THE MAPPING UNIT APPROACH TO SUBCATEGORIZATION 
Robert Bobrow, Robert Ingria, David Stallard 
BBN Systems and Technologies Inc. 
10 Moulton Street, Mailstop 6/4C 
Cambridge, MA 02138 
ABSTRACT 
We present the "mapping unit" approach to representing subeategoriza- 
tion information, a computational framework for encoding subcategorization 
information which has been developed and implemented for BBN's DEL- 
PHI system (the NL component of the HARC spoken language system). 
The advantage of our approach to subeategorization lies in its flexibility, a 
flexibility which in turn offers greater robustness of coverage with respect to 
unanticipated variations of a verbal argument pattern, and easier extension 
of coverage to new patterns. It handles in a quite natural way argument 
order variation, optionality of ~guments, and metonymy. 
INTRODUCTION 
"Subcategorization" refers to the constraints that a verb (or other 
syntactic head) places on the type and relative order of the phrases that 
serve as its arguments and (by some definitions) the effect of these 
argument phrases on the meaning of the whole clause. It is thus 
an important issue for any system which seeks to understand natu- 
ral language, or to distinguish grammatical natural utterances from 
ungrammatical ones. 
Many past approaches have sought to represent subcategorization 
declaratively, often using an approach based on the unification of 
feature values. Such approaches as Definite Clause Grammar \[11\], 
Categorial Grammar \[1\], PATRqI \[13\], and lexicalized TAG \[12\] in- 
elude in one form or another a notion of "subcategorization frame" 
that specifies a sequence of complement phrases and constraints on 
them. Some have also advocated using the feature system to en- 
code semantic information (as for example \[9\]), and this has recently 
characterized our own approach \[3\]. 
"Mapping unit" subcategorization is partly inspired by these ap- 
proaches, but it handles several kinds of variation in natural language 
utterances which cause difficulty for them. These forms of variation 
are not in any sense marginal phenomena, but are instead repeatedly 
seen in the naturally derived data for the ATIS SLS common task 
domain. The phenomena fall into three classes: 
The first is variation in argument order, as seen in 
fly from Denver to Boston 
fly to Boston from Denver 
Such variation can be handled by the frame approach, but only 
at the cost of specifying one frame for each order. Besides such 
lexicaUy-specific variation of order, other sources of order variation 
include interpolation of elements traditionally considered adjuncts 
("What flights leave at 3 pm from Denver") and heaviness effects 
("Show on the screen the fares and departure times of all the flights 
from Boston to Dallas"). 
The second is the optionality of arguments, and the different con- 
sequences thereof, including zero anaphora: 
"what restrictions apply?" 
(= apply TO SOMETHING IN CONTEXT) 
default value: 
"Show the flights.'" 
(= show the flights TO ME) 
existential quantification: 
"fly to Boston" (AT WHATEVER TIME) 
and independent truth-conditions: 
"The Rockettes kicked." 
Each verb that has optional arguments tends to have different prefer- 
ences for what to do with the omitted argument places, as the above 
examples make clear. The frame approach can handle them, but again 
only at the cost of specifying multiple frames. 
The third and final type of variation is the metonymic coercion of 
arguments, as seen below: 
"What wide-body jets serve dinner?'" 
(= "What FLIGHTS on wide-body jets serve dinner?" 
aircraft themselves do not "serve meals") 
"what airlines fly to Dallas?" 
(= "what airfines HAVE FLIGHTS to Dallas?" 
airfines themselves don't "fly") 
185 
In both examples there is a superficial clash of types which is meant 
to be reconciled through the interposition of an implicit binary re- 
lalion between the objects having those types. Our work postulates 
a distinction between two kinds of metonymy: "referential", where 
the argument is taken to be an indirect reference to an object of the 
proper type, and "predicative", where only the argument slot of the 
predicate is coerced and the referent is taken literally. This distinction 
will be discussed in more detail below. 
Most verbs in the ATIS corpora ("fly", "arrive", etc.) have flight, 
source, destination, time of day, and day of the week arguments, most 
of which are not obligatory and can occur in almost any order. The 
number of frames necessary is combinatonally impractical, and to 
this situation the phenomenon of metonyrnic coercion, which makes 
the variation potentially open-ended, only provides the final blow. 
A fundamentally different framework from that of subcategorization 
frames is needed. 
THE "MAPPING UNIT" INFORMATION 
STRUCTURES 
The central idea of the mapping unit approach is that there are 
several different types of subcategorization constraints, which ought 
to be represented as separate constraints, rather than enumerating the 
"cartesian product" of their possible combinations in fixed patterns. 
