DISJUNCTION WITHOUT TEARS 
Allan Ramsay 
Department of Computer Science 
University College Dublin 
Belfield, DUBLIN 4, 
Ireland 
It is now common practice to use structured sets of features to describe syntactic structures, and to compare 
such structured sets by some form of unification. It is extremely tempting to try to encode disjunctive 
information within this framework; unfortunately, general unification of disjunctive structures is NP- 
complete, which is not a desirable property for the basic operation involved in comparing descriptions. We 
note that certain kinds of disjunctfve specifications can be converted to conjunctive ones. This enables us to 
describe a restricted set of disjunctive phenomena without incurring the costs associated with general 
disjunctive unification. 
1 UNIFICATION AND SYNTACTIC 
DESCRIPTION 
We assume that the use of lattices and directed acyclic 
graphs (DAGs) for describing properties of syntactic struc- 
tures, and of unification for combining such descriptions, is 
too well known to require justification at this point. A wide 
variety of notations have been used in this context-- 
PROLOG terms, PATR-II specifications, FUG functional 
descriptors, GPSG category specifications, and so on 
(Pereira and Warren 1980; Shieber 1986; Kay 1985; Gaz- 
dar et al. 1985). The discussion below is couched in a 
FUG-like notation for concreteness, but the argument is 
equally applicable to any of the other standard formalisms. 
(except perhaps GPSG). 
We can use our notation for characterizing objects in 
terms of their properties. We will generally be talking 
about linguistic objects such as words or phrases, though 
there is nothing that restricts this kind of description to 
such objects. We start by considering the word providing. 
We know various things about this word, including the fact 
that it is a present participle. We can represent this specific 
piece of information with the descriptor shown in Figure 1. 
We have included some negative information in this descrip- 
tion, namely the fact the word in question is not tensed, is 
not an infinitive, and is not a past participle or a passive one. 
This information is generally omitted from FUG specifica- 
tions, since it seems to be redundant. In fact it is not 
redundant unless we have specified elsewhere that being a 
participle, being tensed, and being an infinitive are mutu- 
ally exclusive, and similarly for present, past, and passive 
participles. We will continue to include this kind of informa- 
tion locally within specifications, rather than appealing to 
some externally specified set of constraints. In subsequent 
descriptors we will generally write --nTENSED for 
TENSED = _1_, though we will continue to spell out 
positive specifications such as PRESENT = T in full. 
2 Two USES OF DISJUNCTION 
The kind of representation in Figure 1 is appropriate when 
some specific piece of information about some item is 
known--in Figure 1, for instance, the fact that the word in 
question is a present participle. It often happens, however, 
that we know that some item can be described in several 
ways, but that we are not sure which is correct in the 
present circumstances. Consider for instance the word 
provided. This might be a past tense form, or a past 
participle, or a passive participle. There is nothing about 
the word itself that can help us decide which it is, though in 
any actual context only one of these descriptions will be 
appropriate. 
(1) He provided us with everything we needed. 
(2) He has provided us with everything we needed. 
(3) Everything we needed has been provided. 
We could produce three descriptions of the kind in Figure 
1, one for each case. If we did this, however, we would find 
ourselves repeating all sorts of information--the fact that 
it's a verb, for instance, plus whatever we know about its 
subcategorization frame, and so on. It is therefore tempting 
to try to adapt our notation so that it allows disjunctive 
specifications for feature values, as shown in Figure 2. 
Figure 2 represents a description of an item that is either a 
past tense verb or a past or passive participle, with the curly 
bracket {used to indicate a range of options. This kind of 
Computational Linguistics Volume 16, Number 3, September 1990 171 
Allan Ramsay Disjunction without Tears 
SYNTAX = 
CAT = VERB 
MAJOR = \[BAR = 0 
I fPRESENT=T 
MINOR= HEAD = FORM = \[PARTICIPLE= \[PAST=.k 
| \[.PASSIVE = l 
\[.INFINITIVE = ± 
Figure I Present Participle, e.g. providing• 
disjunctive specification is widespread in unification gram- 
mer--the curly bracket, for instance, is standard notation 
in FUG, and most other notations provide some way of 
talking about disjunction. Kasper and Rounds (1986), 
among others, have taken up the question of exactly what 
such notations mean. We are more interested here in 
investigating the circumstances under which they are really 
necessary, and in trying to remove them wherever we can. 
Much the same sort of issue arises when we consider 
syntactic rules, particularly when we consider rules repre- 
senting information about subcategorization frames. Con- 
sider, for instance, the interpretation of the verb be as an 
auxiliary. Be, as an auxiliary, can be combined with either 
a VP whose main verb is a present participle or one whose 
main verb is a passive participle. We might try to represent 
this information with the rule shown in Figure 3. Figures 2 
and 3 are very perspicuous. Figure 2 describes a word that 
is a past tense verb, a past participle, or a passive participle. 
