ZERO MORPHEMES 
IN UNIFICATION-BASED COMBINATORY CATEGORIAL GRAMMAR 
Chinatsu Aone 
The University of Texas at Austin & 
MCC 
3500 West Balcones Center Dr. 
Austin, TX 78759 
(aone@mcc.com) 
Kent Wittenburg 
MCC 
3500 West Balcones Center Dr. 
Austin, TX 78759 
(wittenburg@mcc.com) 
ABSTRACT 
In this paper, we report on our use of 
zero morphemes in Unification-Based 
Combinatory Categorial Grammar. After illus- 
trating the benefits of this approach with several 
examples, we describe the algorithm for compil- 
ing zero morphemes into unary rules, which al- 
lows us to use zero morphemes more efficiently 
in natural language processing. 1 Then, we dis- 
cuss the question of equivalence of a grammar 
with these unary rules to the original grammar. 
Lastly, we compare our approach to zero mor- 
phemes with possible alternatives. 
1. Zero Morphemes in Categorial Grammar 
In English and in other natural 
languages, it is attractive to posit the existence 
of morphemes that are invisible on the surface 
but have their own syntactic and semantic defini- 
tions. In our analyses, they are just like any 
other overt morphemes except for having null 
strings (i.e. " "), and we call them zero mor- 
phemes. Most in Categorial Grammar and relat- 
ed forms of unification-based grammars, on the 
other hand, take the rule-based approach. That 
is, they assume that there are unary rules that 
change features or categories of their arguments 
(cf. Dowty 1977, Hoeksema 1985, Wittenburg 
1986, Wood 1987). Below, we will discuss the 
advantages of our zero morpheme approach 
over the rule-based approach. 
Zero morphemes should be distin- 
guished from so-called "gaps" in wh-questions 
and relative clauses in that zero morphemes are 
not traces or "place holders" of any other overt 
morphemes in a given sentence. There are at 
1. The work described here is implemented in 
Common Lisp and being used in the Lucy 
natural language understanding system at 
MCC. 
188 
least two types of zero morphemes: zero mor- 
phemes at the morphology level and those at 
the syntax level. 
A zero morpheme at the morphology 
level applies to a free morpheme and forms an 
inflected word. Such examples are present 
tense zero morpheme (PRES) as in 'I 
like+PRES dogs" and a singular zero morpheme 
(SG) as in "a dog+SG". These two are the coun- 
terparts of a third person singular present tense 
morpheme C+s" as in "John like+s dogs" and a 
plural morpheme C+s" as in 'two dog+s'~, re- 
spectively. 
(1) dog +SG 
N\[num:null\] N\[num:sg\]~N\[num:null\] 
dog +s 
N\[num:null\] N\[num:pl\]\N\[num:null\] 
Notice that, unlike the rule-based approach, the 
declarative and compositional nature of the zero 
morpheme approach makes the semantic analy- 
sis easier, since each zero morpheme has its 
semantic definition in the lexicon and therefore 
can contribute its semantics to the whole inter- 
pretation just as an overt morpheme does. Also, 
the monotonicity of our 'feature adding" ap- 
proach, as opposed to "default feature" ap- 
proach (e.g., Gazdar 1987), is attractive in com- 
positional semantics because it does not have to 
retract or override a semantic translation contrib- 
uted by a word with a default feature. For exam- 
ple, "dog" in both "dog+SG" and "dog+s" contrib- 
utes the same translation, and the suffixes 
"+SG" and "+s" just add the semantics of num- 
ber to their respective head nouns. In addition, 
this approach helps reduce redundancy in the 
lexicon. For instance, we do not have to define 
for each base verb in the lexicon their present- 
tense counterparts. 
a man REL-MOD the daughter of whom 
N (N\N)/S\[reI:+\] NP/N N (N\N)/NP NP\[rel:+\] 
apply> ..... N\[rel:+\]\N 
apply< .... N\[rel:+\] 
I apply> ,, NP\[rel:+\] 
LIFT S\[reh+\]/(S/NP) 
apply> S\[rel:+\] 
apply> N\N 
John liked 
NP (S\NP)/NP 
~p~pe-raising 
s/NP compose> 
Figure 1: Derivation of "a man the daughter of whom John liked" 
Some zero morphemes at the syntax level 
are those which may apply to a constituent larg- 
er than a single word and change the categories 
or features of the constituent. They are like ordi- 
nary derivational or inflectional morphemes ex- 
cept that their application is not confined within a 
word boundary. In English, one example is the 
noun compounding zero morpheme (CPD), 
which derives a noun modifier from a noun. In 
Categorial Grammar, its syntactic type is 
(N/N)\N. 2 For instance, a noun compound "dog 
food" might have the following derivation. 
