THE INTERPRETATION OF RELATIONAL NOUNS 
Joe de Bruin" and Remko Scha 
BBN Laboratories 
10 Mouiton Street 
Cambridge, MA 02238, USA 
ABSTRACT 
This paper 1 decdbes a computational treatment of 
the semantics of relational nouns. It covers relational 
nouns such as "sister.and "commander; and focuses 
especially on a particular subcategory of them, called 
function nouns ('speed; "distance', "rating'). Rela- 
tional nouns are usually viewed as either requiring 
non-compositional semantic interpretation, or causing 
an undesirable proliferation of syntactic rules. In con- 
trast to this, we present a treatment which is both 
syntactically uniform and semantically compositional. 
The core ideas of this treatment are: (1) The recog- 
nition of different levels of semantic analysis; in par- 
ticular, the distinction between an English-oriented 
and a domain-oriented level of meaning represen- 
tation. (2) The analysis of relational nouns as denoting 
relation-extensions. 
The paper shows how this approach handles a 
variety of linguistic constructions involving relational 
nouns. The treatment presented here has been im- 
plemented in BBN's Spoken Language System, an 
experimental spoken language interface to a 
database/graphics system. 
1 RELATIONAL NOUNS AND THEIR DENOTATIONS 
When Jean Piaget faced his nine year old subject 
Hal with the question ~/Vhat's a brother?; the answer 
was: "When there's a boy and another boy, when 
there are two of them." And, with a greater degree of 
formal precision, ten year old Bern replied to the same 
question: ",4 brother is a relation, one brother to 
another. "\[2\] \[8\] What these children are beginning to 
be able to articulate is that there is something wrong 
with the experimenter's question as it is posed: it talks 
about "brothers" as if they constituted a natural kin d, 
as if there is a way of looking at an individual to find 
out whether he is a brother. But "brother" is normally 
not used that way - a property which it shares with 
words like "co-author; "commander', "speed', 
"distance', and "rating'. 
Nouns of this sort are called relational nouns. As 
1This research was supported by the Advanced Research Projects 
Agency of the Depmlment of Defense under Contract No, 
NO0014-87-C-0(~5. 
"Current address: Cartesian Products BV, WG Plem 316, 1054 SG 
Amsterdam, The Nathedands. 
we shall see in a moment, their semantic properties 
differ significantly from those of other nouns, so that 
the standard treatments of nominal semantics don't 
apply to them. The problem of the semantic inter- 
pretation of relational nouns constitutes the topic of 
this paper. We shall argue that this problem is indeed 
a semantic one, and should preferably not be treated 
in the syntax. The semantic treatment that we present 
uses a multilevel semantics framework, and is based 
on the idea of assigning relation extensions as 
denotations to relational nouns. 
Relational nouns are semantically unsaturated. 
They are normally used in combination with an implicit 
or explicit argument: "John's brother.. The argument 
of a relational noun, if overtly realized in the sentence, 
is connected to the noun by means of a relation- 
denoting lexical element: the verb "have" or one of its 
semantic equivalents (the geni~ve and the preposi- 
tions "of" and "with): "John has a sister', "John's 
sister; "a sister of John's; "a boy with a sister" It has 
been noted that these lexical items interact differently 
with relational nouns than they do with other nouns. 
\[7\] Compare, for instance, the noun "car" in 
(1)/(labcd) with the relational noun "brother" in the 
parallel sentences (2)/(2abcd): (1) entails (labcd), 
but the corresponding (2) does not entail (2abcd).2 
(1) "John's cars are wrecks." 
(la) "Some wrecks of John's are cars." 
( l b) "Some wrecks are John's." 
(1 c) "Some ca~ are John "S. " 
( l d) "John has wrecks." 
(2) "John's brothers are punks." 
#(2a) "Some punks of John's are brothers." 
#(2b) "Some punks are John's." 
#(2c) "Some brothers are John's." 
#(2d) "John has punks." 
A particular subcategory of the relational nouns, 
that we shall consider in some detail, is constituted by 
the function nouns; they are semantically distinct in 
that for every argument they refer to exactly one en- 
tity, which is an element of a linear ordering: a hum- 
ZWe refrain from saying that (2abod) are ungrammatical. Because 
of the semantic open-endedness of "have" and the genitivQ, these 
sentences can certainly be wellformod and meaningful, if uttored in 
an appropriate context. The issue at stake is that the inteqDreta~on 
whic~ is the saJient one for the genitive in (2) is not avaUable for the 
¢ommponciing elements in (2abcd). Sentences displaying this 
property have been marked with the #-sign (rathor than the 
ungrammoticality-aotorisk) in this paper. 
