DISCONTINUOUS CONSTITUENTS IN TREES, RULES, AND PARSING 
Harry Bunt, Jan Thesingh and Ko van der Sloot 
Computational Linguistics Unit 
Tilburg University, SLE 
Postbus 90153 
5000 LE TILBURG, The Netherlands 
ABSTRACT 
This paper discusses the consequences 
of allowing discontinuous constituents in 
syntactic representions and 
phrase-structure rules, and the resulting 
complications for a standard parser of 
phrase-structure grammar. 
It is argued, first, that discontinuous 
constituents seem inevitable in a 
phrase-structure grammar which is 
acceptable from a semantic point of view. 
It is shown that tree-like constituent 
structures with discontinuities can be 
given a precise definition which makes 
them just as acceptable for syntactic 
representation as ordinary trees. However, 
the formulation of phrase-structure rules 
that generate such structures entails 
quite intricate problems. The notions .of 
linear precedence and adjacency are 
reexamined, and the concept of "n-place 
adjacency sequence" is introduced. 
Finally , the resulting form of 
phrase-structure grammar, called 
"Discontinuous Phrase-Structure Grammar" 
is shown to be parsable by an algorithm 
for context-free parsing with relatively 
minor adaptations. The paper describes the 
adaptations in the chart parser which was 
implemented as part of the TENDUM dialogue 
system. 
I. Phrase-structure 
discontinuity 
grammar and 
Context-free phrase-structure grammars 
(PSGs) have always been popular in 
computational linguistics and in the 
theory of programming languages because of 
their technical and conceptual simplicity 
and their well-established efficient 
parsability (Shell, 1976; Tomita, 1985). 
In theoretical linguistics, it was 
generally believed until recently that 
natural language competence cannot be 
characterized adequately by a context-free 
grammar, especially in view of agreement 
phenomena and discontinuities (see e.g. 
Postal, 1964). However, in the early 
eighties Gazdar and others revived an 
idea, due to Harman (1963), of 
formulating phrase-structure rules not in 
terms of monadic category symbols, but in 
terms of feature bundles. With this 
richer conception of PSG it is not at all 
obvious whether natural languages can be 
described by context-free grammars (see 
e .g . Pullum, 1984) . Generalized 
Phrase-Structure Grammar (GPSG; Gazdar et 
al., 1985), represents a recent attempt 
to provide a theoretically acceptable 
account of natural-language syntax in the 
form of a phrase-structure grammar. 
Apart from being important in its own 
right, phrase-structure grammar also 
plays an important part in more complex 
grammar formalisms that have been 
developed in linguistics; in classical 
Transformational-Generative Grammar the 
base component was assumed to be a PSG; 
in Lexical-Functional Grammar a PSG is 
supposed to generate c-structures, and in 
Functional Uni f ication Grammar 
context-free rules generate the input 
structures for the unification operation 
(Kay, 1979). 
Phrase-structure grammar has one more 
attractive side, apart from its 
technical/conceptual simplicity and its 
computational efficiency, namely that it 
seems to fit the semantic requirement of 
compositionality very well. The 
compositionality principle is the thesis 
that the meaning of a natural-language 
expression is determined by the 
combination of (a) the meanings of its 
parts; (b) its syntactic structure. This 
entails, for a grammar which associates 
meanings with the expressions of the 
language, the requirement that the 
syntactic rules should characterize the 
internal structure of every expression in 
a "meaningful" way, which allows the 
computation of its meaning. In this way, 
semantic considerations can be used to 
prefer one syntactic analysis to another. 
PSGs area useful tool for the formulation 
of syntactic rules that meet this 
requirement, as phrase-structure rules by 
their very nature provide a recursive 
description of the constituent structure 
203 
(I 
(2 
(3 
(4 
(5 
(6 Leo is harder gegaan dan ooit tevoren 
(= Leo has been going faster than 
ever before) 
(7) Ik hob een auto gekocht met 5 deuren 
(= I have bought a car with 5 doors) 
(8) Ik hoot dat Jan Marie de kinderen de 
hond heeft helpen leren uitlaten 
(= I hear that John has helped Mary 
to teach the kids to walk the dog) 
John talked, of course, about 
politics 
Which children did Anne expect to get 
a present from? 
This was a better movie than I 
expected 
Wake me up at seven thirty 
~i-il one of your cousins come who 
moved to Denmark? 