(2) dog CPD food 
N (N/N)\N N apply< 
N/N 
N apply> 
In knowledge-based or object-oriented 
semantics (cf. Hirst 1987); which our LUCY sys- 
tem uses, the treatment of compound nouns is 
straightforward when we employ a zero mor- 
pheme CPD. 3 In LUCY, CPD has a list of trans- 
lations in the semantic lexicon, each of which is 
a slot relation (a two-place predicate as its syn- 
tactic type) in the knowledge base. For exam- 
ple, for "dog food" CPD may be translated into 
(food-typically-eaten x y), where x must be an in- 
stance of class Animal and y that of Food. 
Thus, a translation of CPD is equivalent to a 
2. CPD is leftward-looking to parallel the defini- 
tion of a hyphen as in "four-wheeler". 
3. Some compound nouns are considered as 
"idiomatic" single lexical entries, and they do 
not have a CPD morpheme. (e.g. "elephant 
garlic") 
189 
value bound to the "implicit relation" called nn 
that Hobbs and Martin (1987) introduce to re- 
solve compound nouns in TACITUS. In our 
case, having CPD as a lexical item, we do not 
have to introduce such an implicit relation at the 
semantics level. 
An analogous zero morpheme provides 
a natural analysis for relative clauses, deriving a 
noun modifier from S. This zero morpheme, 
which we call REL-MOD, plays an important role 
in an analysis of pied-piping, which seems diffi- 
cult for other approaches such as Steedman 
(1987, 1988). (See Pollard (1988) for his criti- 
cism of Steedman's approach.) Steedman as- 
sumes that relative pronouns are type-raised al- 
ready in the lexicon and have noun-modifier type 
(N\N)/(S/(SINP). In Figure 1, we show a deriva- 
tion of a pied-piping relative clause "a man the 
daughter of whom John liked " using REL- 
MOD.4 s 
Other zero morphemes at the syntax 
level are used to deal with optional words. We 
define a zero morpheme for an invisible 
morpheme that is a counterpart of the overt one. 
An example is an accusative relative pronoun as 
in "a student (who) I met yesterday". Another 
example of this kind is '~ou" in imperative 
4. We assume that accusative wh-words are of 
basic NP type in the lexicon. A unary rule 
LIFT, which is similar to type-raising rule, 
lifts any NP of basic type with \[rel:+\] feature 
to a higher type NP, characteristic of fronted 
phrases. This feature is passed up by way 
of unification. 
5. We actually use predictive versions of com- 
binators in our runtime system (Wittenburg 
1987). 
X 
X/Y y 
I unify 
A/B 
R: X/Y Y ==> X M: A/B 
A A 
-'=> ~ ""-'> I 
A/B B B 
Figure 2: Compiling a zero morpheme 
sentences. Having a zero morpheme for the 
unrealized '~'ou" makes parsing and the 
interpretation of imperative sentences 
straightforward, s 
(3) 
IMP IMP-YOU finish dinner 
S\[mood:imp\]/S NP (S\NP)/NP NP \[case:nom\] 
apply> S\NP 
apply< S apply> 
S 
\[mood:imp\] 
Analogous to the treatment of optional 
words, VP-ellipsis as in "Mary likes a dog, and 
Bill does too" is handled syntactically by defining 
a syntax-level zero morpheme for an elided verb 
phrase (called VP-ELLIPSIS). During the 
discourse process in LUCY, the antecedent of 
VP-ELLIPSIS is recovered. 7 
(4) 
Bill 
NP 
does VP-ELLIPSIS 
S\NP/(S\NP) S\NP 
S\NP 
S 
apply> apply< 
Now to summarize the advantages for 
having zero morphemes, first, zero morphemes 
like PRES and SG reduce redundancy in the 
lexicon. Second, zero morphemes seem to be a 
natural way to express words that do not appear 
6. Each sentence must have one of the three 
mood features -- declarative, interrogative, 
and imperative mood. They are added by 
zero morphemes DECL, QUES, and IMP, 
respectively. 
