reflexives. Like the existential quantifier expressed by other expressions,
such as the adverbial already,595959 [63].  this a phase quantifier. What is
specific here is that the quantification is over a partial order of reference
markers, the two relevant semi-phases over this order include the local
o-commanders and the other reference markers that are not local o-commanders,
respectively for the positive and the negative semi-phases, and the so-called
parameter point in phase quantification is the reference marker of the
eventual antecedent for the anaphoric nominal at stake.

Accordingly, the other three quantifiers — corresponding to the other three
binding Principles B, C and Z — are defined by means of this existential one
being under external negation (quantifier expressed by pronouns), internal
negation (by non pronouns) or both external and internal negation (by long-
distance reflexives).

referential nominals quantificational nominals dual nominals e-type anaphora

Doubly Dual Nominals While these findings deepen the rooting of binding
constraints into the semantics of anaphoric nominals,606060 Their fully-
fledged discussion and justification are outside the scope of the present
paper. A thorough presentation can be found in [19]. more importantly, they
also point towards promising research directions with the potential to advance
our understanding of the grammar of anaphoric binding, in particular, and more
widely, to further our insights into the semantics of nominals, in general.

A shared wisdom is that nominals convey either quantificational or referential
force.

The findings introduced above imply that nominals with “primary” referential
force (e.g. John, the book, he,…) have also a certain “secondary”
quantificational force: they express quantificational requirements — over
reference markers, i.e. entities that live in linguistic representations —,
but do not directly quantify over extra-linguistic entities, like the other
“primarily” quantificational nominals (e.g. every man, most students,…) do.

This duality of semantic behaviour, however, turns out not to be that much
surprising if one takes into account a symmetric duality with regards to
“primarily” quantificational nominals, which is apparent when they are able to
act as antecedents in e-type anaphora. Nominals with “primary”
quantificational force have also a certain “secondary” referential force: they
have enough referential strength to evoke and introduce reference markers in
the linguistic representation that can be picked as antecedents by anaphors —
and thus support the referential force of the latter —, but they cannot be
used to directly refer to extra-linguistic entities, like the other
“primarily” referential terms do.

As a result, the duality quantificational vs. referential nominals appears
thus as less strict and more articulated than it has been assumed. Possibly
taking indefinite descriptions aside, every nominal makes a contribution in
both semantic dimensions of quantification and reference but with respect to
different universes. Primarily referential nominals have a dual semantic
nature — they are primarily referential (to extra-linguistic entities) and
secondarily quantificational (over linguistic entities) —, which is symmetric
of the dual semantic nature of primarily quantificational ones — these are
primarily quantificational (over extra-linguistic entities) and secondarily
referential (to linguistic entities).

###  7.2 Neural

Natural Language Processing Task Some natural language processing tasks, e.g.
question answering, appear as end to end procedures serving some useful, self-
contained application. Some other tasks, in turn, e.g. part-of-speech tagging,
appear more as instrumental procedures to support those downstream, self-
contained applications. To help assess research progress in neural natural
language processing, sets of processing tasks, of both kinds, have been
bundled together, e.g. in the GLUE benchmark.616161[90].

As one such instrumental natural language processing task, possibly
contributing or being embedded into downstream applications, anaphora
resolution, including coreference resolution, is a procedure by means of which
anaphors are paired with their antecedents. It has been addressed with neural
approaches626262[61, 92]. and has been integrated into natural language
processing benchmarks.

While related to anaphora resolution, and eventually instrumental to it,
determining the set of grammatically admissible antecedents for a given
anaphor is a procedure that, as such, has not been addressed yet with neural
approaches, to the best of our knowledge. Like many other instrumental tasks,
this is a challenge that can contribute to make empirically evident and to
appreciate the strength of different neural approaches in handling natural
language processing. Grammatical anaphoric binding is thus an intriguing
research question open to be addressed with neural approaches, and also with a
good potential to provide a research challenge that may pave the way for
neuro-symbolic solutions to emerge.

