The Interpretation of Relational Nouns

THE INTERPRETATION OF RELATIONAL NOUNS

Joe de Bruin" and Remko Scha

BBN Laboratories 10 Mouiton Street Cambridge, MA 02238, USA

ABSTRACT we shall see in a moment, their semantic properties differ significantly from those of other nouns, so that This paper 1 decdbes a computational treatment of the standard treatments of nominal semantics don't the semantics of relational nouns. It covers relational apply to them. The problem of the semantic inter- nouns such as "sister.and "commander; and focuses pretation of relational nouns constitutes the topic of especially on a particular subcategory of them, called this paper. We shall argue that this problem is indeed function nouns ('speed; "distance', "rating'). Rela- a semantic one, and should preferably not be treated tional nouns are usually viewed as either requiring in the syntax. The semantic treatment that we present non-compositional semantic interpretation, or causing uses a multilevel semantics framework, and is based an undesirable proliferation of syntactic rules. In con- on the idea of assigning relation extensions as trast to this, we present a treatment which is both denotations to relational nouns. syntactically uniform and semantically compositional. The core ideas of this treatment are: (1) The recog- Relational nouns are semantically unsaturated. nition of different levels of semantic analysis; in par- They are normally used in combination with an implicit ticular, the distinction between an English-oriented or explicit argument: "John's brother.. The argument and a domain-oriented level of meaning represen- of a relational noun, if overtly realized in the sentence, tation. (2) The analysis of relational nouns as denoting is connected to the noun by means of a relation- relation-extensions. denoting lexical element: the verb "have" or one of its semantic equivalents (the geni~ve and the preposi- The paper shows how this approach handles a tions "of" and "with): "John has a sister', "John's variety of linguistic constructions involving relational sister; "a sister of John's; "a boy with a sister" It has nouns. The treatment presented here has been im- been noted that these lexical items interact differently plemented in BBN's Spoken Language System, an with relational nouns than they do with other nouns. experimental spoken language interface to a [7] Compare, for instance, the noun "car" in database/graphics system. (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 RELATIONAL NOUNS AND THEIR (1) "John's cars are wrecks." DENOTATIONS (la) "Some wrecks of John's are cars." When Jean Piaget faced his nine year old subject ( l b) "Some wrecks are John's." Hal with the question ~/Vhat's a brother?; the answer (1 c) "Some ca~ are John "S. " was: "When there's a boy and another boy, when ( l d) "John has wrecks." there are two of them." And, with a greater degree of formal precision, ten year old Bern replied to the same (2) "John's brothers are punks." question: ",4 brother is a relation, one brother to #(2a) "Some punks of John's are brothers." another. "[2] [8] What these children are beginning to #(2b) "Some punks are John's." be able to articulate is that there is something wrong #(2c) "Some brothers are John's." with the experimenter's question as it is posed: it talks #(2d) "John has punks." about "brothers" as if they constituted a natural kind, as if there is a way of looking at an individual to find A particular subcategory of the relational nouns, out whether he is a brother. But "brother" is normally that we shall consider in some detail, is constituted by not used that way - a property which it shares with the function nouns; they are semantically distinct in words like "co-author; "commander', "speed', that for every argument they refer to exactly one en- "distance', and "rating'. tity, which is an element of a linear ordering: a hum- Nouns of this sort are called relational nouns. As

ZWe refrain from saying that (2abod) are ungrammatical. Because of the semantic open-endedness of "have" and the genitivQ, these 1This research was supported by the Advanced Research Projects sentences can certainly be wellformod and meaningful, if uttored in Agency of the Depmlment of Defense under Contract No, an appropriate context. The issue at stake is that the inteqDreta~on NO0014-87-C-0(~5. whic~ is the saJient one for the genitive in (2) is not avaUable for the ¢ommponciing elements in (2abcd). Sentences displaying this "Current address: Cartesian Products BV, WG Plem 316, 1054 SG property have been marked with the #-sign (rathor than the Amsterdam, The Nathedands. ungrammoticality-aotorisk) in this paper.

