference, and so on. It is worth noting that some of these
predicates have arguments—for example, the LIST-U value, whose value is computed
when the whole relevant grammatical representation is built up. This is a consequence
of packing nonlocal information in such lists. As in Johnson’s approach, it requires
that some delaying device be used, which in this computational grammar was done
by resorting to the Prolog built-in predicate freeze/2.
For the sake of the example, consider the following multiclausal sentence from
Portuguese displaying backward anaphora between a topicalized reflexive and a pro-
noun:
(6) De si pr´oprio, cada estudante disse que ele gosta.
of him self every student said that he likes
‘Himself, every student said that he likes.’
An abridged version of the grammatical representation produced by the imple-
mented grammar for this sentence is presented in Figure 1, where the feature structures
below the tree correspond to partial grammatical representations of the constituents
16 See Kamp and Reyle (1993) for a comprehensive rendering of DRT, and Branco (2000, Chapter 5) for an
overview concerning the semantic representation of different modes of anaphora.
13
Computational Linguistics Volume 28, Number 1
he
 e
v
e
ry 
s
t
u
d
e
n
t
hims
e
l
f
...|
ANAPHORA
REFMARK ANTEC
...|
BINDING
LIST_A LIST_Z LIST_U LIST_LU
24
415
247
54
392
24
392
54
24
392
415
24
247
54
392
24
,,
,
, ,,
,,
,
,
  
  
      
      
         
         
...|
ANAPHORA
REFMARK VAR
...|
BINDING
LIST_A LIST_Z LIST_U LIST_LU
247 54
54 54 415
24
247
54
392
247
54
 
 
      
      
         
         
,,
,
,
,
...|
ANAPHORA
REFMARK ANTEC
...|
BINDING
LIST_A LIST_Z LIST_U LIST_LU
392 24
24
392
54
24
392
415
24
247
54
392
392
 
 
      
      
         
         
, ,,
,,
,
,
sa
i
d
th
a
t
 
ct
x
...CONT
|
CONDS
ARGR
...|
BINDING
LIST_A LIST_Z LIST_U LIST_LU...
... ,,
,
,
415
415
24
247
54
392
415
[]
      
      
        
        
li
k
e
s
tr
ace
LIST_A LIST_Z LIST_U LIST_LU
24
392
54
24
392
415
24
247
54
392
, ,,
,,
,
,
     