These examples do not represent a single 
class of linguistic phenomena, and it is 
doubtful whether they should all be 
handled by means of the same techniques. 
(1o) 
Sentence (I), which has been discussed 
extensively in the literature, presents a 
problem for any analysis in terms of 
adjacent constituents, since the 
parenthetical "of course" divides the verb 
phrase "talked about politics" into 
non-adjacent parts. This means that we are 
forc e d to e i the r consider the 
parenthetical as part of the VP, as Ross 
(1973) has suggested, or as a constituent 
at sentence level, as has been suggested 
by Emonds (1976; 1979). In the latter 
case, the sentence is analysed as 
consisting of the embedded sentence "John 
talked", with "of course" and "about 
politics" as specifiers at sentence level. 
McCawley (1982) provides detailed 
arguments showing that both suggestions 
are inadequate (which seems intuitively 
obvious, from a semantic point of view), 
and suggests, instead, the syntactic 
representation (9). 
(9) 
John talked 
This is of course no longer an 
ordinary tree structure, but should that 
be a reason to reject it? McCawley takes 
the view that we should simply not be 
afraid of constituent structures like 
(9). We will return to this suggestion 
below. 
Example (2) represents a different 
c l a s s o f phenomena, which are 
conveniently thought of in terms of 
movements of parts of phrases. In this 
example, the NP "which children" can be 
thought of as having moved out of the PP 
"from which children", of which only the 
preposition has been left behind. In 
order to deal with such cases, in GPSG a 
special type of syntactic categories have 
be e n i n t rod uced, called "slash 
categories" For instance, the category 
PP/NP is assigned to a prepositional 
phrase which "misses" an NP. In the 
present example, this category would be 
assigned to "from". The assumption that 
an NP is missing propagates to higher 
nodes in the syntactic tree which the 
phrase-structure rules construct for the 
sentence, until it is acknowledged at the 
top level. Diagram (10) illustrates this. 
S 
of complex expressions down to their 
smallest meaningful parts. However, PSG 
has one property that limits its 
applicability in describing constituent 
structure in natural language, namely that 
phrase-structure rules assume the 
constituents of an expression to 
correspond to adjacent substrings. In 
natural language it happens quite often, 
however, that the constituents of an 
expression are not adjacent. The English 
and Dutch example sentences ( I )-(8) 
illustrate this. In (2)-(7) we see 
examples of major phrases, made up of 
parts that are not adjacent; so-called 
discontinuous constituents. We have 
discontinuous noun phrases in (5) and (7), 
a discontinuous adjective phrase in (3), 
discontinuous verb phrases in (1) and (4), 
and a discontinuous adverb phrase in (6). 
NP\[+WH\] AUX NP V NP PREP NP/NP 
which children did Ann et ifts from 0 
If we want to do justice to the 
intuition that the sentence at surface 
level contains a constituent made up by 
"which children" and "from", we would 
have to draw a constituent diagram like 
(11), which, like (9), is no longer an 
ordinary tree structure. 
204 
(11) S 
which children did nn get ifts fr m 
The technique of using phrases that 
miss some constituent cannot be used for 
at least some of the examples (3)-(8), 
such as (5) and (7). In both these 
sentences the discontinuous NP contains a 
full-fledged NP, which cannot sensibly be 
said to "miss" the relative clause or 
prepositional phrase that occurs later in 
the sentence. 
Whatever techniques may be invented to 
deal with such cases, it seems obvious 
that a grammar which recognizes and 
describes discontinuities in natural 
language sentences is a more suitable 
basis for semantic interpretation than one 
that squeezes constituent structures in a 
form in which they cannot be represented. 
It therefore seems worth investigating 
the viability of tree-like structures with 
discontinuities, like (9) and (11). 
2. Trees with discontinuities 
If we want to represent the situation 
that a phrase P has constituents A and C, 
while there is an intervening phrase B, we 
must allow the node corresponding to P to 
dominate the A and C nodes without 
dominating the B, even though this node is 
located between the A and C nodes: 
(12) P 
A B C 
One consequence of allowing such 
discontinuities is that our structures get 
crossing branches, if we still want all 
nodes to be connected to the top node; 
(10) and (11) illustrate this. In what 
respects exactly do these structures 
differ from ordinary trees? McCawley 
(1982) has tried to answer this question, 
suggesting a formal definition for trees 
with discontinuities by amending the 
definition of a tree. 