The basic building block is the "mapping unit", a structure which 
represents the constraints on a particular phrasal argument and the 
contribution this argument makes to the semantics of the clause. Map- 
ping units do not "know" whether they axe optional or not, or in what 
order they occur with respect to other mapping units; this information 
is instead represented in the grammar and in a larger structure called 
a "map", of which the mapping unit is a component. 
The following is an example of a mapping unit: 
SUBJECT 
(NP :trans) 
(FLIGHT :trans) 
(= FLIGHT-OF :trans) 
Each mapping unit has the four components shown here: a gram- 
matical relation (SUBJECT, DIRECT-OBJECT, OTHER-PP ete), a 
syntactic pattern, a type requirement, and semantic role information. 
The syntactic pattern is a unification pattern, and thus retains all the 
advantages of being able to handle partial information that are associ- 
ated with unification. The syntactic pattern (in the example just NP) 
also includes slots for semantic translation (":trans"). 
The semantic type requirement (here "FLIGHT") is also enforced 
by unification, but separately, so that a failure due to semantic type 
clash can be distinguished from one that violates syntactic constraints. 
In this way, ff the type requirement is not met, the mapping unit can be 
metonymically coerced, filling the semantic role not with the original 
complement translation but with an indefinite object related to it via 
a binary relation that resolves the clash. For example, the unit above 
could be coerced to accept an object of type AIRLINE via the binary 
relation FLIGHT-AIRLINE-OF, which maps flights to their airlines, 
thus handling the utterance "What airlines fly to Dallas". 
A final separate representation is the contribution the semantics of 
the argument makes to the semantics of the clause, which is indicated 
by a semantic role constraint. The role is set (with the equality sym- 
bol "=") in the case of ordinary complement arguments and restricted 
(with "<") in the ease of iterable temporal or locative adjunct mod- 
itiers ("in Harvard Square at Out of Town News next to the foreign 
magazine section"). A semantic role can only be set once in any 
given clause (which of course does not exclude it from being set to 
a conjunctive element), but can be rearicted arbitrarily many times. 
The mapping units are combined in a larger structure called a 
"map", of which the following is a (much reduced) example for the 
verb "fly": 
((FLY1 FLIGHT-OF FLIGHT 
ORIG-CITY CITY 
DEST-CITY CITY) 
SUBJECT 
(NP :trans) 
(FLIGHT : trans) 
(= FLIGHT-OF :trans) 
OTHER-PP 
(PP (FROM) (NP :trans)) 
(CITY : trans) 
(-- ORIG-CITY :trans) 
OTHER-PP 
(PP (TO) (NP :trans)) 
(CITY : trans) 
(= DEST-CITY :trans) 
completion (AND (FILLED FLIGHT-OF DEST-CITY) 
(FILLED-OR-ANAPHOR ORIG-CITY) ) 
translation (p-and (fllght-dest FLIGHT-OF 
DEST-CITY) 
(flight-orig FLIGHT-OF 
ORIG-CITY) 
(flight-departure-time 
FLIGHT-OF 
TIME-OF-DAY) ) 
Every map has four components: 
1. a labeled-argument predicate with typed roles 
2. a collection of "mapping units" 
3. a completion condition 
4. a translation rule for the labeled-argument predicate 
The labeled-argument predicate--in the example 'FLY1 '--is the rep- 
resentation of the verb's "meaning", and has an assigned set of typed 
semantic roles which can appear in any application of the predicate 
(but which are not necessarily required to appear in every application). 
The completion condition must be satisfied by any complete clause 
with the verb as head, and includes requirements on the instantiation 
of semantic roles. 1 In the example map, the FILLED completion pred- 
icate requires that the roles FLIGHT-OF and DEST-CITY be filled 
by a literal argument to the verb, while the FILLED-OR-ANAPHOR 
completion predicate allows the role ORIG-CITY to be be implicitly 
filled by a discourse entity. This condition allows "What flights fly 
*This rexluircment, in effect, implements the Functional Complcumcss f~ondition 
of I2G \[4\]. 
186 
to Denver from Boston?", "What flights fly from Boston to Denver" 
and "What flights fly to Denver?" but forbids "What flights fly?". 
Other completion predicates include FILLED-OR-DEFAULT, which 
specifies a defanlt value for a role, FILLED-OR-EXISTS, which gen- 
erates an existential quantification over the range type ff the role is 
unfilled, and GRAMMAR-REL-FILLED, which requires that a par- 
ticular grammatical relation have been assigned. The unqualified op- 
tionality of a semantic role is indicated simply by leaving it out of 
the completion conditions. 2 
The fourth map component, the translation rule, converts labeled- 
argument predicate applications into ordinary logic expressions based 
on the roles they instantiate. Its separation from the rest of the map 
avoids duplicate specification of the details of logical form construe- 
tion. 