Probing for Linguistic Plausibility While providing outstanding performance
scores in many natural processing tasks, neural models have been challenged,
like in other applications areas, due to its opacity and lack of
interpretability, specially when compared to symbolic methods.

As a way to respond to this type of challenge, neural models have been
submitted to ingenious probing procedures aimed at assessing them with respect
to the linguistic knowledge they may eventually have specifically encoded
while having been trained for generic or high level natural language
processing tasks, like for instance language modelling, machine translation,
etc.636363[31, 87, 69], i.a.

This endeavour of unveiling the possible linguistic knowledge represented in
neural models will certainly benefit from integrating the task of grammatical
anaphoric binding in this kind of toolboxes that may be used for linguistic
probing and interpretability.

Inductive Bias for Natural Language An increasingly important research
question in neural natural language processing is to design models that
possibly have an appropriate inductive bias such that their internal
linguistic representations and capabilities resemble as much as possible the
ones of human language learners after being exposed with as little volume of
raw training data as the ones humans learners are exposed to.646464[68].

A most outstanding feature of natural language is the possibility of there
being so called long distance relations, that is relations between expressions
among which a string of other expressions of arbitrary length may intervene.
This builds on another feature that has been widely recognized as underlying
natural language, namely the hierarchical nature of its complex
expressions.656565[27]

As amply documented in the overview above, grammatical anaphoric binding
relations, among anaphors and antecedents, are grammar regulated connections
that are long distance relations par excellence. Hence, anaphoric binding is
essential, and of utmost importance, for the endeavour of designing neural
models with appropriate inductive bias for natural language.

## Appendix

In order to illustrate the combined effect of the binding constraints
specified in Section 4, as well as the outcome obtained from a grammar that
integrates Binding Theory, we work through the example below and the
corresponding grammatical representation in Figure 1.

Every student said [he likes himself].

This is a multi-clausal sentence with two anaphoric nominals in the embedded
clause, a pronoun (he) and a short-distance reflexive (himself), and with a
quantificational NP (every student) in the upper clause. In this sentence, the
reflexive has the pronoun as the only admissible antecedent, and the pronoun,
in turn, can either have the quantificational NP as antecedent or be resolved
against an antecedent not introduced in the sentence.

Figure 1 presents an abridged version of the grammatical representation
produced by the grammar for a discourse that contains only this sentence. The
feature structures below the constituency tree correspond to partial
grammatical representations of the leave constituents, while the ones above
the tree correspond to partial representations of some of its non terminal
nodes.

Figure 1: Partial grammatical representation of Every student said he likes
himself.

### Circumscribing the Anaphoric Context

Let us start by considering the representation of the context.

Taking the representation of obliqueness hierarchies first, one can check that
in the upper nodes of the matrix clause, due to the effect of BDP–Clause III,
the list-z value is obtained from the value of list-a, with which it is token-
identical, thus comprising the list $\langle\raisebox{-3.01385pt}{\sc\openup
1.65761pt\lower 27.83884pt\hbox{\ignorespaces\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 54$}\kern 1.25pt}\kern 1.25pt\vrule}\hrule},\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 247$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}}}\rangle$. In the nodes of the embedded clause, in turn,
the list-z value is the concatenation of that upper list-z value and the
list-a value in the embedded clause
$\langle\raisebox{-3.01385pt}{\em\sc\openup 1.65761pt\lower
27.83884pt\hbox{\ignorespaces\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 24$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}, \lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 392$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}}}\rangle$, from which the list
$\langle\raisebox{-3.01385pt}{\em\sc\openup 1.65761pt\lower
27.83884pt\hbox{\ignorespaces\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 54$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}, \lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 247$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}, \lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 24$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}, \lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 392$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}}}\rangle$ is obtained.

