When Something Is Missing: 
Ellipsis, Coordination and the Chart 
Alberto Lavelli and Oliviero Stock 
Istituto per la Ricerca Scientifica e Tecnologica 
I - 38050 Povo TN, Italy 
lavelli@irst.it / stock@irst.it 
Abstract 
This paper deals with two linguistic 
phenomena which are usually considered cases 
of ill-formedness by the computational 
linguistics community: intersentential ellipsis 
and coordination (possibly with gaps). We 
present an original solution, if compared to 
those already known for the two phenomena. 
This solution is conceived within a relevant 
approach to parsing, i.e. chart parsing, and is 
coherent with the basic ideas of this approach. 
I. Introduction 
The ability to face and resolve problems associated 
with ill-formedness is fundamental in order to make 
natural language interfaces usable (see \[Carbonell and 
Hayes, 1983\] for a review of the problems of ill- 
formedness and of techniques used to resolve them). 
We shall focus on two phenomena: intersentential 
ellipsis and coordination (possibly with gaps). 
Ellipsis is a very common phenomenon and is 
frequently encountered in dialogues between persons. 
Up to the present, studies on natural language 
interaction with computers generally highlight the 
frequency of this phenomenon, (see, for example, 
\[Eastman and McLean, 1981\]). 
For this reason, ellipsis has received much 
attention and different solutions have been proposed 
based on the mechanism used to analyze the sentence: 
semantic grammars (the LIFER/LADDER system 
\[Hendrix, 1977\]), ATN \[Kwasny and Sondheimer, 
1981, Weischedel and Sondheimer, 1982\], or case- 
frame instantiation (the XCALIBUR system 
\[Carbonell et al., 1983\]). 
As far as coordination is concerned, it is also 
frequently considered a phenomenon of ill-fomaedness 
for the following reasons: 
- since every pair of constituents of the same 
syntactic category may be coordinated, if the 
grammar specifically included all these 
possibilities it would greatly increase the size of 
the grammar itself; 
- a constituent inside a coordination may have gaps 
(that is, missing elements) that, in general, are not 
allowed in constituents of the same type. 
Even in the most purely linguistic area, 
coordination has not received in-depth treatment, if not 
recently (for example, see \[Sag et al., 1984\] and 
\[Kaplan and Maxwell, 1988\]). 
Until the beginning of the 80's almost no system 
(the most relevant exception being the SYSCONJ 
module, present in the LUNAR system \[Woods, 
1973\]) has confronted coordination in a generalized 
manner. The 80's have seen renewed computational 
interest in coordination that has brought new efforts 
(see \[Kwasny and Sondheimer, 1981\], \[Dahl and 
McCord, 1983\], \[Fong and Berwick, 1985\], \[Lesmo 
and Torasso, 1985\], \[Kosy, 1986\] and \[Proudian and 
Goddeau, 1987\]). 
In this paper we present a solution to both the 
problems outlined above (that is, ellipsis and 
coordination). The solution is original with respect to 
those presented in the literature in that it is based on 
chart parsing \[Kaplan, 1973, Kay, 1980\], an approach 
little used to treat iU-formedness until now. t For both 
problems the solution is based on a strategy that uses 
the information contained in the structures produced by 
the parser (as is the case in almost all the work 
mentioned in this introduction; for a pragmatics-based 
approach to ellipsis, see \[Carberry, 1989\]). 
Both the solutions proposed have been inserted 
into WEDNESDAY 2 \[Stock, 1989\], a chart-based 
parser used in a dialogue system for Italian; attention 
has been paid to distinctive aspects of this language 
(for example, the relative liberty of order inside a 
single constituent). The process of building the 
analysis is based on a sort of unification. The parser is 
built so that it may be connected to a semantic (and 
possibly pragmatic) discrimination component; in this 
way, the discrimination is carried out incrementally as 
the syntactic analysis proceeds. All examples in this 
paper are in Italian. 
2. Ellipsis 
First, consider an example of ellipsis (upon which an 
informal description of this solution will rely): 
UseE Giotto ritrasse S.Francesco in 
un' opera di Assisi? 
\[Did Giotto portray St.Francis in a 
masterpiece located in Assisi ?\] 
System: si, ad esempio nella Predica agli 
uccelli. 
\[Yes, for example in the Sermon to the 
birds. \] 
USeF. Gioacchino in un affresco di Padova? 
\[Gioacchino in a fresco located in 
Padova ?\] 
In the elliptical sentence two constituents may be 
distinguished: the noun phrase Gioacchino and the 
prepositional phrase in un affresco di Padova. 