7. See Kameyama and Barnett (1989). 190 
on the surface but have their overt counterparts 
(e.g., null accusative relative pronouns, 
vp-ellipsis). Third, since each zero morpheme 
has its own syntax and semantic interpretation in 
much the same way as overt morphemes, and 
since the semantic interpretations of binary rules 
that combine a zero morpheme with its 
argument (or functor) are kept as simple as they 
are in Categorial Grammar, semantic 
interpretations of sentences with zero mor- 
phemes are compositional and straightforward. 
Typically in the rule-based approach, the 
semantic operations of unary rules are more 
complicated: they might perform such operations 
as introducing or retracting some semantic 
primitives that do not exist in the semantic 
lexicon. But with our zero morpheme approach, 
we can avoid such complication. Lastly, using 
zero morpheme REL-MOD makes the analysis 
of pied-piping and preposition fronting of relative 
clauses in Categorial Grammar possible. 
In the following section, we propose an 
approach that keeps all these advantages of 
zero morphemes while maintaining the efficiency 
of the rule approach in terms of parsing. 
2. Compiling Zero Morphemes 
In natural language processing, simply 
proposing zero morphemes at each juncture in a 
given input string during parsing would be a 
nightmare of inefficiency. However, using the 
fact that there are only a few binary rules in 
Categorial Grammar and each zero morpheme 
can combine with only a subset of these rules 
because of its directionality compatibility, we can 
pre-compile zero morphemes into equivalent 
unary rules and use the latter for parsing. Our 
approach is an extension of the predictive com- 
binator compilation method discussed in 
Wittenburg (1987). The idea is that we first unify 
a zero morpheme M with the left or right daugh- 
Let M be a zero morpheme, R be a binary rule. For each M in the grammar, do the following: 
For each binary rule R in the grammar 
if the syntax graph of M unifies with the left daughter of R 
then call the unified binary graph R', and 
make the right daughter of R' the daughter of a new unary rule R1 
make the parent of R' the parent of R1 
if the syntax graph of M unifies with the right daughter of R 
then call the unified binary graph R' 
make the left daughter of R' the daughter of a new unary rule R1 
make the parent of R' the parent of RI. 
Figure 3: Algorithm for compiling zero morphemes 
ter of each binary rule R. If they unify, we create 
a specialized version of this binary rule R', main- 
taining features of M acquired through unifica- 
tion. Then, we derive a unary rule out of this 
specialized binary rule and use it in parsing. 
Thus, if M is of type NB, R is forward applica- 
tion, and M unifies with the left daughter of R, 
the compiling procedure is schematized as in 
Figure 2. 
Now I shall describe the algorithm for 
compiling zero morphemes in Figure 3. During 
this compiling process, the semantic interpreta- 
tion of each resulting unary rule is also calculat- 
ed from the interpretation of the binary rule and 
that of the zero morpheme. For example, if the 
semantics of M is M', given that the semantic in- 
terpretation of forward application is ~,fun- 
;~arg(fun arg), we get Zarg(M' arg) for the se- 
mantic interpretation of the compiled unary rule. 8 
We also have a mechanism to merge 
two resulting unary rules into a new one. That 
is, if a unary rule R1 applies to some category A, 
giving A', and then a unary rule R2 applies to A', 
giving A", we merge R1 and R2 into a new 
unary rule R3, which takes A as its argument 
and returns A". For example, after compiling 
IMP-rule and IMP-YOU-rule from zero mor- 
phemes IMP and IMP-YOU (cf. (3)), we could 
merge these two rules into one rule, IMP+IMP- 
YOU rule. During parsing, we use the merged 
rule and deactivate the original two rules. 
3. The Grammar with Compiled zero mor- 
phemes 
The grammar with the resulting unary 
rules has the same generative capacity as the 
8. See Wittenburg and Aone (1989) for the de- 
tails of Lucy syntax/semantics interface. 
191 
source grammar with zero morphemes in the 
lexicon because these unary rules are originally 
derived by only using the zero morphemes and 
binary rules in the source grammar. Thus, a 
derivation which uses a unary rule can always 
be mapped to a derivation in the original gram- 
mar, and vice versa. For example, look at the 
following example of CPD-RULE vs. zero mor- 
pheme CPD: 
(5) a. dog food 
N N 
N/I~' cpd-rule 
N apply> 
b. dog CPD food 
N (N/N)\N N 
N/N apply< 
N apply> 
Now, if we assume that we use 
Categorial Grammar with four binary rules, 
namely, apply>, apply<, compose>, and com- 
pose<, as Steedman (1987) does, we can pre- 
dict, among 8 possibilities (4 rules and the 2 
daughters for each rule), the maximum number 
of unary rules that we derive from a zero mor- 
pheme according to its syntactic type. 9 If a zero 
morpheme is of type NB, it unifies with the left 
daughters of apply>, apply< and compose> and 
with the right daughters of apply> and corn- 
9. Zero morphemes do not combine with wh- 
word type-raising rule LIFT, which is the only 
unary rule in our grammar besides the com- 
piled unary rules from zero morphemes. 