25 bet, an amount, or a grade. Examples are "length", 2 AGAINST SYNTACTIC TREATMENTS "speed', "distance", "rating". Function nouns can be Often, the complexities mentioned above are used in constructions which exclude other nouns, taken to require a distinction between intransitive relational as well as non-relational. Compare, for in- common nouns and transitive common nouns in the stance: syntax, with a concommittant proliferation of syntactic (3) "The USS Frederick has a speed of 15 knots." rules. Instead, we have chosen to extend a treatment #(3a) "John has a car of ~is wreck." of "ordinary" nouns only at the semantic processing #(3b) "John has a brolher of Peter." stage. We shall now indicate some of the reasons for this choice. The examples above show that there are sig- nificant semantic differences between phrases con- Relational nouns are semantically dependent on necting relational nouns to their functions/values, and an argument. In this respect, they are more reminis- the corresponding, similarly structured phrases built cent of verbs than ot standard nouns like "boy" or around other nouns. This suggests that the standard "chair'. Most verbs of English have one or more ar- treatment of ordinary nouns cannot be applied directly gument places that must be filled for the verb to be to relational nouns and yield correct results. To con- used in a syntactically/semantically felicitous way; this clude this introductory section, we investigate this is- property of verbs is probably an important reason for sue in a little more detail. the persisting tendency to analyze them as n-place predicates rather than sets of situations. The semantic Assume a semantic framework with the following, similarity between relational nouns and verbs has not very unusual, features. Nouns are analyzed as given rise to treatments which model the syntactic set-denoting constants; concomitantly, adjectives are treatment of nouns on the treatment of verbs: one analyzed as one-place predicates, prepositions as introduces lexical subcategories for nouns which in- two-place predicates, verbs as n-place predicates. dicate how many arguments they take and how these Plural noun phrases with "the" or a possessive denote arguments are marked; the syntactic rules combine sets which have the same semantic type as the noun N-bara or noun-phrases with genitive phrases and around which they are built: "John's cars" denotes a preposition-phrases, taking these subcategorizations particular set of cars. In this approach, the represen- into account. [15] We will now argue, however, that tation of the noun phrase "Peter's s/stern'would be: from a syntactic point of view such a move is unattrac- five. {x • SISTERS / POSSESS(PETER, x)}, where SISTERS denotes the set of persons who are a Syntactically, relational nouns do not behave very sister, and POSSESS represents the possessive rela- differentJy from "ordinary" nouns. They combine with tion indicated by the genitive construction. adjectives, determiners, preposition phrases and rela- five clauses to form noun phrases with a standard Now this expression does not have the right X-bar structure; and the noun phrases thus con- properties. It lacks necessary information: the predi- stituted can pa~cipate in all sentence-level structures cate ~ x: POSSESS(PETER, x)) applies to elements that other noun phrases partake in. of the extension of SISTERS; it cannot take into account how this extension was defined. For instance, if Also, no nouns have syntactic properties that in a pa~cular world the set of sisters is co-extensional would be analogous to the sentenco-levei with the set of coauthors, the approach just outlined phenomenon of a verb obligatorily taking one or more would incorrectly assign to "Peter's sisters" the same arguments. The overt realization of the arguments of denotation as to "Peter's co-aulhors". a "transitive noun" is always optional. It is clear what the source of the problem is: the Finally, we may note that relational nouns can be semantic representations for relational nouns con- connected to their arguments/values by a variety of sidered above denote simple sets of individuals, and verbs and prepositions, which constitute a semantic do not contain any information about the relation in- complex that is also used, with exactly the same volved. To salvage a uniform compositional treatment, structure but with a different meaning, to operate on a richer representation is needed. One might think of non-relational nouns. Compare, for instance: invoking Montague's individual concepts [3] [6], or en- "The Chevrolet of Dr. Johnson" riching one's ontology with qua-individuals / "The speed of Frederick" (distinguishing between Mary qua sister and Mary qua "Dr. Johnson's Chevrolet" aunt) [4]. In section 4 we will present our solution to / "Frederick's speed ~ this problem. First, we discuss why we didn't choose "The Chevrolet that Dr. Johnson has" for a more syntactically oriented approach. / "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 English. A feature of EFL which is both unusual and the relation between a function and its argument. important, is the fact that descriptive constants are These terms (like "of', "have" and "with" ) are highly allowed to be ambiguous. Within each syntactic cats- polysemous, and any language processing system gory, every word is represented in EFL by a single must encompass mechanisms for disambiguating descriptive constant, no matter how many senses the their intended meaning in any particular utterance. word may have. An EFL expression can thus be seen as an expression schema, where every constant can To summarize: relational nouns do not distinguish be expanded out in a possibly large number of dif- themselves syntactically from other nouns, and they ferent ways. (See [5] for details on the model theory mark their function-argument structures by means of of such a logic.) polysemous descriptive terms. We therefore conclude that it would be theoretically elegant as well as com- The ambiguity of EFL follows from its domain- putationaily effective to treat relational and non- independence. All descriptive words of a language are relational nouns identically at the syntactic level, and polysernous, and only when used in the context of a to account for the semantics of relational noun con- particular subject domain do they acquire a single structions by exploiting independently motivated dis- precise meaning - a meaning which cannot be articu- ambiguation mechanisms. The remainder of this lated independently of that subject domain. Even paper describes such a treatment. within one subject domain, many words have a range of different meanings. Joint representations for such First, Section 3 discusses the multilevel semantics sets of possible expansions are computationaJly ad- architecture which constitutes the framework for our vantageous; and when the range of possibilities is approach. Section 4 presents our answer to a basic defined in an open-ended way, they are even neces- question about relational nouns: what should their sary. Such cases occur when we attempt to account denotations be? This section then goes on to for the interpretation of metonymy, metaphor and describe the semantic transformations which derive nominal compounds [12], or the interpretation of mul- the desired analyses of constructions involving rela- tilevel plural noun phrases [11]. tional nouns. Section 5 briefly discusses the interface with a Discourse Model, which is necessary to recover The logical language used at the domain- arguments of a relation that are left implicit in an ut- dependent level of representation is called the World terance. Section 6 shows that our treatment is useful Mode/Language (WML). This is an unambiguous lan- for the purpose of response-formulation in question- guage, with an ordinary model-theoretic interpretation. answering. Its constants are chosen to correspond to the concepts which cons~tute the domain of discourse.4 We can illustrate the distinction between EFL and 3 MULTILEVEL SEMANTICS. WML by means of an example involving relational Our approach to the problem of relation~d nouns is noiJns. Compare (4) and (5) below. Sentence (4) will based on the idea of multilevel semantics, the distinc- usually be translated into something like (4a): s tion between different levels of semantic analysis. (4) "John has a house in Hawaii." [1] [10] In this approach, interpreting a natural language sentence is a multi-stage process, which starts (4a) 3 he {he HOUSES/IN(h,HAWAII)}: HA VE(JOHN, h) out with a high-level meaning representation which reflects the semantic structure of the English sentence Now consider (5) instead; a single-level architecture rather directly, and then applies translation rules would have to analyse this sentence as (5b) rather which specify how the English-oriented semantic than (Sa), since (5b) is the representation one would primitives relate to the ones that are used at deeper prefer to end up with. levels of analysis. (5) "Frederick has a speed of 15 knots." At every level of analysis, the meaning of an input (Sa) "~ c ~ {c e SPEEDS utterance is represented as an expression of a logical / OF(c, amount(15, KNOTS))}: language.3 The languages used at the various levels HA VE(FREDERICK, c) 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. 4To provide a smooth interface with underlying applicationsys- At the highest semantic level, the meaning of an tems, there is a third level of semantic interpretation.The language input utterance is represented as an expression of the used at this level is called the Data Base Language (DBL). Its Eng/ish-oriented Formal Language (EFL). The con- constants stand for the fites and attributes of the _,~tP_t'.,~e_ [o be accessed, and the avaiiablegraphics system opemUonsand their stants of EFL correspond to the descriptive terms of parameters. SAccommoda~ng discourse anaphore may motivate a different treatmentof the indefinitenoun phrase, repre~mtingits semanticsby 3BBN's Siren LanguageSystem uses a higher-o~erintensienel a Skelem-constantor a similer device, ratherthan by the traditional logic hased on Church's iaffC.3~Pcak:ulus,comDining fe~oJre6 from existentialquantifier. For the presentdiscussion we may ignorethis PHLIQA'slogical language[5] with Montague'$Intensionel Logic [6]. issue.