A tree is often defined as a set of 
elements, called "nodes", on which two 
relations are defined, immediate dominance 
(D) and linear precedence (<), which are 
required to have certain properties to 
the effect that a tree has exactly one 
root node, which dominates every other 
node (immediately or indirectly); that 
every node in a tree has exactly one 
"mother" node, etc. (see e.g. Wall, 
1972). 
Given the relations of immediate 
dominance and linear precedence, 
dominance is defined as the reflexive and 
transitive closure D' of D, and adjacency 
as linear precedence without intervening 
nodes. 
A node in a tree is called terminal if 
it does not dominate any other node; the 
terminal nodes in a tree are totally 
ordered by the < relation. For 
nonterminal nodes the precedence relation 
satisfies the requirement that x < y if 
and only if every node dominated by x 
precedes every node dominated by y. 
Formally: 
(13) for any two nodes x and y in the 
node set of a tree, x < y if and 
only if for all nodes u and v, if x 
dominates u and y dominates v, then 
u < v. 
Part of the definition of a tree is 
also the stipulation that any two nodes 
either dominate or precede one another: 
(14) for any two nodes x and y in the 
node set of a tree, either x D' y, 
or y D' x, or x < y, or y < x. 
This stipulation has the effect of 
excluding discontinuities in a tree, for 
suppose a node x would dominate nodes y 
and z without having a dominance relation 
with node w, where y < w < z. By (14), 
either x < w or w < x. But x dominates a 
node to the right of w, so by (13) x does 
not precede w; and w is to the right of a 
node dominated by x, so w does not 
precede x either. 
McCawley's definition of trees with 
discontinuities comes down to dropping 
the condition that any two nodes should 
either dominate one another or have a 
left-right relation. Instead, he proposes 
the weaker condition that a node has no 
precedence relation to any node that it 
dominates: 
(15) for any two nodes x and y in the 
node set of a tree, if x D' y then 
neither x < y nor y < x. 
We shall call a node u, situated 
between daughters of a node x without 
being dominated by x, internal context of 
X. 
205 
McCawley's definition of trees with 
discontinuities is inaccurate in several 
respects; however, his general idea is 
certainly correct : trees with 
discontinuities can be defined essentially 
by relaxing condition (14) in the 
definition of trees. 
However, this is only the beginning of 
what needs to be done. The next question 
is how discontinuous trees can be produced 
by phrase-structure rules. This question, 
which is not addressed by McCawley, is far 
from trivial and turns out to have 
interesting consequences for the notion of 
adjacency in discontinuous tre 
es. 
3. Adjacency in phrase-structure rules for 
discontinuous constituents 
A phrase-structure rule rewrites a 
constituent into a sequence of pairwise 
adjacent constituents. This means that we 
need a notion of adjacency in 
discontinuous trees, for which the obvious 
definition, given the < relation, would 
seem to be: 
(16) two nodes x and y in the node set of 
a tree are adjacent if and only if x 
< y and there is no z such that x < 
z < y. 
We shall write "x + y" to indicate that 
x and y are adjacent (or "neighbours"). A 
moment's reflection shows that this notion 
of adjacency unfortunately does not help 
us in formulating rules that could do 
a n y thi n g w i t h in t e rnal context 
constituents. The following example 
illustrates this. Suppose we want to 
generate the discontinuous tree structure: 
(17) VP /k 
Wake your friend up 
To generate the top node, we need a 
rule combining the V and the NP, like: 
(18) VP --> V + NP 
Since the V dominates nodes at either 
side of the NP, however, there is no 
left-right order between the NP and V 
nodes, leave alone a neighbour relation. 
For the same reason there would be no 
left-right relation between overlapping 
discontinuous constituents, as in (19). 
These deficiencies can be remedied by 
replacing clause (14) in the definition of 
a tree by the more general clause (20). 
(19) VP 
g NP 
Wake the man up who lives next door. 
(20) A nonterminal node x in a tree is 
to the left of a node y in the tree 
if and only if x's leftmost 
daughter is left of y's leftmost 
daughter. 
(We refrain here from a formal 
definition of "leftmost daughter" node, 
which is intuitively obvious.) 