25 
bet, an amount, or a grade. Examples are "length", 
"speed', "distance", "rating". Function nouns can be 
used in constructions which exclude other nouns, 
relational as well as non-relational. Compare, for in- 
stance: 
(3) "The USS Frederick has a speed of 15 knots." 
#(3a) "John has a car of ~is wreck." 
#(3b) "John has a brolher of Peter." 
The examples above show that there are sig- 
nificant semantic differences between phrases con- 
necting relational nouns to their functions/values, and 
the corresponding, similarly structured phrases built 
around other nouns. This suggests that the standard 
treatment of ordinary nouns cannot be applied directly 
to relational nouns and yield correct results. To con- 
clude this introductory section, we investigate this is- 
sue in a little more detail. 
Assume a semantic framework with the following, 
not very unusual, features. Nouns are analyzed as 
set-denoting constants; concomitantly, adjectives are 
analyzed as one-place predicates, prepositions as 
two-place predicates, verbs as n-place predicates. 
Plural noun phrases with "the" or a possessive denote 
sets which have the same semantic type as the noun 
around which they are built: "John's cars" denotes a 
particular set of cars. In this approach, the represen- 
tation of the noun phrase "Peter's s/stern'would be: 
{x • SISTERS / POSSESS(PETER, x)}, 
where SISTERS denotes the set of persons who are a 
sister, and POSSESS represents the possessive rela- 
tion indicated by the genitive construction. 
Now this expression does not have the right 
properties. It lacks necessary information: the predi- 
cate ~ x: POSSESS(PETER, x)) applies to elements 
of the extension of SISTERS; it cannot take into ac- 
count how this extension was defined. For instance, if 
in a pa~cular world the set of sisters is co-extensional 
with the set of coauthors, the approach just outlined 
would incorrectly assign to "Peter's sisters" the same 
denotation as to "Peter's co-aulhors". 
It is clear what the source of the problem is: the 
semantic representations for relational nouns con- 
sidered above denote simple sets of individuals, and 
do not contain any information about the relation in- 
volved. To salvage a uniform compositional treatment, 
a richer representation is needed. One might think of 
invoking Montague's individual concepts \[3\] \[6\], or en- 
riching one's ontology with qua-individuals 
(distinguishing between Mary qua sister and Mary qua 
aunt) \[4\]. In section 4 we will present our solution to 
this problem. First, we discuss why we didn't choose 
for a more syntactically oriented approach. 
2 AGAINST SYNTACTIC TREATMENTS 
Often, the complexities mentioned above are 
taken to require a distinction between intransitive 
common nouns and transitive common nouns in the 
syntax, with a concommittant proliferation of syntactic 
rules. Instead, we have chosen to extend a treatment 
of "ordinary" nouns only at the semantic processing 
stage. We shall now indicate some of the reasons for 
this choice. 
Relational nouns are semantically dependent on 
an argument. In this respect, they are more reminis- 
cent of verbs than ot standard nouns like "boy" or 
"chair'. Most verbs of English have one or more ar- 
gument places that must be filled for the verb to be 
used in a syntactically/semantically felicitous way; this 
property of verbs is probably an important reason for 
the persisting tendency to analyze them as n-place 
predicates rather than sets of situations. The semantic 
similarity between relational nouns and verbs has 
given rise to treatments which model the syntactic 
treatment of nouns on the treatment of verbs: one 
introduces lexical subcategories for nouns which in- 
dicate how many arguments they take and how these 
arguments are marked; the syntactic rules combine 
N-bara or noun-phrases with genitive phrases and 
preposition-phrases, taking these subcategorizations 
into account. \[15\] We will now argue, however, that 
from a syntactic point of view such a move is unattrac- 
five. 
Syntactically, relational nouns do not behave very 
differentJy from "ordinary" nouns. They combine with 
adjectives, determiners, preposition phrases and rela- 
five clauses to form noun phrases with a standard 
X-bar structure; and the noun phrases thus con- 
stituted can pa~cipate in all sentence-level structures 
that other noun phrases partake in. 
Also, no nouns have syntactic properties that 
would be analogous to the sentenco-levei 
phenomenon of a verb obligatorily taking one or more 
arguments. The overt realization of the arguments of 
a "transitive noun" is always optional. 