Substitution of some constituents of the preceding 
sentence is foreseen with the recognized constituents 
1 Always in the area of chart-based parsin 8 see \[Mellish, 
1989\], who, however, deals with other problems of ill- 
formedness, i.e. the presence of unknown words and of 
spurious constituents. 
184 
in the elliptical sentence, respecting, in essence, the 
ordering of the two sentences (this means that the 
elliptical sentence In un affresco di Padova 
GLoacchino? \[lit. In a fresco located in 
Padova Gioacchino .9\] wollld not be roc0gnizab\]e and 
the associated ellipsis would not be resolvable). In this 
case it is necessary to find the points in the preceding 
sentence in which to insert the fragments 
Gioacehinoand in un alfresco di Padova. Onc~ 
the points of insertion are found, the parser restarts. 
The semantic correctness of the proposed hypothesis is 
checked through the usual semantic control during 
unification. In this example, the first possible 
solution, starting from the left and moving right, is: 
- Gioacehino ins~ad0f Giotto 
- in un alfresco di Padova instc~qd of in 
un'opera di Assisi 
which gives the sentence Gioacchino ritrasse 
S,Franeesco in un affresco di Padova? \[Did 
Gioacchino portray St. Francis in a fresco 
located in Padova ?\]. Actually, already during an 
initial unification this possibility is rejected for 
semantic and contextual reasons (given that there is no 
painter named Gioacchino). The following 
substitution is then tried: 
Gioaechino instead 0f s. Francesco 
in Eua affresco di Padova instead of in 
un'opera di Assisi 
which produces the sentence Giotto ritrasse 
Gioacchino in un alfresco di Padova? \[Did 
Giotto portray Gioacchino in a fresco 
located in Padova ?\]. This represents tile correct 
interpretation of the ellipsis. 
It must be emphasized the fact that work is never 
duplicated; this positive characteristic of the chart is 
respected by our solution since (as will be seen in the 
algorithm) the base mechanism of the general case is 
preserved. 
2.1. The algorithm 
Now the algorithm for resolving ellipsis will be 
described more formally. That will be done by 
considering the most complex case, substitution (even 
multiple), in the general case. Firstly, provision is 
made for saving the chart, called model chart, built for 
the preceding sentence (in which all the edges, active 
and inactive, that have contributed to building the 
correct analysis for that sentence are saved). Then, an 
attempt is made to analyze the next elliptical sentence, 
partially building another structure, called fragments 
chart (the construction of this second structure can be 
carried on and concluded during resolution of the 
ellipsis). 
The algorithm tbr treatment of ellipsis consists of 
alternate scanning of the model chart and fragments 
chart. When a vertex is tbund in the model chart from 
which a cycling edge exits that is of the same category 
as the inactive edge I' exiting the vertex of the 
fragments chart upon which it is positioned, then the 
inactive edge I (generated from the given cycling edge) 
of the model chart is substituted by the inactive edge I' 
of the fragments chart. Thereafter the parser is restarted 
by the usual mechanism (the substitution concerns not 
only edge 1, but all the inactive edges that that edge 
subsumes and all the active edges that subsume edge I 
or some of the edges subsumed by I. This aspect of 
the algorithm is consistent with some of the 
techniques used in \[Wir6n, 1989\]). In essence the 
algorithm is expectation-driven, given that the 
fragment is inserted where there is a cycling edge that 
wants it. In this way, the expectations created by the 
preceding sentence are taken into account to guide the 
search tot a solution to the ellipsis. 
Because an agenda is used to manage the chart, the 
algorithm is sufficiently simple and causes only 
limited changes in normal functioning of the parser. 
~Ihere ~tre two different phases: 
i) activation of the mechanism (that is, the search 
for the vertex where to insert the first fragment that 
restarts the usual mechanism); 
ii) the next phase brings only effects of the 
modification of the function that selects the tasks 
contained in the Agenda. 