Note that (20) is indeed a 
generalization of the usual notion of 
precedence in trees, which could also be 
defined by (20). The recursion in (20) 
comes to an end since the terminal nodes 
are required to be totally ordered. 
It should also be noted that (20) is 
not consistent with clause (14): by (2@), 
we do get a precedence relation between a 
node and its daughter nodes (except the 
leftmost one) and internal context nodes. 
This is not quite unreasonable. In (21), 
for example, we do want that X < Y, and 
(21) X 
A B Y C 
since Y < C, that X < C, but not that X < 
B. We therefore adapt clause (14) to the 
effect that a mother node only precedes 
internal context nodes and daughter nodes 
which have internal context nodes to 
their left. Formally: 
(22) For any nodes x and z in the node 
set N of a tree, if x D z and there 
are no nodes u,v in N such that x D 
u, not x D v, and u < v < z, then 
neither x < z nor z < x. 
With the modifications (16) and (22), 
we have a consistent definition of 
"discontinuous trees" which allows us to 
write phrase-structure rules containing 
discontinuous constituents as follows: 
(23) X --> A + B + \[Y\] + C 
where the square brackets indicate that 
the NP is not dominated by the X node, 
but is only internal context. The "+" 
symbol represents the notion of 
adjacency, defined as before but now on 
the basis of te revised precedence 
relation "<": 
206 
(24) Two nodes x and y in a tree are 
adjacent if and only if x < y and 
there is no node z in the tree such 
that x < z < y. 
Upon closer inspection, the neighbour 
relation defined in this way is 
unsatisfactory, however, as the following 
example illustrates. 
Suppose we want to generate the 
following (part of a) tree structure: 
(25) S 
A B C D E 
To generate the S node, we would like 
to write a phrase-structure rule that 
rewrites S into its constituents, like 
(26): 
(26) S --> P + Q + E 
However, this rule would be of no help 
here, since P, Q and E do not form a 
sequence of adjacency pairs, as Q and E 
are not adjacent according to our 
definition. Rather, the correct rule for 
generating (25) would be (27): 
(27) S --> P + Q + \[C\] + \[D\] + E 
This is ugly, and even uglier rules are 
required in more complex trees with 
discontinuities at different levels. 
Moreover, there seems to be something 
fundamentally wrong, since the C and D 
nodes are on the one hand internal context 
for the S node, according to rule (27), 
while on the other hand they are also 
dominated by S. That is, these nodes are 
both "real" constituents of S and internal 
context of S. 
To remedy this, we introduce a new 
concept of adjacency sequence, which 
generalizes the traditional notion of a 
sequence of adjacency pairs. The 
definition goes as follows: 
(28) A sequence (a, b, ..., n) is an 
(n-place) adjacency sequence if and 
only if: 
(i) every pair (i,j) in the 
sequence is either an adjacency 
pair or is connected by a 
sequence of adjacency pairs of 
which all members are a 
constituent of some element in 
the subsequence (a, b,..., i); 
(ii) the elements in the sequenc~ do 
not share any constituents. .) 
For example, in the structure (25) the 
triple (P, Q, E) is an adjacency sequence 
since (P, Q) is an adjacency pair and Q 
and E are connected by the sequence of 
adjacency pairs Q-C-D-E, with C and D 
constituents of P and Q, respectively. 
Another example of an adjacency sequence 
in (25) is the triple (P, B, D). The 
triple (P, B, C), on the other hand, is 
not an adjacency sequence, since P and C 
share the constituent C. 
The use of this notion of adjacency 
sequence is now that the sequence of 
constituents, into which a nonterminal is 
rewritten by a phrase-structure rule, 
forms an adjacency sequence in this 
sense. The phrase-structure grammar 
consisting of rules of this kind we call 
Discontinuous Phrase-Structure Grammar or 
DPSG. ~j 
It may be worth emphasizing that this 
notion of phrase-structure rule is a 
generalization of the usual notion, since 
an adjacency sequence as defined by (28) 
subsumes the usual notion of sequence of 
adjacency pairs. We have also seen that 
trees with discontinuities are a 
generalization of the traditional tree 
concept. Therefore, phrase-structure 
rules of the familiar sort coincide with 
DPSG rules without discontinuous 
constituents, and they produce the 
familiar sort of trees without 
discontinuities . In other words, 
DPSG-rules can simply be added to a 
classical PSG (including GPSG ,-~'--~ith the 
result that the grammar generates trees 
with discontinuities for sentences with 
discontinuous constituents, while doing 
everything else as before. 