In any point of the grammatical representation, the list-a values are obtained
from the subcategorisation frames of the local verbal predicators, as
constrained by BDP–Clause II and the lexical constraints in (4.2) and (4.2).
Therefore, $\langle\raisebox{-3.01385pt}{\sc\openup 1.65761pt\lower
27.83884pt\hbox{\ignorespaces\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 24$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule},\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 392$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}}}\rangle$ is the list-a value of likes, and
$\langle\raisebox{-3.01385pt}{\sc\openup 1.65761pt\lower
27.83884pt\hbox{\ignorespaces\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 54$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule},\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 247$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}}}\rangle$ is the list-a value of said.

Taking into account list-lu, as one ascends in the representation of the
syntactic constituency, the list gets longer since, by the effect of
BDP–Clause I, the list-lu value at a given node gathers the reference markers
of the nodes dominated by it. Consequently, at the discourse top node, list-lu
ends up as a list including all reference markers: both those introduced in
the discourse by the NPs in the example sentence and  $\scriptstyle 415$ , the
one available in the non linguistic context, from which the list
$\langle\raisebox{-3.01385pt}{\em\sc\openup 1.65761pt\lower
27.83884pt\hbox{\ignorespaces\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 415$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}, \lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 54$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}, \lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 247$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}, \lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 24$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}, \lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 392$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}}}\rangle$ is the result.

Note that in cases where the discourse contains more than one sentence,
BDP–ClauseI (i.) ensures that list-lu ends up with all reference markers from
every sentence of the discourse.

BDP–Clause I also ensures that this list of all reference markers is passed to
the list-u value of the top node, and that this list-u value is then
percolated down to all nodes of the grammatical representation, including the
nodes of anaphoric nominals.

### Circumscribing the Anaphoric Potential

To consider the representation of the NPs, we should take a closer look at the
leaf nodes in the constituency tree.

Contribution to the context Let us consider first how the NPs contribute to
the representation of the context.

Every phrase contributes to the global anaphoric context by passing the tag of
its reference marker into its own list-lu.

In the case of a quantificational NP, like _every student_ , two tags are
passed, corresponding to the var value  $\scriptstyle 54$ — token-identical
with the dref value of the restrictor and providing for bound-variable
anaphora interpretations — and the r-mark value  $\scriptstyle 247$ —
providing for e-type anaphora. e-type anaphora

While the semantic types of anaphora — including bound-variable and e-type
anaphora — are addressed in further detail in Section 5.2, it is of note at
this point that a DRT account of e-type anaphora is followed here.666666 [53,
p.311ff]. Accordingly, a quantificational NP contributes a plural reference
marker to the semantic representation of the discourse that may serve as the
antecedent in (e-type) anaphoric links. In a sentence like Every bald man
snores, for instance, the quantificational NP contributes the plural reference
marker which stands for the bald men that snore. Such marker is introduced in
the discourse representation via the application of the DRT Abstraction
operator $\Sigma$, which takes the restrictor and the nuclear scope of the
determiner and introduces the plural marker that satisfies the corresponding
semantic conditions.676767 [53, p.310].

In order to incorporate such an account of e-type anaphora into Underspecified
DRT,686868 [39]. the reference marker standing for the plurality satisfying
the semantic condition obtained with $\Sigma$-abstraction, in the conds value
of a determiner, is made token-identical with its r-mark value. The synsem of
the lexical entry for every, for instance, results thus as follows, where
$\scriptstyle 1$ is the marker obtained via $\Sigma$-abstraction:

$\mskip-3.0mu\left[\hskip 0.0pt\vbox{\vskip
1.65761pt\halign{\avmjfont\strut#\unskip\hfil&&\hskip\avmjhskip\avmjvalfont#\unskip\hfil\cr\sc
loc$\,|\,$cont &10.00002pt\it$\mskip-3.0mu\left[\hskip 0.0pt\vbox{\vskip
1.65761pt\halign{\avmjfont\strut#\unskip\hfil&&\hskip\avmjhskip\avmjvalfont#\unskip\hfil\cr\sc
ls &10.00002pt\it$\mskip-3.0mu\left[\hskip 0.0pt\vbox{\vskip
1.65761pt\halign{\avmjfont\strut#\unskip\hfil&&\hskip\avmjhskip\avmjvalfont#\unskip\hfil\cr\sc
l-max &\hskip 10.00002pt\it\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 4$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule} \\\ \sc l-min &\hskip 10.00002pt\it\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 5$}\kern 1.25pt}\kern 1.25pt\vrule}\hrule}
\crcr}\vskip 1.65761pt}\hskip 0.0pt\right]\mskip-3.0mu$\ignorespaces\\\ \sc
subord &10.00002pt\it\rm$\mskip-3.0mu\left\\{\hskip 0.0pt\vbox{\vskip
1.65761pt\halign{\avmjfont\strut#\unskip\hfil&&\hskip\avmjhskip\avmjvalfont#\unskip\hfil\cr\sc\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 4$}\kern 1.25pt}\kern 1.25pt\vrule}\hrule}>\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 3$}\kern 1.25pt}\kern 1.25pt\vrule}\hrule},\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 4$}\kern 1.25pt}\kern 1.25pt\vrule}\hrule}>\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 5$}\kern 1.25pt}\kern 1.25pt\vrule}\hrule},\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 8$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}$\geq$\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 5$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}\crcr}\vskip 1.65761pt}\hskip
0.0pt\right\\}\mskip-3.0mu$\ignorespaces\\\ \sc conds
&10.00002pt\it$\mskip-3.0mu\left\\{\hskip 0.0pt\vbox{\vskip
1.65761pt\halign{\avmjfont\strut#\unskip\hfil&&\hskip\avmjhskip\avmjvalfont#\unskip\hfil\cr\sc$\mskip-3.0mu\left[\hskip
0.0pt\vbox{\vskip
1.65761pt\halign{\avmjfont\strut#\unskip\hfil&&\hskip\avmjhskip\avmjvalfont#\unskip\hfil\cr\sc
label &\hskip 10.00002pt\it\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 4$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}\\\ \sc rel &10.00002pt\it every\\\ \sc res &\hskip
10.00002pt\it\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 3$}\kern 1.25pt}\kern 1.25pt\vrule}\hrule}\\\ \sc
scope &\hskip 10.00002pt\it\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 5$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule} \crcr}\vskip 1.65761pt}\hskip
0.0pt\right]\mskip-3.0mu$\ignorespaces, $\mskip-3.0mu\left[\hskip
0.0pt\vbox{\vskip
1.65761pt\halign{\avmjfont\strut#\unskip\hfil&&\hskip\avmjhskip\avmjvalfont#\unskip\hfil\cr\sc
label &\hskip 10.00002pt\it\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 3$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}\\\ \sc dref &\hskip 10.00002pt\it\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 2$}\kern 1.25pt}\kern 1.25pt\vrule}\hrule}