pose>. Thus, there are 5 possible unary rules 
for this type of zero morpheme. If a zero mor- 
pheme is of type A\B, there are also 5 possibili- 
ties. That is, it unifies with the left daughter of 
apply< and compose<, and the right daughters 
of apply>, apply< and compose<. If a zero mor- 
pheme is of basic type, there are only 2 possibil- 
ities; it unifies only with the left daughter of 
apply< and the right daughter of apply>. 
Furthermore, in our English grammar, 
we have been able to constrain the number of 
unary rules by pre-specifying for compilation 
which rules to unify a given zero morpheme 
with. 1° We add such compiler flags in the 
definition of each zero morpheme. We can do 
this for the morphology-level zero morphemes 
because they are never combined with anything 
other than their root morphemes by binary rules, 
and because we know which side of a root 
morpheme a given zero affix appears and what 
are the possible syntactic types of the root 
morpheme. As for zero morphemes at the 
syntax level, we can ignore composition rules 
when compiling zero morphemes which are in 
islands to "extraction", since these rules are only 
necessary in extraction contexts. CPD, 
REL-MOD and IMP-YOU are such syntax-level 
zero morphemes. Additional facts about English 
have allowed us to specify only one binary rule 
for each syntax-level zero morpheme in our 
English grammar. An example of a zero 
morpheme definition is shown below. 
(6) (defzeromorpheme PRES 
:syntax S\[tns:pres\]\S\[tns :null\] 
:compile-info (:binary-rule compose< 
:daughter R)) 
4. Comparison in View of Parsing Zero 
Morphemes 
In this section, we compare our 
approach to zero morphemes to alternative 
ways from the parsing point of view. Since we 
do not know any other comparable approach 
which specifically included zero morphemes in 
natural language processing, we compare ours 
to the possible approaches which are analogous 
to those which tried to deal with gaps. For 
example, in Bear and Karttunen's (1979) 
treatment of wh-question and relative pronoun 
gaps in Phrase Structure Grammar, a gap is 
proposed at each vertex during parsing if there 
is a wh-question word or a relative pronoun in 
the stack. We can use an analogous approach 
for zero morphemes, but clearly this will be 
extremely inefficient. It is more so because 1) 
there is no restriction such as that there should 
be only one zero morpheme within an S clause, 
and 2) the stack is useless because zero mor- 
phemes are independent morphemes and are 
not "bound" to other morphemes comparable to 
wh-words. 
Shieber (1985) proposes a more 
efficient approach to gaps in the PATR-II 
formalism, extending Earley's algorithm by using 
restriction to do top-down filtering. While an 
approach to zero morphemes similar to 
Shieber's gap treatment is possible, we can see 
one advantage of ours. That is, our approach 
does not depend on what kind of parsing 
algorithm we choose. It can be top-down as well 
as bottom-up. 
5. Conclusion 
Hoeksema (1985\] argues for the 
rule-based approach over the zero morpheme 
approach, pointing out that the postulation of 
zero morphemes requires certain arbitrary 
decisions about their position in the word or in 
the sentence. While we admit that such 
arbitrariness exists in some zero morphemes we 
have defined, we believe the advantages of 
positing zero morphemes, as discussed in 
Section 1, outweigh this objection. Our 
approach combines the linguistic advantages of 
the zero morpheme analysis with the efficiency 
of a rule-based approach. Our use of zero 
morphemes is not restricted to the traditional 
zero-affix domain. We use them, for example, to 
handle optional words and VP-ellipsis, extending 
the coverage of our grammar in a natural way. 
ACKNOWLEDGEMENTS 
We would like to thank Megumi 
Kameyama and Michael O'Leary for their help. 
10. In fact, we use more than two kinds of com- 
position rules for the compilation of the mor- 
phology-level zero morphemes. (e.g. PRES 
in (1)) But this does not cause any "rule pro- 
liferation" problem for this reason. 
192 
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