The algorithm uses pointers to the vertices of the 
two charts: Remaining-ModelChart for the model chart 
and Remaining-FragmentsChart for the fragments 
chart, which are initialized at the initial vertex of the 
respective chart. First of all, consider the activation 
phase: 
1. for all cycling edges C exiting from the vertex of 
Remaining-ModelChart, a check is done to 
determine whether among the inactive edges 
leaving the vertex of Remaining-FragmentsChart 
there is one, I', of the same syntactic category as 
C; if yes, go to point 2, otherwise move 
Remaining-ModelChart to the next vertex in the 
model chart and return to the beginning of point 1; 
2. save the preceding context (what this means will be 
made clearer at the end of the algorithm 
formulation); 
3. remove the edge I, generated from the cycling edge 
C, from the model chart (together with those 
specified above) and put a task into the Agenda that 
inserts the edge I' into the model chart; 
4. move the pointers Remaining-ModelChart and 
Remaining-FragmentsChart to the arrival vertex of 
the inactive edges selected in the model chart and 
fragments chart respectively; 
5. start the normal mechanism (with the only change 
being that to the selection function indicated 
below) on the model chart thus modified; 
6. if the process in point 5 does not succeed, it is 
necessary to backtrack, which means return to 
point 1 after having reestablished the preceding 
context and having moved Remaining-ModelChart 
to the next vertex of the model chart. 
Now, we analyze the way in which tile function 
that selects the tasks contained in the Agenda is 
modified: 
1. when a task that extends an active edge A with an 
inactive edge I is to be executed, check whether 
among the inactive edges leaving the vertex of 
Remaining-FragmentsChart there is one, I', of the 
same syntactic category as I; if yes, go to point 3, 
otherwise go to point 2; 
2. move Remaining-ModelChm't to the arrival vertex 
of edge I and exit from the function normally 
2 185 
executing the task selected; 
3. save the preceding context (what this means will be 
made clearer at the end of the algorithm 
formulation); 
4. the task selected is removed from the Agenda; 
5. remove edge I from the model chart (together with 
those specified above) and put a task into the 
Agenda that inserts the edge I' into the model chart; 
6. move the pointers Remaining-ModelChart and 
Remaining-FragmentsChart to the arrival vertex of 
the inactive edges selected in the model chart and 
fragments chart respectively; 
7. start the normal mechanism on the model chart thus 
modified; 
8. if the process in point 7 does not succeed, 
backtrack, which means go to point 2 after having 
reestablished the preceding context. 
Some aspects of the backtracking mechanism are 
now specified (and with them the reason for saving and 
reestablishing the contexts): backtracking is here 
intended exclusively as a nondeterministic strategy 
relative to the insertion of ellip~m__¢__0~. This 
does not impinge in any way upon the chart 
mechanism, which continues to provide flexible and 
efficient nondeterministic management. Furthermore, 
intuitively, the ellipsis resolution algorithm will only 
have to work on a very limited number of fragments, 
as they occur in man-machine interaction. This 
considered, the complexity of the algorithm remains, 
in practice, within acceptable limits (as well-known 
for the chart). 
How this is applied to the example given at the 
beginning of this section (and repeated here) will now 
be considered: 
User: Giotto ritrasse S.Francesco in 
un'opera di Assisi? 
\[Did Giotto portray St.Francis in a 
masterpiece located in Assisi ?\] 
System: si, ad esempio nella Predica agli 
uccelli. 
\[Yes, for example in the Sermon to the 
birds. \] 
User: Gioacchino in un affresco di Padova? 
\[Gioacchino in a fresco located in 
Padova ?\] 
Figure l shows the model sentence with the 
relevant cycling edges; Figure 2 shows the inactive 
edges for Gioacchino and in un affresco di 
Padova. The activation phase immediately brings into 
operation the substitution of the inactive edge that 
goes from vertex 1 to vertex 2 (Giotto) with the 
inactive edge of the fragments chart that represents 
Gioacchino; after this substitution and opportune 
changes to Remaining-ModelChart mad to Remaining- 
FragmentsChart, the parser is restarted, but it fails 
because of a violation of semantic restrictions. This 
failure causes backtracking to begin and therefore to 
seek another vertex in which to make the substitution. 
This vertex is number 3, from which an inactive edge 
terminating in 4 that has recognized s. Francesoo 
exits. This edge is then substituted with the inactive 
edge of the fragments chart that represents 
Gioacchino. The parser works normally until 
Remaining-ModelChart points to vertex 4 and the task 
selection function must extend the active S edge with 
an inactive PP edge (which extends from vertex 4 to 
vertex 9). In this case it can substitute the inactive PP 
edge \[in un'opera di Assisi\] with in un 
affresco di Padova and therefore restart the chml, 
which reaches the conclusion of the analysis. 