\crcr}\vskip 1.65761pt}\hskip 0.0pt\right]\mskip-3.0mu$\ignorespaces,\\\
\sc$\mskip-3.0mu\left[\hskip 0.0pt\vbox{\vskip
1.65761pt\halign{\avmjfont\strut#\unskip\hfil&&\hskip\avmjhskip\avmjvalfont#\unskip\hfil\cr\sc
label &\hskip 10.00002pt\it\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 5$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}\\\ \sc dref &\hskip 10.00002pt\it\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 7$}\kern 1.25pt}\kern 1.25pt\vrule}\hrule}
\crcr}\vskip 1.65761pt}\hskip 0.0pt\right]\mskip-3.0mu$\ignorespaces,
$\mskip-3.0mu\left[\hskip 0.0pt\vbox{\vskip
1.65761pt\halign{\avmjfont\strut#\unskip\hfil&&\hskip\avmjhskip\avmjvalfont#\unskip\hfil\cr\sc
label &\hskip 10.00002pt\it\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 8$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}\\\ \sc rel &10.00002pt\it$\Sigma$-abstraction\\\ \sc arg1
&\hskip 10.00002pt\it\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 2$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}\\\ \sc arg2 &\hskip 10.00002pt\it\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 7$}\kern 1.25pt}\kern 1.25pt\vrule}\hrule}\\\ \sc
dref &\hskip 10.00002pt\it\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 1$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule} \crcr}\vskip 1.65761pt}\hskip
0.0pt\right]\mskip-3.0mu$\ignorespaces\crcr}\vskip 1.65761pt}\hskip
0.0pt\right\\}\mskip-3.0mu$\ignorespaces\\\ \sc anaph
&10.00002pt\it$\mskip-3.0mu\left[\hskip 0.0pt\vbox{\vskip
1.65761pt\halign{\avmjfont\strut#\unskip\hfil&&\hskip\avmjhskip\avmjvalfont#\unskip\hfil\cr\sc
r-mark &\hskip 10.00002pt\it\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 1$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}\\\ \sc var &\hskip 10.00002pt\it\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 2$}\kern 1.25pt}\kern 1.25pt\vrule}\hrule}
\crcr}\vskip 1.65761pt}\hskip
0.0pt\right]\mskip-3.0mu$\ignorespaces\crcr}\vskip 1.65761pt}\hskip
0.0pt\right]\mskip-3.0mu$\ignorespaces\\\ \sc nonloc$\,|\,$bind
&10.00002pt\it$\mskip-3.0mu\left[\hskip 0.0pt\vbox{\vskip
1.65761pt\halign{\avmjfont\strut#\unskip\hfil&&\hskip\avmjhskip\avmjvalfont#\unskip\hfil\cr\sc
list-a &10.00002pt\it list(refm) \\\ \sc list-z &10.00002pt\it list(refm) \\\
\sc list-u &10.00002pt\it list(refm) \\\ \sc list-lu
&10.00002pt\it$\mskip-3.0mu\left\langle\hskip 0.0pt\vbox{\vskip
1.65761pt\halign{\avmjfont\strut#\unskip\hfil&&\hskip\avmjhskip\avmjvalfont#\unskip\hfil\cr\sc\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 2$}\kern 1.25pt}\kern 1.25pt\vrule}\hrule}, \lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 1$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}\crcr}\vskip 1.65761pt}\hskip
0.0pt\right\rangle\mskip-3.0mu$\ignorespaces\crcr}\vskip 1.65761pt}\hskip
0.0pt\right]\mskip-3.0mu$\ignorespaces\crcr}\vskip 1.65761pt}\hskip
0.0pt\right]\mskip-3.0mu$