Finally, we may note that relational nouns can be 
connected to their arguments/values by a variety of 
verbs and prepositions, which constitute a semantic 
complex that is also used, with exactly the same 
structure but with a different meaning, to operate on 
non-relational nouns. Compare, for instance: 
"The Chevrolet of Dr. Johnson" 
/ "The speed of Frederick" 
"Dr. Johnson's Chevrolet" 
/ "Frederick's speed ~ 
"The Chevrolet that Dr. Johnson has" 
/ "The speed that Frederick has" 
"Dr. Johnson acquired a rusty Chevrolet" 
/ "Frederick acquired a formidable speed" 
"A philosopher with a rusty Chevrolet" 
/ ",4 ship wi~ a formidable speed" 
The same set of terms is used in English for the 
26 
ownership relation, for the part-whole relation, and for 
the relation between a function and its argument. 
These terms (like "of', "have" and "with" ) are highly 
polysemous, and any language processing system 
must encompass mechanisms for disambiguating 
their intended meaning in any particular utterance. 
To summarize: relational nouns do not distinguish 
themselves syntactically from other nouns, and they 
mark their function-argument structures by means of 
polysemous descriptive terms. We therefore conclude 
that it would be theoretically elegant as well as com- 
putationaily effective to treat relational and non- 
relational nouns identically at the syntactic level, and 
to account for the semantics of relational noun con- 
structions by exploiting independently motivated dis- 
ambiguation mechanisms. The remainder of this 
paper describes such a treatment. 
First, Section 3 discusses the multilevel semantics 
architecture which constitutes the framework for our 
approach. Section 4 presents our answer to a basic 
question about relational nouns: what should their 
denotations be? This section then goes on to 
describe the semantic transformations which derive 
the desired analyses of constructions involving rela- 
tional nouns. Section 5 briefly discusses the interface 
with a Discourse Model, which is necessary to recover 
arguments of a relation that are left implicit in an ut- 
terance. Section 6 shows that our treatment is useful 
for the purpose of response-formulation in question- 
answering. 
3 MULTILEVEL SEMANTICS. 
Our approach to the problem of relation~d nouns is 
based on the idea of multilevel semantics, the distinc- 
tion between different levels of semantic analysis. 
\[1\] \[10\] In this approach, interpreting a natural lan- 
guage sentence is a multi-stage process, which starts 
out with a high-level meaning representation which 
reflects the semantic structure of the English sentence 
rather directly, and then applies translation rules 
which specify how the English-oriented semantic 
primitives relate to the ones that are used at deeper 
levels of analysis. 
At every level of analysis, the meaning of an input 
utterance is represented as an expression of a logical 
language. 3 The languages used at the various levels 
of analysis differ in that at every level the descriptive 
constants are chosen so as to correspond to the 
semantic primitives which are assumed at that level. 
At the highest semantic level, the meaning of an 
input utterance is represented as an expression of the 
Eng/ish-oriented Formal Language (EFL). The con- 
stants of EFL correspond to the descriptive terms of 
3BBN's Siren Language System uses a higher-o~er intensienel 
logic hased on Church's iaffC.3~Pcak:ulus, comDining fe~oJre6 from PHLIQA's logical 
language \[5\] with Montague'$ Intensionel Logic \[6\]. 
English. A feature of EFL which is both unusual and 
important, is the fact that descriptive constants are 
allowed to be ambiguous. Within each syntactic cats- 
gory, every word is represented in EFL by a single 
descriptive constant, no matter how many senses the 
word may have. An EFL expression can thus be seen 
as an expression schema, where every constant can 
be expanded out in a possibly large number of dif- 
ferent ways. (See \[5\] for details on the model theory 
of such a logic.) 
The ambiguity of EFL follows from its domain- 
independence. All descriptive words of a language are 
polysernous, and only when used in the context of a 
particular subject domain do they acquire a single 
precise meaning - a meaning which cannot be articu- 
lated independently of that subject domain. Even 
within one subject domain, many words have a range 
of different meanings. Joint representations for such 
sets of possible expansions are computationaJly ad- 
vantageous; and when the range of possibilities is 
defined in an open-ended way, they are even neces- 
sary. Such cases occur when we attempt to account 
for the interpretation of metonymy, metaphor and 
nominal compounds \[12\], or the interpretation of mul- 
tilevel plural noun phrases \[11\]. 
The logical language used at the domain- 
dependent level of representation is called the World 
Mode/Language (WML). This is an unambiguous lan- 
guage, with an ordinary model-theoretic interpretation. 