2? (Sb) F-SPEED(FREDERICK). amount(15, KNOTS) FUNC TIONS(U(SHIPS, PLANES, LAND-VEHICLES), AMOUNTS(SPEED.UNITS)), In a multilevel semantics architecture, however, one would prefer to maintain a completely uniform first which denotes the set of functions whose domain is stage in the semantic interpretation process, where the union of the sets of ships, of planes and of land (5) would be treated exactly as (4), and therefore be vehicles, and whose range is the set of amount- analyzed as (5a). By applying appropriate EFL-to- expressions whose units are members of the set of WML translation rules, the EFL expression (5a) would speed-units. then be transformed into the WML expression (5b). Given the types of the constants occurring in it, Taking natural language at semantic face value thus the type of a complex expression is determined by simplifies the process of creating an initial meaning formal rules. For instance, the expression representation. The remaining question then is, F-SPEED(FREDERICK) would have the type whether one can in fact write EFL-to-WML translation AMOUNTS(SPEED-UNITS). The rules which define rules which yield the desired results. This is the ques- the types of complex expressions also define when an tion we will come back to in section 4. In the expression does not have a legitimate type, and is remainder of the present section, we first give some therefore not considered to be a bona fide member of more detail on the general properties of the translation the language. For instance, F-SPEED(GUAM) does rules and the logical languages. not have a legitimate type, because the type- The interpretive rules which map syntactic struc- computation rule for function-application expressions tures onto EFL expressions are compositional, i.e., requires that the type of the argument not be disjoint they correspond in a direct way to the syntactic rules with the domain of the function. which define the legal input strings. There is a The semantic type constraints make it possible to methodological reason for this emphasis on com- express the possible interpretations of ambiguous positionality: it makes it possible to guarantee that all EFL constants by means of local translation rules, possible combinations between syntactic rules are in without running the danger of creadng spurious non- fact covered by the interpretive rules, and to minimize sensical combinations. For instance, if "Guam" were surprises about the way the rules interact. Similar the name of a ship as well as the name of a location, considerations apply when we think about the defini- there could be one EFL constant GUAM.EFL with tion of the EFL-to-WML translation: we wish to two WML-expansions: GUAM-LOC with type guarantee that the WML translations of every EFL LOCATIONS and GUAM-SHIP with type SHIPS. Ap- expression are defined in an effectively computable plying the EFL-to-WML rules to way, and that the different rules which together F-SPEED(GUAM-EFL) would nevertheless yield only specify the translation interact in a predictable lash- one result, since the other combination would be ion. This is achieved by specifying the EFL-to-WML deemed illegitimate. translation using strictly Ioca/rules: rules operating only on constants, which specify for every EFt. con- In the next section we show how relational noun slant the WML expressions that it translates into. denotations and EFL-to-WML translations may be chosen in such a way that sentences involving rela- Translation by means of local rules, which expand tional nouns after an initially uniform treatment end up constants into complex expressions, tends to create with plausible truth conditions - so that, for instance, fairly large and complicated formulas. The result of (5) above can be initially analyzed as (5a) and then the EFL-to-WML translation is therefore processed by translated into (5b) in a principled way. a logical simplification module; this keeps formulas from becoming too unwieldy to handle and impossible to evaluate. 4 MULTILEVEL SEMANTICS FOR Local rules by themselves do not specify what RELATIONAL NOUNS combinations between them will lead to legitimate The treatment we propose is based on a simple, results. Since the rules can be applied independently yet powerful idea: analyse a relational noun as denot- of each other, we need a separate mechanism for ing the extension of the corresponding relation R (i.e., checking the meaningfulness of their combined opera- the set of pairs such that R(x,y)), and allow lion. This mechanism is the semantic type system. predicates to apply not only to individuals but also to EFL, WML and DBL are typed languages. This such pairs. 6 means that for every expression of these languages, As an example, consider again the phrase a semantic type is defined. The denotation of an ex- "Peter's sisters." that we discussed in section 1 pression is guaranteed to be a member of the set above, in the treatment we propose, this phrase denoted by its type. In WML, for instance, would get the EFL analysis (6a). 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 locations; CARRIERS and SHIPS both have the type eTerminoiogy:We assumedirected relation~ If is a pair in a SETS(SHIPS) which denotes the powerset of the set relation-extension,we call x the argumentand y the value. of all ships; F-SPEED has the type