This last point is important because a map can have multiple units 
on the same semantic role to represent multiple syntactic realizations 
of it. For example, the utterance "fly DENVER to Boston" (meaning 
"fly FROM DENVER to Boston") can be aecomodated simply by 
adding the following unit to the map above: 
OTHER-NP 
(NP :trans) 
(CITY :trans) 
(= ORIG-CITY :trans) 
and the function of the translation rule is exactly the same. 
Any semantic role can be frilled only once, so that overgeneration 
from multiple mapping units assigning the same role ("fly Boston 
from Denver", "fly Denver from Denver") is prevented. 3 
Certain grammatical relations can also be assigned only once in 
the derivation of any clause. These are the "major" grammatical re- 
lations ---SUBJECT, DIRECT-OBJECT, INDIRECT-OBJECT. The 
OTHER-(eat) relations can be assigned arbitrarily many times, sub- 
ject only to the constraint that semantic roles be filled only once. 
Multiple mapping units that assign the same major grammatical re- 
lation are also allowed, subject only to the above constraint and of 
course to the constraint on the unique assignment of semantic roles. 
This is useful for handling certain types of polysemy---specifically, 
the semantic overloading of syntactic argument positions. 
For modifiers which are normally treated as adjuncts, such as tem- 
poral or locative modifiers, our framework provides a notion of "free" 
mapping units associated with distinguished roles (such as TIME-OF- 
DAY, etc.). Such units do not have to be included in the map for 
individual lexical items whose labeled-argument predicate translation 
includes the role. In the example map above, TIME-OF-DAY is such 
a "free" mapping unit. 
Finally, we should point out that while the map information struc- 
tures can handle a considerable degree of variation, it is not necessary 
2Note that this assumption of optionality means that, as far as any given lexieal 
itern is concerned, any grammatical realization of a semantic role is optional, includ- 
ing SUBJECT. However, as is well known, English, unlike Italian or Greek, requires 
an overt subject in finite clauses. This requirement is imposed by the grammar, rather 
than by individual lexical items. 
3This requirement, in effect, implements the Functional Consistanqt Condition 
of LFG \[4\]. This requirement and the requirement that completion predicates be 
satisfied, in effect, implements the Theta Criterion of GB theory \[5\]. 
for any one map to handle all the possible variations associated with a 
verb. A verb can have multiple maps in the case of conventional lex- 
ieal ambiguity, just as it can have multiple subeategorization frames 
in other approaches. 
USE OF MAPPING UNITS IN GRAMMAR AND 
SEMANTIC INTERPRETATION 
Standard phrase structure rules augmented with features \[11\] are 
in our approach further augmented with the non-constituent predicates 
AVAILABLE, VP-BIND, and COMPLETE-WFF, along with the se- 
lector CONST1T. The following is an example of the grammar nile 
that assigns DIRECT-OBJECT, reduced to include only features of 
interest (non-constituent predicates appear in curly brackets): 
(VP :MAP :BINDINGS2) 
-> 
(VP :MAP :BINDINGSl) 
{AVAILABLE DIRECT-OBJECT :MAP :BINDINGS1} 
(NP : TRANS) 
{VP-BIND DIRECT-OBJECT :MAP 
{CONSTIT (NP) (I) } 
: BINDINGS1 : BINDINGS2 } 
The predicate AVAILABLE takes a grammatical relation, a map, and 
a bindings li~, which is a list pairing mapping units with role fillers. It 
is satisfied if there is a unit in the map with that grammatical relation 
such that the semantic role of that unit is not set in the bindings list, 
and the grammatical relation is not assigned in the bindings list (if it 
is a "major" grammatical relation). 
The predicate VP-BIND takes a grammatical relation, a map, an 
entire constituent (retrieved by the function CONSTIT as seen above) 
an input bindings list and an output bindings list. If it succeeds, it 
preduees a new bindings list containing an additional pair of unit 
and filler. It will succeed ff it finds a free unit in the map that 
can be matched with the passed-in constituent both syntactically and 
semantically. VP-BIND will have more than one solution ff it finds 
multiple units with these properties, in which case there are multiple 
parses. (Note that the AVAILABLE predicate is really only necessary 
to prevent the parser from looking for a constituent that would only 
wind up not being attachable to the VP.) 