Returning to a more general consideration on the 
working of the algorithm, note that sluicing (for 
example, Giotto dipinse affreschi in Veneto? 
\[Did Giotto paint frescoes in Venetia?\] Sai 
quando? \[Do you know when ?\]) since it includes wh- 
words, causes the bottom-up introduction of a cycling 
edge for a sentence with long distance dependencies. 
Expansion is much simpler - it is convenient to 
allow adjunctive adverbs to be inserted only at a fixed 
position in the sentence (e.g., extreme left), with 
obvious advantages of efl'iciency for the parser. 
1 2 3 4 5 6 
Giotto ritrasse ~ ~ S.Francesco in un' opera 
U U k/ NP NP PP NP 
Figure 1. Model sentence with the cycling edges relevant for the example. 
NP 
Gioacchino 
7 8 9 
• .... O di Assisi 
PP 
PP 
m un affresco di Padova 
Figure 2. The inactive edges of the fragments Gioacchino and in un alfresco di Padova. 
186 3 
Ix l~a 
Figure 3. Coordination rule. 
We conclude this section with a couple of remarks. 
The first one concerns preferences for the insertion of 
fragments: for many kinds of dialogues it seems 
reasonable to use a heuristics that favors the insertion 
of the elements of the fragments chart all at the same 
level inside one constituent. The second one concerns 
unification (or any other mechanism that one would 
use for functional control in connection with the 
chart); this would prevent the analysis of: Giotto 
nacque a Padova? \[Was Giotto born in Padova 
?\] I Lorenzetti a Siena? \[The Lorenzetti 
broth,grs in Siena ?\] (ill which the subjects of the 
two sentences differ in some features, in this case the 
number). This aspect emphasizes the need to employ 
relaxation techniques in the unification mechanism in 
order to be able to accept this kind of elliptical 
sentence. 
3. Coordination 
If the pm'ser uses a top-down strategy (as is usual in 
ATN and logic grammars), it must hypothesize a 
structure for the second conjunct without any 
knowledge of its actual structure. Since this may be 
any structure that parallels that of a constituent that 
ends immediately before the conjunction, the parser 
must build and check all these possibilities to find the 
right ones; all this leads to a combinatorial explosion 
of possfbilities. 
A chart-based approach allows a natural 
factorization in constituent construction, thereby 
limiting the exponential explosion of possible 
analyses, a negative characteristic of SYSCONJ and 
other systems. Moreover, a bottom-up strategy 
provides further inlormation to guide the parser in the 
analysis of successive coordination constituents. 
In the following, only coordination of constituents 
belonging to the same syntactic category and adjacent 
is considered. 
Three changes to the normal chart mechanism are 
necessary to treat coordination (plus the introduction 
of metarules for the coordination of constituents 
containing gaps, see § 3.1) and concern: 
1) the configuration of an inactive edge Ix followed 
by an inactive edge Iand (conjunction type), 
that causes the insertion of new active edges; 
2) features that must be associated with coordinated 
exlges; 
3) for a system that incorporates a mechanism 
based on unification (see, for example, 
\[Shieber, 1986\]), the way in which the 
mechanism is activated when an active edge 
incorporates an inactive ont. 
The first change (shown in Figure 3) causes the 
insertion of an active edge AX (of the same category as 
Ix and nmrked as destined to recognize a coordinated 
==5 
IX IAnd 
A'x 
structure) that covers the two inactive edges i x and 
IAnd, and of a cycling edge A'X of the same category as 
Ix (if not there already). The cycling extge A'x is meant 
to recognize the coordinated constituent. 
As for tile features associated with the edge, in case 
of coordination it may occur that a noun phrase has 
some features (in particular gender and number) 
different from those of the coordinated elements: for 
example, the noun phrase il ragazzo e la 
ragazza (the boy and the girl) has the features 
"Gender Masculine, Ntnnber Plural", in part different 
from those of the noun phrases that compose it. This 
modification is necessary for running control of 
agreement (as, tor example, between subject and verb). 
Finally, it is necessary to modify the unification 
mechanism so as to permit manipulation of sets of 
elements (as it occurs in coordination): such 
modifications allow correct management of the 
features of sets (as illustrated in the preceding 
paragraph) and must keep track of the semantic 
representation with which to label the sets. 