Its constants are chosen to correspond to the con- 
cepts which cons~tute the domain of discourse. 4 
We can illustrate the distinction between EFL and 
WML by means of an example involving relational 
noiJns. Compare (4) and (5) below. Sentence (4) will 
usually be translated into something like (4a): s 
(4) "John has a house in Hawaii." 
(4a) 3 he {he HOUSES/IN(h,HAWAII)}: 
HA VE(JOHN, h) 
Now consider (5) instead; a single-level architecture 
would have to analyse this sentence as (5b) rather 
than (Sa), since (5b) is the representation one would 
prefer to end up with. 
(5) "Frederick has a speed of 15 knots." 
(Sa) "~ c ~ {c e SPEEDS 
/ OF(c, amount(15, KNOTS))}: 
HA VE(FREDERICK, c) 
4To provide a smooth interface with underlying application sys- 
tems, there is a third level of semantic interpretation. The language 
used at this level is called the Data Base Language (DBL). Its 
constants stand for the fites and attributes of the _,~tP _t'.,~e_ \[o be 
accessed, and the avaiiable graphics system opemUons and their 
parameters. 
SAccommoda~ng discourse anaphore may motivate a different 
treatment of the indefinite noun phrase, repre~mting its semantics by 
a Skelem-constant or a similer device, rather than by the traditional 
existential quantifier. For the present discussion we may ignore this 
issue. 
2? 
(Sb) F-SPEED(FREDERICK). amount(15, KNOTS) 
In a multilevel semantics architecture, however, 
one would prefer to maintain a completely uniform first 
stage in the semantic interpretation process, where 
(5) would be treated exactly as (4), and therefore be 
analyzed as (5a). By applying appropriate EFL-to- 
WML translation rules, the EFL expression (5a) would 
then be transformed into the WML expression (5b). 
Taking natural language at semantic face value thus 
simplifies the process of creating an initial meaning 
representation. The remaining question then is, 
whether one can in fact write EFL-to-WML translation 
rules which yield the desired results. This is the ques- 
tion we will come back to in section 4. In the 
remainder of the present section, we first give some 
more detail on the general properties of the translation 
rules and the logical languages. 
The interpretive rules which map syntactic struc- 
tures onto EFL expressions are compositional, i.e., 
they correspond in a direct way to the syntactic rules 
which define the legal input strings. There is a 
methodological reason for this emphasis on com- 
positionality: it makes it possible to guarantee that all 
possible combinations between syntactic rules are in 
fact covered by the interpretive rules, and to minimize 
surprises about the way the rules interact. Similar 
considerations apply when we think about the defini- 
tion of the EFL-to-WML translation: we wish to 
guarantee that the WML translations of every EFL 
expression are defined in an effectively computable 
way, and that the different rules which together 
specify the translation interact in a predictable lash- 
ion. This is achieved by specifying the EFL-to-WML 
translation using strictly Ioca/rules: rules operating 
only on constants, which specify for every EFt. con- 
slant the WML expressions that it translates into. 
Translation by means of local rules, which expand 
constants into complex expressions, tends to create 
fairly large and complicated formulas. The result of 
the EFL-to-WML translation is therefore processed by 
a logical simplification module; this keeps formulas 
from becoming too unwieldy to handle and impossible 
to evaluate. 
Local rules by themselves do not specify what 
combinations between them will lead to legitimate 
results. Since the rules can be applied independently 
of each other, we need a separate mechanism for 
checking the meaningfulness of their combined opera- 
lion. This mechanism is the semantic type system. 
EFL, WML and DBL are typed languages. This 
means that for every expression of these languages, 
a semantic type is defined. The denotation of an ex- 
pression is guaranteed to be a member of the set 
denoted by its type. In WML, for instance, 
FREDERICK has the type SHIPS which denotes the 
set of all ships; GUAM and INDIAN-OCEAN have the 
type LOCATIONS which denotes the set of all loca- 
tions; CARRIERS and SHIPS both have the type 
SETS(SHIPS) which denotes the powerset of the set 
of all ships; F-SPEED has the type 
FUNC TIONS(U(SHIPS, PLANES, LAND-VEHICLES), 
AMOUNTS(SPEED.UNITS)), 
which denotes the set of functions whose domain is 
the union of the sets of ships, of planes and of land 
vehicles, and whose range is the set of amount- 
expressions whose units are members of the set of 
speed-units. 
Given the types of the constants occurring in it, 
the type of a complex expression is determined by 
formal rules. For instance, the expression 
F-SPEED(FREDERICK) would have the type 
AMOUNTS(SPEED-UNITS). The rules which define 
the types of complex expressions also define when an 
expression does not have a legitimate type, and is 
therefore not considered to be a bona fide member of 
the language. For instance, F-SPEED(GUAM) does 
not have a legitimate type, because the type- 
computation rule for function-application expressions 
requires that the type of the argument not be disjoint 
with the domain of the function. 