The pair of map and bindings effectively constitutes the meaning 
of the VP, and can be likened to a an application of lambda-expression 
(the map) to arguments (the bindings). The difference is that while 
the arguments to a regular lambda-expression can either be bound all 
at once or in some fixed order (e.g. through currying) the arguments 
to a map are referred to by label, and can be applied in any order we 
plea. 
Currently, the maps only provide optionality information, while 
the relative order of complements is enforced by the grammar via 
grammatical relmions. This has the advantage that certain order- 
ing constraints need only be stated once, as opposed to over and 
over again in map entries. An example of a rule imposing ordering 
constraints is the ditransitive VP rule, which handles "Show me the 
flights": 
187 
(VP :HAP :BINDINGS2) 
-> 
(VP :MAP :BINDINGS) 
{AVAILABLE INDII~ECT-OBJECT :MAP :BINDINGS} 
{AVAILABLE DIRECT-OBJECT :MAP :BINDINGS} 
(NP :TRANSi) 
{VP-BIND INDIRECT-OBJECT :MAP {CONSTIT (NP)(1)} 
:BINDINGS :BINDINGSl} 
(NP :TRANS2) 
{VP-BIND DIRECT-OBJECT :MAP {CONSTIT (NP)(2)} 
:BINDINGS1 :BINDINGS2} 
The constraint that the subject precedes post-venal complements 
is expressed by the clause-level S rule, which assigns the relation 
SUBJECT: 
(ROOT-S (QUESTION) :MAP :BINDINGS2) 
-> 
(NP :TRANS) 
(VP :MAP :BINDINGSl) 
{VP-BIND SUBJECT :MAP {CONSTIT (NP) (i)} 
:BINDINGSl :BINDINGS2} 
The completion conditions for the clause are enforced by the rule for 
the top-most node, START. This rule contains a predicate COMPLETE- 
WFF that takes a map, bindings list, and delivers an output formula: 
(START (QUERY :WFF)) 
-> 
(ROOT-S (QUESTION) :MAP :BINDINGS) 
{COMPLETE-WFF :MAP :BINDINGS :WFF} 
COMPLETE-WFF enforces the completion conditions of the map 
and reduces the map and bindings combination to a formula ff these 
conditions are satisfied. 
The formula to be generated is specified by the translation rule 
component of the map. This translation rule can really be regarded 
as a kind of meaning postulate for the predicate that is associated 
with it directly. It consists of an ordinary logic expression containing 
references to the argument labels of the predicate. Repeated below is 
the translation for the predicate 'FLY1 ': 
(P-AND (flight-dest FLiGHT-OF DEST-CITY) 
(flight-orig FLIGHT-OF ORIG-CITY) 
(flight-departure-time FLIGHT-OF 
TIME-OF-DAY) 
To generate the formula, the fillers of the argument roles are substi- 
tuted for these references. The P-AND is a meta-conjunction operator 
with the property that ff any of the role references of one of its eon- 
juncts are unfilled, that conjunct is left out of the final formula. In 
this way we are not required to generate an existential quantification 
for a missing argument place (as for example the departure time of 
the flight). 
There are certain instances in which an existential quantification 
is generated, however. If a semantic role has merely been restricted 
instead of fired, a narrow-scope existential quantification is generated 
and the variable of this quantification substituted for the role reference 
in the translation rule. Thus for "Flight 1 flies before 3 pm" we would 
have: 
(exists t (precede t (time 3 0 pm)) 
(flight-departure-tlme (fllght-no i) 
t)) 
PREDICATIVE METONYMY 
Another case in which narrow-scope existentials are generated is 
the case of predicative metonomy, in which the semantic role in ques- 
tion has been type-coerced to accept an argument of a type different 
from its restriction. In this type of metonymy, the referent of this 
argument does not change. Instead a relation is established between 
it and an indefinite, existentially quantified object of the proper type. 
Thus for "Delta Airlines flies from Boston to Baltimore" we would 
have: 
(exists x flight (airline-of x Delta) 
(and (orig-clty x boston) 
(dest-city x baltimore))) 
The distinction between referential and predicative metonymy only 
becomes visible when the actual referents of NPs are sought, as in: 
What airlines fly to Boston? 
What wide-body jets serve dinner? 
In the first, it is implausible that "airlines" is being used to refer to 
some set of flights, since every flight is on some airline and there is 
no constraint. In the second, "wide-body jets" is far more likely to 
refer to some set of flights, since not every flight is on a wide-body 
jet. 