4. DPSG and parsing 
From a parser's point of view, a 
definition of adjacency as given in (24) 
is not sufficient, since it only applies 
to nodes within the context of a tree. A 
parser has the job of constructing such a 
set from a collection of substructures 
that may or may not fit together to form 
one or more trees for the entire 
sentence. Whether a number of subtrees 
fit together is not so easy if the end 
product may be a tree with 
discontinuities, since the adjacency 
relation defined by (20) and (24) allows 
neighbouring nodes to have common 
daughters. This is clearly undesirable. 
We therefore modify the definition (20) 
of adjacency by adding the requirement 
that two substructures (or their top 
nodes) can only have a precedence 
relation if they do not share any 
constituents: 
207 
(29) A node x in a collection of 
substructures for a potential tree 
(possibly with discontinuities) is 
to the left of a node y in the same 
qollection if and only if x's 
leftmost daughter is left of y's 
leftmost daughter, and there is no 
node z which is shared by x and y. 
If the nodes x and y in this definition 
belong to the same tree, the additional 
requirement that x and y do not share any 
constituent is automatically satisfied, 
due to the "single mother" condition. 
A parser for DPSG meets certain 
complications which do not arise in 
context-free parsing. To see these 
complications, we consider what would 
happen when a chart parser for 
context-free parsing (see Winograd, 1983) 
is applied to DPSG. 
Context-free chart parsing is a matter 
of fitting adjoining pieces together in a 
chart. For example, consider the grammar: 
(30) S --> VP NP 
NP --> DET N 
VP --> V 
For the input "V DET N", a chart parser 
begins by initializing the chart as 
follows: 
(31) 
1 2 3 4 
Given the arc V(1,2) in the chart, we look 
up all those rules which have a "free" V 
as the first constituent. These rules are 
placed in a separate list, the "active- 
rule list". We "bind" the V's in these 
rules to the V(1,2) arc, i.e. we establish 
links between them. When all constituents 
in a rule are bound, the rule is applied. 
In this case, the VP(I,2) will be built. 
This procedure is repeated for the new VP 
node. When nothing more can be done, we 
move on in the chart. The final result in 
this example is the chart (32). 
(32) 
VP NP 
I 2 3 4 
When we use DPSG rules and follow the same 
procedure, we run into difficulties. 
Consider the example grammar (33). 
(33) S --> VP + NP 
NP --> DET + N 
VP --> V + \[NP\] + PART 
For the input "V DET N PART" the first 
constituent that can be built is NP(2,4); 
the second is VP(I,5). The VP will 
activate the S rule, but this rule will 
not be applied since the NP does not have 
a binding. And even if it did, the rule 
would not be applicable as the VP(I,5) 
and the NP(2,4) are not adjoining in the 
traditional sense. 
In the next section we describe the 
provisions, added to a standard chart 
parser in order to deal with these 
difficulties. 
5. A modified chart parser for DPSG 
5.1 Finding all applicable rules 
To make sure that the parser finds all 
applicable rules of a DPSG, the following 
addition was made to the parsing 
algorithm. 
If a rule with internal context is 
applied, we first follow the standard 
procedure; subsequently we go through all 
those rules that appear on the active- 
rule list as the result of applying the 
standard procedure, giving bindings to 
those free constituents that correspond 
in category to the context-element(s) in 
the rule that was applied. 
In the case of (33), this means that 
just before application of the VP rule 
(after the PART has been bound), we have 
the active-rule list (34). (Underlining 
indicates that a constituent is bound). 
(34) VP --> V ÷ \[NP\] + PART 
VP --> \[ + \[NP\] + PART 
VP --> ~+ \[NT\] + PART 
w 
We now apply the rule building the VP. 
The standard procedure will add one rule 
to this list, namely S --> VP + NP. The 
VP is given a binding, so we obtain the 
following active-rule list: 
(35) S --> VP + NP 
VP --> 9--+ \[NP\] + PART 
VP --> \[ ÷ \[NP\] + PART 
VP --> ~ + \[N~\] + PART 
Since the VP-building rule contained 
an internal context element, the 
additional procedure mentioned above is 
now applied; a binding is given to the NP 
in (a copy of) the S rule. The S arc is 
now built in the chart, which does not 
cause any new rules to be added to the 
active-rule list. There are no free S's 
208 
in the old active rule list either, which 
should be given a binding. So, we can look 
for other rules containing a free NP. 
