Coordination as Direct Process

1. Introduction
Coordination has always been a centre of academic interest, be it in linguistic theory or in computational linguistics. The problem is that the assumption according to only the constituents of the
same category (1) may be conjoined is false; indeed, coordinations of different categories (2, 3)
and of more than one constituent (4, 5, 6, 7) shoud
not be dismissed as marginal.
(1) Jean danse la valse et le tango.
(Jean dances the waltz and the tango.)
(2) Je sais son âge et qu’elle est venue ici.
(I know her age and that she came here.)
(3) Un livre intéressant et que j’aurai du plaisir à lire.
(An interesting book and which I will enjoy to read.)
(4) Je demande à Pierre son vélo et à Marie sa canne à pêche.
(I ask Peter for his bike and Mary for her fishing rod.)
(5) Je demande à Pierre son vélo et à Marie d’où elle vient.
(I ask Peter for his bike and Mary where she comes
from.)
(6) Pierre vend un vélo et donne une canne à pêche à Marie.
(Peter sells a bike and gives a fishing rod to Mary.)
(7) Pierre a acheté un livre à Marie et un disque à Pierre pour
100F.
(Peter has bought a book for Mary and a CD for Peter
for 20 $.)
Consequently, this problem challenges the initial
choice of categories of description which is crucial
in the conception of the linguistic formalism. We
claim here that the constructive power of lexical
heads, encoded in the subcategorization feature,
explains the previous linguistic facts. In the coordinate structure, conjuncts may be of different
categories as well as of more than one constituent,
they just have to satisfy the subcategorization
constraints imposed by their functor if they are in
position of argument or to impose compatible
subcategorization constraints if they are functors,
where, as in Categorial Grammars (Dowty, 1988),
functors categories are those that bear unsatisfied
subcategorization requirements.
Our approach which is independent of any framework, is easily and precisely encoded in the formalism of Head Driven Phrase Structure Grammar (Pollard & Sag, 1994), which is based on
feature structures and makes available the feature
sharing mechanism we need.
The paper is organized as follows. Section 2 is a
brief account of previous approaches and section
3 is devoted to our approach. The french coordination with et serves throughout the paper as an
example.
2. Previous approaches
There exists a classical way to eschew the question
“what can be coordinated?” if one assumes a deletion analysis. Indeed, according to this approach
(Chomsky, 1957), (Banfield, 1981), only coordination of sentences are basic and other syntagmatic coordinations should be considered as coordinations of reduced sentences, the reduction being
performed by deleting repeated elements. This
approach comes up against insurmountable obstacles, chiefly with the technical difficulty of reversing the deletion process, in the analysis process
(Schachter, 1973), (Mela, 1992).
(Sag et al., 1985) have tried to make a direct
description of the conjoined expressions in reducing the constraint from requiring the same category for conjuncts to a weaker constraint of category compatibility. Technically, the compatibility
is checked by computing a “generalization” of
categories and imposing the generalization comprises all features expected in the given context.
For example, the context in (8), that is, the verb
être (to be), expects an predicative argument and
both categories NP and AP are just predicative
categories.
(8) Il est le père de Marie et fier de l’être . (NP + AP)
(He is Mary’s father and proud of it.)
However, this solution cannot be applied generally because all coordinations have not such “natural” intersection (cf.(2)). So we claim that we have
nothing else to do but explicitly enumerate, within
the head subcategorization feature, all the structures allowed as complement for a given lexical
head, that is, we will assume that the subcategorization feature has disjunctive values.
3. Our approach
Our proposal involves three stages. We begin by
formulating constraints on coordinate structures,
then we define how to build the coordinate structures and we end by specifying how the previous
constraints filter through such coordinate structures.
3.1. Constraints on coordinate structures
We distinguish the role of functor and that of
argument, where, as in Categorial Grammars,
functors categories are those that bear unsatisfied
subcategorization requirements. Lexical heads are
functors in relation to the arguments which they
select and, by composition, any expression that
contains an unsaturated functor is a functor (6)-(7)
and inherits the unsatisfied requirement from the
main functor. Arguments are the complements
selected by the head. As suggested by (Miller,
1991), adjuncts could be accorded the same status
as arguments by integrating them into the subcategorization requirement through an optional lexical rule. That would enable us to account for
coordination of adjuncts of different categories as
well as coordination of more than one constituent
with adjuncts.
In all cases, an argument may often be realized by
different categories. For example, the argument
required by savoir (to know) may be a NP or a
Completive: we say that the requirement is disjunctive and we represent the different alternatives
within subcategorization feature disjunctive values. When the lexical head requires several complements (to ask somebody something), the requirement is said to be a n-requirement. A
n-requirement is a multi-set of simple requirements. We claim then that :
(C1) A subcategorization 1-requirement is satisfied either by one of the disjuncts or by a coordination of disjuncts.
(C2) A subcategorization n-requirement is satisfied by m arguments, 0 <m < n, either by a sequence of m arguments such that each argument satisfies one and only one element of the requirement
or by a coordination of such sequences. The result
has a n-m requirement.
Note that (C1) and (C2) should be computed simultaneously in order to account for structures as (4).
The notion of partial saturation in (C2) allows us
to account for coordination of sub-series of arguments as in (5). As an entity can be both functor
and argument (1), our coordination criterion (necessary condition) is the following one :
The conjuncts must satisfy the same simple or
multiple subcategorization requirement and impose compatible subcategorization requirements.
In order to compute this compatibility, we define
u+
,an extension of the feature structure unification
to disjunctive and set values.
3.2. How coordinate structures are built
As in (Cooper, 1991), if son âge is a NP and
qu’elle est venue ici is a Completive, son âge et
qu’elle est venue ici is a conjunctive composite
categorie NP ^ Compl. We extend the operation
“^” to complex categories and we use a new connector in order to represent the expressions of
more than one constituent within a tuple. With
these two connectors, < > in order to represent the
expressions of more than one constituent within a
tuple. With these two connectors, a total structuring of complements is possible and all coordinate
structures may have a status. Nevertheless, the
extension to complex categories is not uniform:
coordinate structure features are not necessarily
composites or tuples of corresponding features
from each conjunct. In fact, features which are
allowed to have conflicting values are compounded, whereas other features as Subcat must unify.
This structuring is encoded within the following
HPSG-like lexical entry of et:
Phon \ et \
Synsem < [1], . . M < [1' ], . . M'
Part < C ,..,C > < C' ,..,C' >
Subcat
[1]
Part C
Subcat {} ,.. M
Part C
Subcat
[1' ]
Part C'
Subcat {} ,.. M'
Part C'
Subcat
1M 1 M
1 M
M
1 M
M
M + M
,[ ] ,[ ]
,[ ]
,[ ] >∧ >
∧