An example of coordination of complete 
constituents is now considered, to illustrate what 
happens inside the chart: 
Giotto e Orcagna dipinsero un alfresco a 
Padova? 
\[Did Giotto andOrcagna paint a fresco in 
Padova .6\] 
Here coordination concerns the two noun phrases 
Giotto and Oreagna; obviously, the verb is 
conjugated in the third person plural because it agrees 
with the two coordinated noun phrases that must 
therefore have the features "Gender Masculine, Num~r 
Plural" (confirming the necessity of the change 
previously presented on the features of tile sets formed 
because of coordination). 
3.1. Coordination of constituents with 
gaps 
Our approach to the problem of constituents 
containing gaps consists of introducing metarules 
associated with some configurations of the rules. The 
memrules allow an active edge to be inactivated under 
conditions for which this normally is not permitted 
(for example, when the head of a constituent has not 
yet been found). These metarules must be applicable 
only to active edges contiguous with a conjunction 
type inactive edge (thereby limiting the growth of 
inactive edges introduced by metarules). Introduction 
of metarules carries out only a part of the work 
necessary to treat coordination of constituents 
containing gaps ; the remaining part must be carried 
out during unification of the edges that have 
recognized the two conjuncts. At this point it is 
necessary to fill the gaps, using intormation brought 
4 187 
by the complete constituent. Several proposals have 
been made for carrying out this role (among them \[Sag 
et al., 1984\] and \[Kaplan, 1987\]). For example, 
priority union (proposed in \[Kaplan, 1987\] as a means 
of assigning correct interpretations to constructions 
containing gaps in the framework of Lexical- 
Functional Grammar) which, in Kaplan's original 
formulation, is an operator that transforms a pair of f- 
structures into a new f-structure, so that the values of 
one of the two f-structures (that with priority) are 
conserved and the other f-structure furnishes default 
values, if any. The suitability of this method for 
confronting the phenomenon needs further study, as do 
many aspects of metarules. 
The following sentence will be used as an 
example: 
Giotto dipinse un affresco e Orcagna un 
polittico? 
\[Did Giotto paint a fresco and Orcagna a 
polyptych .9\] 
The parser works normally until an active S edge 
(that covers the sentence fragment Oreagna un 
poZittico) is inserted into the chart to the immediate 
right of the conjunction. Such an edge may be made 
inactive by a metarule that establishes that a type S 
(coordinated) constituent may be accepted even without 
its head. The parser then continues working regularly 
until unification of the edges that recognize the 
conjunction is attempted and an effort is made to fill 
the gap present in the second conjunct using the head 
of the first conjunct. 
In applying metarules it is possible to use 
heuristics that put restrictions on the ordering of the 
constituents contained in the second conjunct. For 
example, it is more likely that the correct 
interpretation is that in which the last constituent 
present (linearly) in the input part of the sentence 
recognized by the right conjunct corresponds to the 
constituent that is found furthest to the right in the 
first conjunct. Another possibility is that of imposing 
that the order of the constituents inside the two 
conjuncts must be parallel; but, in this case, the 
sentence Giotto dipinse un alfresco e un 
polittico Orcagna? tilt. Did Giotto portray a 
fresco and a polyptych Orcagna ?\] would not be 
correctly interpretable. Certainly, sentences such as 
this last are to be considered correct, even if unusual in 
spoken language. On the other hand, these restrictions 
serve to limit the proliferation of interpretations that 
afflicts languages such as Italian that have relatively 
free ordering of the elements inside single 
constituents, 
4. Conclusions 
We have presented a solution for two phenomena of 
ill-formedness (that is, ellipsis and coordination), a 
solution that fits coherently into a chart-based 
approach. 
As for intersentential ellipsis, it has been shown 
that no changes are needed for either the grammar or 
the basic parser: the algorithm requires only a 
resettlement of the chart (that is, the working 
memory) and the introduction of a new selecting 
function. Evidently, this is a great advantage in terms 
of clarity and modularity that is combined with the 
efficiency of the entire approach. 
For coordination it has been shown how changes 
that are brought to the apparatus are modularized so as 
not to fall into the intractability of other approaches. 
Both the algorithms have been implemented as 
enhancements of the WEDNESDAY 2 parser. The parser 
is used in the ALFresco interactive system, a 
multimodal dialogue prototype for the exploration of 
art history. 2 The examples in this paper refer to that 
prototype. Note, however, that the solutions proposed 
for ill-formed input in this paper are generally valid for 
other chart-based approaches. 
2The ALFresco (Automatic Language-Fresco) interactive 
system has been developed in InterLisp and CommonLisp 
on Xerox 1186 and Sun4. 

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