Figure 3 describes a grammatical constraint, namely that 
be may be followed by a VP whose main verb is either a 
present participle or a passive one. The placeholder ?H is 
used to indicate that the form of the VP that results from 
combining an instance of be with a suitable complement 
has the same HEAD features as the instance of be. Unfor- 
tunately, the introduction of disjunctions into our descrip- 
tions has drastic effects on the computational properties of 
unification, particularly when it is combined with the use of 
placeholders or other ways of specifying reentrance. To see 
this, suppose we want to see whether some VP whose main 
verb has the properties ascribed to provided fits the con- 
straints imposed by be (in other words, we are trying to 
SYNTAX = 
CAT = VERB 
'MAJOR = \[.BAR = 0 
MINOR= HEAD= FORM=, 
TENSED { ~PRESENT 
= \[PAST = T 
~PARTICIPLE 
• ~INFINITIV E 
• ~TENSED \[ 
~PRESENT 
PARTICIPLE = \[PAST = T 
I 
k~PASSIVE 
• ~INFINITIVE 
\[-TENSED \[-PRESENT 
l-PAST I PARTICIPLE LPASSIVE = T 
k ~INFIN1TIVE 
Figure 2 Underdetermined Verb 
Form, e.g. provided. 
\[CAT = VERB 
SYNTAX =: MAJOR = \[BAR = 2 
\].MINOR = \[HEAD = ?H 
==~ I =\[CAT=VERB 
SYNTAX== MAJOR \[BAR=O 
\[.MINOR = IHEAD = ?H 
CAT = VERB 
'MAJOR = \[BAR = 2 " 
SYNTAX = 
MINOR = FIEAD = PORM = 
-TENSED T 
I PARTICIPLE= \[PRESENT= \[ ~INFIN ITIV E 
•-TENSED ~-PRESENT 
PARTICIPLE = \[~PAST 
' \[.PASSIVE = T 
•-INFINITIVE 
Figure 3 Underdetermined 
Rule--Subcategorization Frame for be. 
parse (3)). At some point we will have to compare 
--nPRESENT 
TENSED =\[PAST = r 
7PAR TICIPLE 
~INFINITIVE 
-'7 TENSED "TPRESENT 
PARTICIPLE = PAST = T 
7PASSIVE 
\[7INFINITIVE 
7TENSED 
TPRESENT 
PARTICIPLE = 17PAST 
\[PASSIVE =- T 
7INFINITIVE 
with 
I -7 TENSED PARTICIPLE = ~INFINITIVE 
"--7 TENSED 
PARTICIPLE = 
7INFINITIVE 
"PRESENT = T 
7PAST 
7PASSIVE 
TPRESENT 
7PAS T 
PASSIVE ~ T 
We will have to try various possibilities--is 
--nPRESENT 
"TENSED = \[PAST = T 
7PARTICIPLE 
~INFINITIVE 
172 Computational Linguistics Volume 16, Number 3, September 1990 
Allan Ramsay Disjunction without Tears 
the same as 
"~TENSED 
PARTICIPLE = 
~INFINITIVE 
"PRESENT = T 
~PAST 
-1PASSIVE 
and so on. Eventually we will compare the part of the 
description of solved that says it might be a passive partici- 
ple with the part of the rule that says that a VP whose main 
verb is a passive participle is acceptable here. At this point 
we will realize that the given text fits the rule, but only after 
trying out numerous options that led nowhere. 
Worse than this, there may be several locally compatible 
sets of options, only one of which may lead to a globally 
coherent description of the complete text being examined. 
If this is a possibility then the process of unifying two 
structures turns out to be NP-complete, a most undesirable 
consequence of our decision to allow disjunctive feature 
descriptions. 
3 EXTRA CONSTRAINTS 
If we look again at the descriptions in Figures 2 and 3 we 
see that we know rather more about the FORM part of 
these descriptions than is explicitly stated. In particular, we 
know that the FORM of any verb whatsoever is drawn from 
the range of options shown in Figure 4. Given this extra 
information, we see that a disjunctive description such as 
the one we have been using for provided can be replaced by 
a conjunctive one containing nothing but negative informa- 
tion. The descriptions of the FORM of the lexical item 
provided and the complement of be, for instance, can be 
replaced by the following purely conjunctive descriptions: 
'TENSED = \[-~PRESENT 
PARTICIPLE = \[-1PRESENT 
and 
~INFINITIVE 
TENSED \[-aPRESENT 
\[ =\['-nPAST 
PARTICIPLE = -nPAS T 
\[-nINFINITIVE 
The equivalence depends on the fact that in any specific 
case FORM has exactly one of the values given in Figure 4. 
TENSED = \[PRESENT = T PARTICIPLE = \[PRESENT = T 
TENSED = \[PAST = T PARTICIPLE = \[PAST = T 
INFINITIVE = T PARTICIPLE = \[PASSIVE = T 
Figure 4 Possible Values for FORM for Verbs. 
If we know what values it doesn't have, we can infer the 
range that the value it does have must be drawn from. 