     
LIST_A LIST_Z LIST_U LIST_LU
24
392
54
24
392
415
24
247
54
392
392
, ,,
,,
,
,
      
      
LIST_A LIST_Z LIST_U LIST_LU
54 54 415
24
247
54
392
24
247
54
,,
,
,
,,
      
      
LIST_A LIST_Z LIST_U LIST_LU
54 54 415
24
247
54
392
24
247
54
392
,,
,
,
,,
,
      
      
LIST_A LIST_Z LIST_U LIST_LU
415
24
247
54
392
415
24
247
54
392
,,
,
,
,,
,
,
      
      
Figure 1
Abridged grammatical representation for the example sentence (9).
14
Branco Binding Machines
in the leaves of the tree, while the ones above the tree correspond to partial represen-
tations of some nonterminal nodes.
First, consider LIST-Z. In the outer nodes of the matrix clause, due to the effect of
the Binding Domains Principle, Clause III, the LIST-Z value is obtained from the value
of LIST-A, with which it is token identical, comprising the list with a single element
h54i. In the nodes of the embedded clause, the LIST-Z value is the concatenation of that
upper LIST-Z value and the LIST-A value h24 , 392i in the embedded clause, from which
the list h54 , 24 , 392i is the result. LIST-A values are obtained from the representation of
the subcategorization frames of the verbal predicators.
Next, consider LIST-LU. Reading upward, note that at each higher level in the
constituency representation, the list gets longer; by the effect of the Binding Domains
Principle, Clause I, the LIST-LU value at a given node gathers the reference markers of
the nodes dominated by it. At the discourse top node, LIST-LU includes all the reference
markers of the NPs in the example, the listh415 , 24 , 247 , 54 , 392i. The Binding Domains
Principle, Clause I, also ensures that this list of all reference markers is passed to the
LIST-U value of the top node and that it is then percolated down to all relevant nodes
of the grammatical representation.
Taking a closer look at the NPs, it is easy to check that every phrase contributes to
the global anaphoric potential of its linguistic context by passing the tag of its reference
marker into its own LIST-LU. In the case of the quantificational NP every student, two
tags are passed, corresponding to the REFMARK value, providing for e-type anaphora,
and the VAR value, providing for bound anaphora interpretations. And in the case of
the ctx node, to illustrate how the nonlinguistic context may be taken into account
in the linguistic representation, the reference marker h415i is obtained from the set of
semantic conditions that conventionally may capture the nonlinguistic context.
On the other hand, the context also contributes to establishing the anaphoric po-
tential of each NP. This is ensured by the different clauses of the Binding Domains
Principle, which enforce the presence of suitable values of LIST-A, LIST-Z, and LIST-U at
the different nodes.
Finally, token identity is ensured between the ANTEC value and the outcome of the
different relational constraints that are lexically associated with each NP and express
binding constraints. The value of ANTEC is a list that, at this stage of anaphor resolution,
records the grammatically admissible antecedents of the corresponding anaphor only
in the light of binding constraints.
6. Conclusions
Departing from the coindexation-driven approach for encoding anaphoric dependen-
cies in grammatical representations, we have proposed an alternative methodology
where binding constraints are viewed as contributing to circumscribing their contex-
tually determined semantic value. This semantics-driven approach allows a principled
integration of binding constraints into grammar that supports both a specification for-
mat and a verification methodology free from previous difficulties. Importantly, it also
permits a neat interface between the grammatical module of binding and systems of
reference processing.
Appendix
In this article, we consider the version of binding constraints formulated within Head-
Driven Phrase Structure Grammar (Pollard and Sag 1994, Chapter 6). Recent devel-
opments indicate that there are four binding constraints (Xue, Pollard, and Sag 1994;
15
Computational Linguistics Volume 28, Number 1
Branco and Marrafa 1999). Here, the definition of each binding constraint is followed
by an illustrative example.
(7) Principle A
A locally o-commanded short-distance reflexive must be locally o-bound.
Lee
i
thinks [Max
j
saw himself
 i=j
].
(8) Principle Z
An o-commanded long-distance reflexive must be o-bound.
[O amigo do Rui
i
]
j
acha que o Pedro
k
gosta dele pr´oprio
 i=j=k
.
[the friend of the Rui] thinks that the Pedro likes of he PR
´
OPRIO
‘[Rui’s friend]
j
thinks that Pedro
k
likes him
j
/himself
k
.’ (Portuguese)
(9) Principle B
A pronoun must be locally o-free.
Lee
i
thinks [Max
j
saw him
i= j
].
(10) Principle C
A nonpronoun must be o-free.
[Kim
i
’s friend]
j
thinks [Lee saw Kim
i= j
].
These constraints are defined on the basis of some auxiliary notions.
The notion of local domain involves the partition of sentences and associated gram-
matical geometry into two zones of greater or lesser proximity with respect to the
anaphor. The exact definition of the boundary separating the local from the nonlocal
domain may vary from language to language. Typically, the local domain tends to
correspond to the structure in the grammatical representation that is affected by the
selectional capacity and requirements of a predicator.
O-command is a partial order under which, in a clause, the subject o-commands the
direct object, the direct object o-commands the indirect object, and so on, following the
usual obliqueness hierarchy of grammatical functions, while in a multiclausal sentence,
the upward arguments o-command the successively embedded arguments.
The notion of o-binding is such that x o-binds y iff x o-commands y and x and y
are coindexed, where coindexation is meant to represent anaphoric links.
Acknowledgments
I am grateful to Hans Uszkoreit for advice
and helpful discussion, and to Mark
Johnson for clarifying criticisms. I am solely
responsible for remaining errors.
The results presented here were obtained
while I was on leave at the Language
Technology Group of the DFKI-German
Research Center on Artificial Intelligence,
Saarbr ¨ucken, Germany, whose hospitality
and enthusiastic atmosphere I was very
fortunate to enjoy and I hereby gratefully
acknowledge.

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