Contribution by the context Let us consider now at how the representation of
the context is encoded in each NP.

It should be noted that the suitable values of list-a, list-z and list-u at
the different NP nodes are enforced by the combined effect of the three
Clauses of BDP.

Due to, respectively, BDP–Clause II (iii.) and BDP–Clause I (iii.i.), list-z
and list-u values result from token-identity, respectively, with list-z and
with list-u of the immediately dominating node in the constituency tree — that
is the case, for instance, with the lists
$\langle\raisebox{-3.01385pt}{\sc\openup 1.65761pt\lower
27.83884pt\hbox{\ignorespaces\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 54$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule},\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 247$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}}}\rangle$ and $\langle\raisebox{-3.01385pt}{\sc\openup
1.65761pt\lower 27.83884pt\hbox{\ignorespaces\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 415$}\kern 1.25pt}\kern 1.25pt\vrule}\hrule},\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 54$}\kern 1.25pt}\kern 1.25pt\vrule}\hrule},\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 247$}\kern 1.25pt}\kern 1.25pt\vrule}\hrule},\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 24$}\kern 1.25pt}\kern 1.25pt\vrule}\hrule},\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 392$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}}}\rangle$ in the non-pronoun every student and in the
sentential node dominating it.

Due to BDP–Clause II (i.), list-a value, in turn, is obtained via token-
identity with list-a of the subcategorising predicator — that is the case, for
instance, with the list $\langle\raisebox{-3.01385pt}{\sc\openup
1.65761pt\lower 27.83884pt\hbox{\ignorespaces\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 24$}\kern 1.25pt}\kern 1.25pt\vrule}\hrule},\lower
0.86108pt\vbox{\hrule\hbox{\vrule\kern 1.25pt\vbox{\kern
1.25pt\hbox{$\scriptstyle 392$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}}}\rangle$ in the reflexive himself and in its predicator
likes.

Realisation of anaphoric potential As to the anaphoric nominals, let us
consider how their anaphoric potential is circumscribed in each specific
occurrence.

The value of antec is a list that records the grammatically admissible
antecedents of the corresponding anaphor at the light of binding constraints.

As the result of the relational constraint principleA/2, the semantic
representation of the reflexive himself includes the attribute antec with the
singleton list $\langle\raisebox{-3.01385pt}{\em\sc\openup 1.65761pt\lower
27.83884pt\hbox{\ignorespaces\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 24$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}}}\rangle$ as value, indicating that the only antecedent
candidate available in this sentence is the pronoun in the embedded clause
whose reference marker is identified as  $\scriptstyle 24$ in its own semantic
representation.

The semantic representation of the pronoun he, in turn, includes the feature
antec with a value that is the list of its antecedent candidates,
$\langle\raisebox{-3.01385pt}{\em\sc\openup 1.65761pt\lower
27.83884pt\hbox{\ignorespaces\lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 415$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}, \lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 247$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}, \lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 54$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}, \lower 0.86108pt\vbox{\hrule\hbox{\vrule\kern
1.25pt\vbox{\kern 1.25pt\hbox{$\scriptstyle 392$}\kern 1.25pt}\kern
1.25pt\vrule}\hrule}}}\rangle$, thus indicating that, in this sentence, the
pronoun can be anaphorically linked to every nominal except itself, in line
with the relational constraint principleB/3.

This antec list includes antecedent candidates for the pronoun that will be
dropped out by preferences or constraints on anaphoric links other than just
the grammatical binding constraint expressed in Principle B. For instance, the
plural reference marker  $\scriptstyle 247$ , which is the r-mark value of
every student, will eventually be excluded by the anaphora resolver given that
the singular pronoun he cannot entertain an e-type anaphoric link with a
universally quantified NP whose reference marker obtained by
$\Sigma$-abstraction is a plurality.

Also the marker  $\scriptstyle 392$ of the reflexive will be eventually
discarded from this antec list as a suitable antecedent by the resolver system
since this would lead to an interpretive loop where the pronoun and the
reflexive would be the sole antecedents of each other.

Non-linguistic context Finally, in order to illustrate how the non linguistic
context may be represented in the linguistic representation of sentences, in
this example, the reference marker  $\scriptstyle 415$ was introduced in the
semantic representation of the ctx node.

The conds value of this node is meant to capture the possible contribution of
the non-linguistic context at stake for the interpretation of the discourse.
Like in the lexical entries of nominals, in the feature representation of ctx,
the reference marker  $\scriptstyle 415$ is integrated in the list-lu value.
By the effect of BDP–Clause I, this reference marker ends up added to the list
of all reference markers, from both the linguistic discourse and the non-
linguistic context, which is the shared value of features list-lu and list-u
at the top node in Figure 1.

## Abbreviations

BDP - Binding Domains Principle
DRT - Discourse Representation Theory
HPSG - Head-Driven Phrase Structure Grammar
UDRT - Underspecified Discourse Representation Theory

## Acknowledgements

The research reported in this paper was partially supported by the Research
Infrastructure for the Science and Technology of Language (PORTULAN CLARIN).

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