There is one such rule, the second in 
(35), but this one will be neglected 
because it was already present in the rule 
list before; see (34). Note that it is 
essential that this rule is neglected, as 
there is already a version of the VP-rule 
on the active-rule list containing an NP 
with the s a me binding as the 
context-element. 
It may also be noted that we have 
combined constituents in this example that 
are not adjoining in the traditional sense 
(i.e., in the sense of successive vertex 
numbers). In particular, we have applied 
the rule S --> VP(I,5) + NP(2,4). In a 
case like this, where the vertex numbers 
indicate that the constituents in a rule 
are overlapping, we must test whether 
these constituents form an adjacency 
sequence. This test is described below. 
5.2 The adjacency sequence test 
In order to make sure that only 
consituents are combined that form an 
adjacency sequence, the parser keeps track 
of daughter nodes and internal context in 
a so-called "construction list", which is 
added to each arc in the chart; internal 
context nodes are marked as such in these 
lists. Whether two (or more) nodes share a 
constituent, in the sense of common 
domination, is easily detected with the 
help of these lists. 
By organizing these lists in a 
particular way, moreover, they can also be 
used to determine whether a sequence of 
constituents is an adjacency sequence in 
the sense of definition (28). This is 
achieved by ordering the elements in 
construction lists in such a way that an 
element is always either dominated by its 
predecessor in the list, or is internal 
context of it, or is a right neighbour of 
it. For instance, in the above example 
(25), P and Q have the construction lists 
(36): 
(36) P:(A, \[B\], C) 
Q:(B, \[C\], D). 
The rule S --> P + Q + E is now 
applicable, since the construction list 
for S would be the result of merging P's 
and Q's lists with that of E, which is 
simply E:(), with the result S:(A, B, C, 
D, E). From this list, it can be concluded 
that the triple (P, Q, E) is an adjacency 
sequence, since (P, Q) is an adjacency 
pair (since P's leftmost daughter, i.e. A, 
is adjacent to Q's leftmost daughter, i.e. 
B, as can be seen also in the construction 
lists), and Q and E are separated in S's 
construction list by the adjacency pair 
(C, D), whose elemehts are both daughters 
of P. 
An example where the adjacency 
sequence test would give a negative 
result, is where the rule Y --> X + B + E 
is considered for a constituent X with 
construction list X:(A, \[B\], \[C\], D). The 
rule is not applicable, since the triple 
(X, B, E) would not form an adjacency 
sequence according to the construction 
list that the node Y would get, namely: 
(37) Y:(A, B, \[C\], D, E). 
The constituents B and E are separated 
in (37) by the sequence (\[C\], D), where C 
is marked as internal context; therefore, 
C is not dominated by either X or B, and 
hence the test correctly fails. 
The currently implemented version of 
the DPSG parser is in fact based on a 
more restricted notion of adjacency 
sequence, where two constituents are 
viewed as sharing a constituent z not 
only if they both dominate z, but also if 
one of them dominates z and the other has 
an internal context node that dominates z 
(see note I). This means that structures 
like (38) are not generated, since P and 
T would share node B, and T and R would 
share node C. 
(38) T 
A B C D E 
Note that a structure like (38) would 
be an ill-formed tree, since the nodes B 
and C violate the single-mother 
condition, and the nodes Q and R, 
moreover, are not connected to the root 
node. 
To deal with this more restricted 
notion of adjacency sequence, the 
administration in the construction lists 
is actually slightly more complicated 
than described above. 
6. Conclusions 
Our findings concerning the use of 
discontinuous constituents in syntactic 
representations, phrase-structure rule, 
and parsers may be summarized as follows. 
I. Tr e e- 1 i ke s t r uctures with 
discontinuities can be given a precise 
definition, which makes them formally 
as acceptable for use in syntactic 
209 
representation as the familiar ord~ 
tree structures. 
2. Discontinuous constituents can be 
allowed in phrase-structure rules 
generating trees with discontinuities, 
provided we give a suitable 
generalization to the notion of 
adjacency. 