The semantic type constraints make it possible to 
express the possible interpretations of ambiguous 
EFL constants by means of local translation rules, 
without running the danger of creadng spurious non- 
sensical combinations. For instance, if "Guam" were 
the name of a ship as well as the name of a location, 
there could be one EFL constant GUAM.EFL with 
two WML-expansions: GUAM-LOC with type 
LOCATIONS and GUAM-SHIP with type SHIPS. Ap- 
plying the EFL-to-WML rules to 
F-SPEED(GUAM-EFL) would nevertheless yield only 
one result, since the other combination would be 
deemed illegitimate. 
In the next section we show how relational noun 
denotations and EFL-to-WML translations may be 
chosen in such a way that sentences involving rela- 
tional nouns after an initially uniform treatment end up 
with plausible truth conditions - so that, for instance, 
(5) above can be initially analyzed as (5a) and then 
translated into (5b) in a principled way. 
4 MULTILEVEL SEMANTICS FOR 
RELATIONAL NOUNS 
The treatment we propose is based on a simple, 
yet powerful idea: analyse a relational noun as denot- 
ing the extension of the corresponding relation R (i.e., 
the set of pairs <x,y> such that R(x,y)), and allow 
predicates to apply not only to individuals but also to 
such pairs. 6 
As an example, consider again the phrase 
"Peter's sisters." that we discussed in section 1 
above, in the treatment we propose, this phrase 
would get the EFL analysis (6a). 
eTerminoiogy: We assume directed relation~ If <x.y> is a pair in a 
relation-extension, we call x the argument and y the value. 
28 
(6) "Peter's sisters" 
(6a) {x ~ R-SISTER / POSSESS(PETER,x)}, 
where R-SISTER, with the type 7 
U(MALES, FEMALES) X FEMALES, 
denotes the extension of the sister-relation, and 
where POSSESS has as one of its types: 
FUNCTIONS ((U(MALES, FEMALES) X FEMALES), 
TRUTHVALUES). 
(6a) can be transformed into a plausible expression 
for (6) by applying the translation rule: 
POSSESS ,,> ('A. u,v: u =v\[l\]) 
where u has type THINGS and v has type THINGS X 
THINGS. Applying this rule to (6a) yields after 
~reduction: 
(6b) {x e R-SISTER / PETER ,, x\[l\]}, 
which is equivalent to: 
(6c) {u,v / u = PETER & R-SISTER(u,v)} 
Thus, we see that by allowing the semantic trans- 
lation of "Peter's'to select over pairs consisting of a 
person and the sister of that person, we can end up 
with a representation of "Peter's sisters" which comes 
close to having the right denotation: it denotes the 
correct set of persons, but they are still paired up with 
Peter. This "extra information" is of course a problem. 
For instance, "Peter's sisters are Mary's aunts." as- 
serts the equality of two sets of persons, not two sets 
of pairs of parsons. 
it turns out that we have two distinct cases to deal 
with: to account for the interaction between a rela- 
tional noun and the phrases which indicate its ar- 
guments and values, we would like to treat it as 
denoting a relation-extension; but to account for its 
interaction with everything else, we would like to treat 
it as denoting a set of individuals. In order to make the 
relational treatment yield the right results, we must 
assume that part of the meaning of ordinary descrip- 
tive predicates is an implicit projection-operator, which 
projects tuples onto their value-elements. This is the 
solution we adopt. We formalize it by means of a 
meaning-postulate schema which applies to avery 
function F which is not among a small number of ex- 
plicitly noted exceptions: V x,y: F(x) =, F(<y,x>) 
The copula "be" is not an excep~on to this mean- 
ing postulate schema: it operates on values rather 
than relation-elements. This is the reason why "John" 
is not available as an argument for "brother" in (2ac) 
above ('Some punks of John's are brothers." "Some 
brothers are John's') 
We shall now consider the actual EFL-to-WML 
7Notation: A X B denotes the set of pairs <x.y> such that x is in 
the denotation of A and y is in the denotation of B. 
translation rules which handle the relational nouns in 
a little more detail. The EFL relations have many 
different translations into WML; which ones are 
relevant in a given case, is decided by considering the 
semantic types of the arguments to which they are 
applied. Consider again, for example, the part of the 
EFL-to-WML translation rules that deals with the inter- 
pretation of the possessive relation as specifying a 
relational argument, as in "Peter's sister', "Frederick's 
speed':. 