Predicative metonymy is an essentially local phenomenon, while 
referential metonymy is an essentially global one. Our present im- 
plementation assumes predicative metonymy only and allows only a 
limited set of binary relations. Processing is such as to prefer attach- 
ments that do not require metonymy, by assigning a lower probability 
at parse-time to parses which do require it \[2\]. This is necessary to 
exclude an unreasonable parse of: 
Show flights to Denver on wide-body jets serving dinner. 
OTHER BENEFITS 
The combination of labeled-argument predicate mad translation 
rule offers several benefits not yet mentioned. One is that a given 
predicate can be shared between different lexical entries which pro- 
vide different syntactic realizations of it. For example, in the ATIS 
domain the verbs "depart" and "originate" have very similar core 
meanings, yet have semantic roles realized by different prepositions: 
The flight departs from Boston. 
The flight originates in Boston. 
*The flight departs in Boston. 
188 
The words are not synonyms in the normal sense that one can be 
substituted for the other in such a way as to preserve grammatieality. 
But their common semantic content can be represented. 
Another advantage is that a denotational semantics with optional- 
ity is implemented without requiring Davidsonian-style event quan- 
tifications \[7\]. While event objects make sense in some contexts, 
having an existontial quantification over events for every verb is fre- 
quently inconvienent in further processing. Certainly it is so in the 
ATIS domain, where the chief semantic outcome of clauses seems to 
be a set of predications on attributes of flight-individuals and there 
really are no "events" as such at all. Event quanfifieations are not pre- 
cluded, however--they could be produced with a different translation 
rale schema. 
COMPARISON WITH OTHER WORK 
Our treatment of the syntactic aspects of subeategofization is most 
like that of PATR-II \[13\]. Both PATR-II and the mapping units ap- 
proach use recursive VPs, with each level of VP structure, in effect, 
"peeling off" a single constituent of the head verb's complement list. 4 
A major difference between the two approaches is that the PATR-II 
system of subcategofization is essentially limited to popping con- 
stituents off the subcategorization list, in fixed order, requiring a sep- 
arate subeategorizatlon list for each variation in order. Our approach 
allows complements to be found in whatever order the grammar will 
allow them. In this respect, it is more like the UD system \[8\], which 
has an operator for "non-deterministic extraction from arbitrary list 
positions". 5 However, our system does not literally remove units 
from the map, but rather simply marks them as no longer available 
for binding. Moreover, the mechanism of allowing multiple syntactic 
realizations for a given semantic relation in a single representation of 
complement structure is, to our knowledge, unique. 
Related work on the semantic aspects of argument optionality has 
been reported by Palmer \[10\], \[6\]. Our work differs from this mainly 
in the tighter coupling of syntax and semantics during processing and 
the use of recursive VP structures, which Potentially allows for an el- 
egant solution of cases of nun-consituent conjunction, not addressed 
in the other work. Our system also has a finer grained treatment of 
optionality; whereas \[10\] and \[6\] divide argument roles into OBLIG- 
ATORY, ESSENTIAL, and NON-ESSENTIAL roles, we provide a 
richer set of possibilities. The dccoupling of syntactic realizations 
of a role in a mapping unit from the semantic typing constraints on 
that role, to allow for different types of metonymie extension is also a 
distinction. On the other hand, the use of named thematic or semantic 
roles which cut across particular predicates in \[10\] and \[6\] might pro- 
vide a more compact form for capturing linguistic generalizations, to 
the extent that such a theory of thematic relations is well-motivated. 
CONCLUSIONS AND FUTURE WORK 
We have presented a framework for handling three unruly phe- 
nomena: argument-order variation, optionality, and metonymy. Yet 
this framework is simple and does not sacrifice formal goals such as 
declarativeness. 
We are currently working on extending the mapping unit to other 
parts of speech such as nouns and adjectives. We are also working 
4Our approach allows morn than a single complement constituent to appear at a 
given level, however, as the ditransitive VP rule above shows. 
~Other systems which have a similar mechanism include the Lilog system of IBM 
Germany and the MLMo machine translation system. 
on more lexically-based ways to encode order, perhaps by a system 
of precedence among mapping units. 
Other furore work will include referential metonymy, the inter- 
action of metonymy with anaphora, and non-constituent conjunction 
phenomena. 
ACKNOWLEDGEMENTS 
The work repoRed here was supported by the Advanced Research 
Projects Agency and was monitored by the Office of Naval Research 
under Contract No. N00014-89-C-0008. The views and conclusions 
contained in this document are those of the authors and should not 
be interpreted as necessarily representing the official policies, either 
expressed or implied, of the Defense Advanced Research Projects 
Agency or the United States Government. 
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