3. Trees with discontinuities are 
generalizations of ordinary tree 
structures, and phrase-structure rules 
with discontinuous constituents are 
generalizations of ordinary 
phrase-structure rules. Both concepts 
can be added to ordinary 
phrase-structure grammars, including 
GPSG, with the effect that such 
grammars generate trees with 
discontinuities for sentences with 
discontinuous constituents, while 
everything else remains the same. 
4. Phrase-structure rules with 
discontinuities can be handled by a 
chart parser for context-free grammar 
by making two additions in the 
administration; one in the active-rule 
list for rules containing a 
discontinuous element to make sure that 
no parse is overlooked, and one in the 
arcs in the chart to check the 
generalized adjacency relation. 
NOTES 
I) In this paper, sharing a constituent 
has been taken simply as common domination 
of that constituent. An interesting issue 
is whether we should take sharing a 
constituent to include the following 
situation. A node x dominates a 
constituent z, while another node y is 
related to z in such a way that z is 
dominated by a node w which is internal 
context for y. (And still more complex 
definitions of constituent sharing are 
conceivable within the framework of DPSG.) 
Decisions on this point turn out to have 
far-reaching consequences for the 
generative capacity of DPSG. With the 
simple notion of sharing used in this 
paper, it is easily proved that DPSG is 
more powerful than context-free PSG, while 
further restrictions on the precedence 
relation in terms of constituent sharing 
may have the effect of making DPSG weakly 
equivalent to context-free grammar. 
2) For applications of DPSG and a 
predecessor, which was called "augmented 
phrase-construction grammar" in 
syntactic/semantic analysis and automatic 
generation of sentences, the reader is 
referred to Bunt (1985; 1987). 
ACKNOWLEDGEMENTS 
I would like to thank Masaru Tomita 
for stimulating discussions about phrase- 
structure grammar and parsing in general, 
and DPSG in particular. 
REFERENCES 
Bunt, H.C. (1985) Mass terms and 
model-theoretic semantics. Cambridge 
University Press, Cambridge, England. 
Bunt, H.C. (1987) Utterance generation 
from semantic representation augmented 
with pragmatic information. In G. Kempen 
(ed.) Natural language generation. 
Kluwer/Nijhoff, The Hague. 
Bunt, H.C., Beun, R.J., Dols, F.J.H., 
Linden, J.A. van der, & Schwartzenberg, 
G.O. thoe (1985) The TENDUM dialogue 
system and its theoretical basis. IPO 
Annual Progress Report 19, 105-113. 
Emonds, J.E. (1976) A transformational 
approach to English syntax. Academic 
Press, New York. 
Emonds, J.E. (1979) Appositive 
relatives have no properties. Linguistics 
Inquiry 10, 211-243. 
Gazdar, G., Klein. E., Pullum, G.K. & 
Sag, I.A. (1985) Generalized 
Phrase-Structure Grammar. Harvard 
University Press, Cambridge, MA. 
Harman, G. (1963) Generative grammars 
without transformaton rules: a defense of 
phrase structure. Language 39, 597-626. 
Kay, M. (1979) Functional grammar. In 
Proc. -Fifth An~ual' ~eeting of the 
Berkeley Linguistics Society. Berkeley, 
CA, 142-158. ' 
McCagl~- J.D. (1982) Parentheticals 
and Discontinuous Constituent Structure. 
Linguistic Inquiry 13 (I), 91-106 
Postal, P.M (1964) Constituent 
structure. Supplement to International 
Journal of American Linguistics 30. 
Pullum, G.K. (1984) On two recent 
attempts to show that English is not a 
CFL. Computational Linguistics 10 (3/4), 
182-187. 
Ross, J.R. (1973) Slifting. In M. 
Gross, M. Halle & M.P. Sch~tzenberger 
(eds.) The formal analysis of natural 
language. Mouton, The Hague. 
Sheil, B. (1976) Observations on 
context-free parsing. Statistical Methods 
in Linguistics, 71-109. 
Tomita, M. (1986) Efficient parsing 
for natural language. Kluwer Academic 
Publishers, Boston/Dordrecht. 
Wall, R.E. (1972) Introduction to 
Mathematical Linguistics. 
Prentice-Hall, Englewood Cliffs. 
Winograd, T. (1983) Language as a 
cognitive process. Addison-Wesley, 
Reading, MA. 
210 