28 (6) "Peter's sisters" translation rules which handle the relational nouns in (6a) {x ~ R-SISTER / POSSESS(PETER,x)}, a little more detail. The EFL relations have many different translations into WML; which ones are where R-SISTER, with the type7 relevant in a given case, is decided by considering the U(MALES, FEMALES) X FEMALES, semantic types of the arguments to which they are applied. Consider again, for example, the part of the denotes the extension of the sister-relation, and EFL-to-WML translation rules that deals with the inter- where POSSESS has as one of its types: pretation of the possessive relation as specifying a relational argument, as in "Peter's sister', "Frederick's FUNCTIONS ((U(MALES, FEMALES) X FEMALES), speed':. TRUTHVALUES). POSSESS -> ~. u,v: u ,, v[l]) (6a) can be transformed into a plausible expression for (6) by applying the translation rule: where u has type THINGS and v has type THINGS X THINGS. Being a local translation rule, this rule could POSSESS ,,> ('A.u,v: u =v[l]) be applied to any occurrence of POSSESS in an EFL formula. However, many such applications would give where u has type THINGS and v has type THINGS X rise to semantically anomalous WML formulas (with THINGS. Applying this rule to (6a) yields after necessarily denotationless sub-expressions) which ~reduction: are filtered out if there are any other non-anomalous (6b) {x e R-SISTER / PETER ,, x[l]}, interpretations. For instance, the above rule for POSSESS would yield an anomalous expression if which is equivalent to: applied to the representation of "Peter's cars', be- (6c) {u,v / u = PETER & R-SISTER(u,v)} cause the EFL constant CARS does not denote a set of pairs but a set of individual entities. It would also Thus, we see that by allowing the semantic trans- yield an anomalous expression if applied to "The USS lation of "Peter's'to select over pairs consisting of a Frsderick's sisters', because the type of the EFL con- person and the sister of that person, we can end up stant FREDERICK, which is SHIPS, is disjoint with the with a representation of "Peter's sisters" which comes argument type of R-SISTER, which is close to having the right denotation: it denotes the U(MALES, FEMALES). correct set of persons, but they are still paired up with Peter. This "extra information" is of course a problem. To avoid spurious generation of anomalous ex- For instance, "Peter's sisters are Mary's aunts." as- pressions, the semantic types of the arguments of an serts the equality of two sets of persons, not two sets EFL function or EFL relation are checked before the of pairs of parsons. EFL-to-WML rule for that function or relation is applied. For instance, the above rule for POSSESS will it turns out that we have two distinct cases to deal only be applied to an expression-of the form with: to account for the interaction between a rela- POSSESS(A,B), if A and B have types ¢¢ and ~ such tional noun and the phrases which indicate its ar- that guments and values, we would like to treat it as denoting a relation-extension; but to account for its 3P, Q: fJ,,PXQ & NON-EMPTY(atoP). interaction with everything else, we would like to treat it as denoting a set of individuals. In order to make the As noted above, the interdefinability which exists relational treatment yield the right results, we must between "have; "of', the genitive, and "wi/h', when assume that part of the meaning of ordinary descrip- they are used, for instance, in reference to ownership, tive predicates is an implicit projection-operator, which carries over to their use for indicating the relation be- projects tuples onto their value-elements. This is the tween a relational noun and its argument. Thus, the solution we adopt. We formalize it by means of a EFL representations of "of', "have; and "w/th" have meaning-postulate schema which applies to avery WML translations which, modulo the order of their ar- function F which is not among a small number of ex- guments, are all identical to the rule for POSSESS plicitly noted exceptions: V x,y: F(x) =, F() discussed above. The copula "be" is not an excep~on to this mean- Function nouns, like "speed" and "length', induce ing postulate schema: it operates on values rather a special interpretation on preposition phrases with than relation-elements. This is the reason why "John" "of'. Such phrases can be used to connect the func- is not available as an argument for "brother" in (2ac) tion noun with its va/ue. The treatment of relational above ('Some punks of John's are brothers." "Some nouns sketched in the previous section can also ac- brothers are John's') commodate this phenomenon, as we shall show now. We shall now consider the actual EFL-to-WML 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- 7Notation: A X B denotes the set of pairs such that x is in ing a non-relational noun would get. (Cf. (4) and (4a).) the denotationof A and y is in the denotationof B.