POSSESS -> ~. u,v: u ,, v\[l\]) 
where u has type THINGS and v has type THINGS X 
THINGS. Being a local translation rule, this rule could 
be applied to any occurrence of POSSESS in an EFL 
formula. However, many such applications would give 
rise to semantically anomalous WML formulas (with 
necessarily denotationless sub-expressions) which 
are filtered out if there are any other non-anomalous 
interpretations. For instance, the above rule for 
POSSESS would yield an anomalous expression if 
applied to the representation of "Peter's cars', be- 
cause the EFL constant CARS does not denote a set 
of pairs but a set of individual entities. It would also 
yield an anomalous expression if applied to "The USS 
Frsderick's sisters', because the type of the EFL con- 
stant FREDERICK, which is SHIPS, is disjoint with the 
argument type of R-SISTER, which is 
U(MALES, FEMALES). 
To avoid spurious generation of anomalous ex- 
pressions, the semantic types of the arguments of an 
EFL function or EFL relation are checked before the 
EFL-to-WML rule for that function or relation is ap- 
plied. For instance, the above rule for POSSESS will 
only be applied to an expression-of the form 
POSSESS(A,B), if A and B have types ¢¢ and ~ such 
that 
3P, Q: fJ,,PXQ & NON-EMPTY(atoP). 
As noted above, the interdefinability which exists 
between "have; "of', the genitive, and "wi/h', when 
they are used, for instance, in reference to ownership, 
carries over to their use for indicating the relation be- 
tween a relational noun and its argument. Thus, the 
EFL representations of "of', "have; and "w/th" have 
WML translations which, modulo the order of their ar- 
guments, are all identical to the rule for POSSESS 
discussed above. 
Function nouns, like "speed" and "length', induce 
a special interpretation on preposition phrases with 
"of'. Such phrases can be used to connect the func- 
tion noun with its va/ue. The treatment of relational 
nouns sketched in the previous section can also ac- 
commodate this phenomenon, as we shall show now. 
Consider example (7) below, which is identical to 
(5) above. It gets, in the treatment we propose, the 
EFL analysis (5a); this analysis is exactly analogous 
to the one that a syntactically similar sentence involv- 
ing a non-relational noun would get. (Cf. (4) and (4a).) 
29 
(7) "Frederick has a speed of 15 knots." 
(7a) 3 s • {s e F-SPEED 
/ OF(s, amount(15, KNOTS))}: 
HA VE(FREDERICK, s) 
It is the task of the EFL-to-WML translafion rules to 
define a transformation on EFL expressions which 
would turn (5a) into (5b) or a logically equivalent for- 
mula. 
(7b) F-SPEED(FREDERICK). 
amount(15, KNOTS) 
To achieve the desired result, we need a rule for 
HAVE which is precisely analogous to the rule for 
POSSESS above; and we need a rule for OFwhich is 
not analogous to the rule for POSSESS above: "a 
speed of 15 knots" is unlike "the speed of the USS 
Frederick" in that in the former case we must connect 
the relation with its value rather than its argument. 
The rule for OFthat we need here is as follows: 
OF => ~. u, v: u\[2\] = v) 
Note that different rules for one EFL constant can 
coexist without conflict, because of the assumption of 
lexical ambiguity in EFL. (In the general case, an EFL 
expression will have several WML expansions for this 
reason; often, many rule-applications will be blocked 
by semantic type-checking.) 
This basic approach makes it possible to trans- 
form the EFL representation of any of the construc- 
tions shown in the examples in section 1 into reason- 
able World Model Language and Data Base Lan- 
guago formulations of the intended query. We shall 
illustrate the process of applying the EFL-to-WML 
translations and logical simplifications in a little more 
detail while showing how to extend this treatment to 
function nouns which can take more than one ar- 
gument. Such nouns interact with specific kinds of 
preposition phrases to pick up their arguments. For 
instance: "Frederick's distance to Hawaii; "the dis. 
tance from Hawaii to Guam". As an example, we will 
now discuss the noun "readiness" as used in the U.S. 
Navy, which designates a two-argument function. 