When we attempt to unify these two specifications, we find 
that they lead to the following more precise description: 
--aPRESENT 
'TENSED = \[~PAST 
-'aPRESENT 
PARTICIPLE = -'aPAS T 
~INFINITIVE 
The only way for this to be compatible with the general 
constraint that the value of FORM must be drawn from the 
values in Figure 4 is if it is in fact a passive participle. We 
have obtained the required effect without complicating our 
unification algorithm, simply by making use of the extra 
information that the value in question must be drawn from 
a known finite range. Note that we do not need to refer 
explicitly to the information in Figure 4 when we want to 
know whether two specifications for FORM are compati- 
ble. Rather we have used this information to construct our 
specifications, which can be compared directly using ordi- 
nary unification. 
Many of the situations that seem to call for disjunctive 
descriptions can be dealt with this way. The NP the sheep 
could be either third person singular or third person plural? 
Then describe it as not first person singular or first person 
plural or second person singular or second person plural. 
The pronoun he is nominative, whereas it may be either 
nominative or accusative? Then describe he as not accusa- 
tive, and say nothing about it. When we can replace 
disjunctive descriptions by ones that embody a conjunction 
of negations, we can save a considerable amount of work, 
since our unification algorithm no longer needs to plod 
through a series of possible analyses, keeping track of the 
options that have been tried and possibly backtracking 
when some analysis that looked plausible leads to a dead 
end. We cannot hope to eliminate disjunction from our 
grammar entirely, since if we could then parsing would 
become a trivial deterministic task, which it does not look 
like becoming. We can, however, eliminate it in a lot of 
places where it looks as though it would be useful; which 
doesn't make parsing a trivial task, but it does mean that 
we can avoid doing more work than we really need. 
4 LIMITATIONS 
The example discussed above shows how we can replace 
disjunctive descriptions by conjunctive ones in two specific 
cases, namely in the description of the FORMs of lexical 
items and VP complements. We further suggested that this 
technique might be extendable to other uses of disjunctive 
specifications, such as the agreement properties of the NP 
the sheep or the case marking of the pronoun it. We have 
not, however, banished disjunction from the grammar of 
Computational Linguistics Volume 16, Number 3, September 1990 173 
Allan Ramsay Disjunction without Tears 
English. We could hardly expect to, given that in some 
versions of unification grammar, e.g. FUG, the entire 
grammar is specified by a single disjunctive descriptor, 
which is required to unify with the description of any legal 
sentence. Just what are the limits of our technique? 
The following two restrictions seem crucial. (i) The 
elements of the disjunction must pick out points in some 
finite partition of the space of possibilities, preferably a 
small finite partition. (ii) The disjunction must not contain 
any placeholders (reentrance conditions). Consider for in- 
stance the word changes. For the sake of argument we will 
assume that this item has exactly two interpretations, as a 
plural noun and as a third person singular verb. We could 
represent the fact that it can be seen either as a noun or as a 
verb as follows: 
SYNTAX = MAJOR = 
• MINOR 
"~ADJECTIVE 
CAT= ~ADVERB 
~PREPOSITION 
LBAR 0 
This indicates that we can specify the major category of 
changes in terms of what it is not, though it does seem that 
this may be too cumbersome to be worthwhile. The real 
problem, however, is that the MINOR features will be 
expected to specify some value for AGR; but the value of 
AGR for this word depends on whether it is in fact a noun 
or a verb---it is plural as a noun, but singular as a verb. We 
simply cannot deal with this within our framework, and if 
we try to adapt the framework to accommodate it, then all 
the computational complexity will return. 
This is particularly significant when we consider informa- 
tion about subcategorization. It is widely, and very sensi- 
bly, argued that as much information as possible about 
constituent structure should be associated directly with 
lexical items. FUG, for instance, permits the description of 
a lexical item to contain a pattern that describes its comple- 
ments, and UCG (Calder 1988) even goes so far as to 
specify that for many lexical items the major category is 
the subcategorization frame. It is clear that the range of 
possible subcategorization frames cannot effectively be 
expressed in terms of a small finite set; and even if it could, 
our technique would be inapplicable because of the com- 
plex dependencies between the choice of subcategorization 
frame and the values of other features. This is the critical 
restriction on our technique--that it cannot be used to 
eliminate the disjunctions that arise from different subcate- 
gorization frames and different phrase structure rules. Our 
aim is to replace unnecessary disjunctions, not to eliminate 
them from syntactic description entirely. 
We end by returning to our earlier remark that "the 
argument is equally applicable to any of the other standard 
formalisms (except perhaps GPSG)." Our analysis of our 
main example depended on the fact that we have general 
knowledge about the range of possible values for the fea- 
ture FORM, which we used to modify local descriptions of 
this feature. In GPSG, however, local information about 
feature structures is not complete, since there is a full 
default logic specifying possible restrictions on what values 
are po,;sible or mandatory in various circumstances. It 
seems; likely that the interactions between this logic and our 
use of general knowledge about features will interact in 
ways that are at best hard to predict, and may even make 
our approach completely infeasible. 

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