 

 

 




 

 

 



























































| Cat
Φ
Φ
Φ Φ
'
u ' 







203
The following LP-constraint on the lexical entry
of et ensures the correct order between conjunction and conjuncts :
[1] < ..< [M] < conj < [1’] < .. < [M’].
The coordination of m-tuples, as well as the coordination of simple conjuncts (M=1) stems from
the saturation of the conjunction et. As required by
linguistic facts, only the last element of the tuple
CM (or C’M) can be unsaturated and be the source
of inheritance.
3.3. Saturation schemata
It remains now to say how a general structured
complement satisfies a general requirement, that
is to say, where the checking of the conditions C1
and C2 is activated. They are called from a saturation schemata which is intended to replace the
HPSG Subcategorization Principle. This saturation schemata allows either a partial (Ψ ≠ {}) or
total saturation (Ψ = {}) by saturated complements
(Ψ’ = {}), or total saturation (Ψ = {}) by complements, the latter being partially (Ψ’ ≠ {}) or totally
saturated (Ψ’ = {}) :
where Σ satisfies Φ
and Φ is a m-requirement, Ψ n-m requirement, Σ
a general structured complement, Ψ or Ψ’ is empty.
3.4. Example of analysis
Example of resulting HPSG-like analysis is given
in figure 1 for the underlined phrase in (9):
(9) Jean conseille à son père d’acheter et à sa mère d’utilis
er un lave-vaisselle.
(Jean advises his father to buy and his mother to use a
dish washer.)
4. CONCLUSION
This approach based on concept of functor, argument and subcategorization allows us to account
for many coordination datas.
Its formalization comprises two parts which are
conceptually independants. On one hand, we have
extended the feature structure unification to disFigure 1. Analysis of conseille à son père d’acheter et à sa mère d’utiliser un lave-vaisselle
204
junctive and set values in order to check the compatibility and the satisfiability of subcategorization requirements by structured complements. On
the other hand, we have considered the conjunction et as the head of the coordinate structure,
so that coordinate structures stem simply from the
subcategorization specifications of et and the general schemata of the head saturation.
Both parts have been encoded within HPSG using
the same resource that is the subcategorization and
its principle which we have just extended to account for our disjunctive values of requirements
and structured categories.
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