"Readiness; as used in the Navy baffle manage- 
merit domain, refers to the degree to which a vessel - 
to be more precise, a unit - is prepared for combat or 
for a specific mission. This degree is indicated on a 
five-point scale, using either c-codes (C1 to C5), if 
referring to combat readiness, or m-codes (M1 to M5), 
if referring to mission readiness. The readiness for 
combat can furthermore be the overall readiness (the 
default case) or the readiness with respect to one of 
the four resource readiness areas: personnel, train- 
ing, equipment or supplies. Therefore, 
READINESS-OF is a function which maps two ar- 
guments, an element of SHIPS and an element of 
READINESS-AREAS, into READINESS-VALUES. 
Consider as an example the noun phrase "/he 
readiness of Frederick: If we ignore for the moment 
the effect of the "singular the" operator (see section 
5), its initial translation is: 
{x • READINESS-OF I OF(x, FREDERICK)} 
The parts of this expression are translated as follows. 
A logical transformation translates the function- 
constant READINESS-OF into the following equiv- 
alent expression, which will be convenient for sub- 
sequent processing: 
{x • domain (READINESS-OF) 
X range(READINESS-OF) 
/ READINESS-OF(x\[1\]), x\[2\]} 
which in its turn is equivalent to 
{x ~ (SHIPS X READINESS-AREAS) 
X READINESS.VALUES 
/ READINESS-OF(x\[ 1\]) = x\[2\]} 
The relation OF is eliminated in the EFL-to-WML 
transformation by a variant ~ of the translation rule 
mentioned above. It transforms 
OF(x, FREDERICK) into x\[1\]\[1\], FREDERICK 
The net result of these logical and descriptive trans- 
formations is the following expression: 
{x ~ {z • (SHIPS X READINESS-AREAS) 
X READINESS-VALUES 
/ READINESS-OF(# 1\]) ,, z\[2\]} 
/ #1\]\[1\] ,, FREDERICK} 
This expression is then simplified to: 
{z G ({FREDERICK~ X READINESS-AREAS) 
X READINESS-VALUES 
/ READINESS-OF(z\[1\]), z\[2\]} 
which in its turn can be transformed into a logically 
equivalent but more optimally evaluable expressions: 
(for: {FREDERICK} X READINESF-AREAS, 
apply: ~ x: <x, READINESS-OF(x)>)) 
(The actual system may apply further transformations 
(from WML into DBL), if it has to account for dis- 
crepancles between the database structure and the 
canonical domain model, possibly followed by further 
optJmizations at the DBL leveL) 
Other restrictions on "readiness; as in "the readi- 
ness o.n.n personnel', "the personnel readiness, or "a 
c l readiness', are handled in an analogous manner: 
ON -> ~u,v: u\[l\]\[2\],,v) 
PREMOD ,,> (~ u,v: u\[l\]\[2\] ,, v) 
PREMOD ,,> ~ u,v: u\[2\] - v) 
where PREMOD is the EFL translation of the elided 
relation in a noun-noun compound. (Note that if the 
same preposition is used with different nouns to mark 
different argument places, we need a more elaborate 
notation which identifies the arguments of a function 
by labels rather than by position.) 
*MuIti-an:jument func~ns are viewed as functions on n-tuplas. OF 
specifies, in this case, the first element of the argument-n-tuple. 
°Notation: (for: A. Iplldy: F) denotas the beg contmning the results 
of all applications of the function F to elements of the set A. 
30 
Because of the essentially local character of the 
descriptive transformations on HAVE, OF, ON, 
PREMOD, etc., and the completely general character 
of the simplifications dealing with intersections of sets 
and tuples, a small number of transformations (a few 
for each EFL relation) covers a wide variety of expres- 
sions. 
5 IMPLICIT ARGUMENTS. 
One or more of the arguments of a relation may 
be unspecified in the input sentence, while the intent 
of the utterance is nevertheless that a particular ar- 
gument should be filled in. The present section dis- 
cusses briefly how this issue can be dealt with during 
a phase of semantic processing which follows the 
EFL-to-WML translation. 
The most important case arises from the usa of 
definite descriptions in the English input sentence. 
The phrase *the readiness of Frederick", for instance, 
leads to an expression which has the operator "the" 
wrapped around the expression which represents 
"readiness(as) of Frederick'. "the" is a pragmatic 
operator, which selects the single most salient ele- 
ment out of the set that it operates on. 
Where the expression representing "readiness of 
Frederick on personnel" would denote a set contain- 
ing exactly one tuple, the expression representing 
"readiness of Frederick" denotes a set containing a 
number of different tuples: ones with EQUIPMENT, 
PERSONNEL, OVERALL, etc., filled in as the second 
argument, l=timinating the "the" operator consists in 
accessing a Discourse Model to find out which of the 
fillers of the second argument place is contextually 
most accessible. (We assume that available discourse 
referents are stored at every level of embedding in a 
recursive model of discourse surface structure, such 
as \[9\]). If none of the readiness areas were mentioned 
in an accessible discourse constituent, the system 
defaults to the "unmarked" readiness area, i.e., 
OVERALL 
Plural definite noun phrases are treated in a 
similar fashion. For instance, "the readineesas of 
Frederick" leads to an expression in which a prag- 
matic operator selects the contextually salient multiple 
element subset of the tuples in the extension of 
READINESS-OF which have FREDERICK as a first 
argument. In this case, if no particular subset of the 
readiness areas can be construed as a discourse 
referent, the system defaults to the assumption that 
here the overall readiness plus the four resource 
readinesses are intended. (Another possibility being 
the reference to the ship's readiness history:, a se- 
quence of past, current and projected future 
readinesses.) 
6 RELATION EXTENSIONS AS 
ANSWERS. 
The decision to treat relational nouns as denoting 
relation extensions has an immediate consequence, 
of some practical importance for question-answering 
systems, concerning the way in which wh-questions 
involving relational nouns are answered. For ex- 
ample, the request "List the speeds of the ships in 
the Indian Ocean." could be answered in three ways, 
of ascending informativeness: 1) with a set of speed 
values (possibly of smaller cardinality then the set of 
ships in the Indian Ocean) 2) with a bag of speed 
values (of the same cardinality as the set of ships) 
and 3) with a set of <ship, speed> ordered pairs, such 
that each ship is paired off with its speed. 
Clearly, 3) is most likely to be the desired 
response (although it is possible to envision situations 
where reponses 1) and 2) are desired). One cannot 
obtain this response, however, if the semantic trans- 
lation of the noun phrase "the speeds of the ships in 
the Indian Ocean" does not retain the information of 
which speed goes with which ship. An important ad- 
vantage of our approach to the relational noun 
problem is that it preserves this information, making 3) 
the normal reponse and 1 ) and 2) derivable from it. 
This may be compared to the "procedural 
semantics" approach to this same problem, as found 
in the work on LUNAR \[14\]. In this work, meaning is 
regarded as procedural in nature, and quantifications 
are represented in terms of nested iterations. The 
request "List the speeds of the ships in the In.an 
Ocean'would be represented as: 
(FOIt ~.L X / slrrps 
: (nl X ZNDT.3UI-OCLIkIB) 
; (~RZa'Jr (s~mm x) ) ) 
where the action of this representation would be to 
iterate over the class SHIPS, for each member 
checking to see if it is IN the INDIAN.OCEAN, and if 
so, printing its speed. The PRINT operator is made 
"smart" enough to detect the occurrence of the free 
vadable in its argument and to add in a printout the 
value of this variable for each iteration. 
Note that while this representation provides for the 
tuple response (3), and perhaps, if the "smartness" is 
made optional, for the bag response (2), the set 
response (1) would seem out of reach. In contrast, 
the approach this paper presents allows for all three, 
by generating as a default response the tuple set, and 
then optionally "projecting" on its second column. 
7 CONCLUSION 
Relational nouns are of primary importance for 
natural language interfaces to databases and expert 
systems, since they are commonly used to refer to 
database relations and to arithmetical functions. This 
paper has presented a treatment of relational nouns 
which manages to maintain uniformity and generality 
31 
at the level of syntactic analysis and initial semantic 
interpretation. This treatment has been incorporated 
into the semantic framework of BBN's Spoken Lan- 
guage System without writing additional LISP code. 
The semantic transformations necessary for the treat- 
ment are all carried out by general algorithms which 
were part of the pre-existing semantic framework. Im- 
plementing the treatment consisted in writing descrip- 
tive (EFL to WML) translation specifications for the 
EFL relations involved with function nouns, and a few 
dozen logical transformations to supplement the exist- 
ing set of simplifications. 
Further work on this topic should investigate how 
our perspective on relational nouns carries over to an 
account of the temporal and spatial modifiers that can 
be used with any noun. This will then make it possible 
to explore its connections with the work on the 
semantics of time-dependent nouns that has been 
done in the Montague-tradition. \[:3\] \[13\] 
ACKNOWLEDGMENTS 
We thank David Stallard for important contribu- 
tions to the ideas presented here; Jan Landsbergen 
for his share in the development of the conceptual 
framework that inspired this research; Damaris Ayuso 
and Scan Boisen for their assistance in applying our 
results to BBN's Spoken Language System. 
\[1\] 
\[2\] 
\[3\] 
\[4\] 
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32 