29 (7) "Frederick has a speed of 15 knots." {x • READINESS-OF I OF(x, FREDERICK)} (7a) 3 s • {s e F-SPEED The parts of this expression are translated as follows. / OF(s, amount(15, KNOTS))}: A logical transformation translates the function- HA VE(FREDERICK, s) constant READINESS-OF into the following equiv- It is the task of the EFL-to-WML translafion rules to alent expression, which will be convenient for sub- define a transformation on EFL expressions which sequent processing: would turn (5a) into (5b) or a logically equivalent formula. {x • domain (READINESS-OF) X range(READINESS-OF) (7b) F-SPEED(FREDERICK). / READINESS-OF(x[1]), x[2]} amount(15, KNOTS) which in its turn is equivalent to To achieve the desired result, we need a rule for HAVE which is precisely analogous to the rule for {x ~ (SHIPS X READINESS-AREAS) POSSESS above; and we need a rule for OFwhich is X READINESS.VALUES not analogous to the rule for POSSESS above: "a / READINESS-OF(x[ 1]) = x[2]} speed of 15 knots" is unlike "the speed of the USS The relation OF is eliminated in the EFL-to-WML Frederick" in that in the former case we must connect transformation by a variant~ of the translation rule the relation with its value rather than its argument. mentioned above. It transforms The rule for OFthat we need here is as follows: OF(x, FREDERICK) into x[1][1], FREDERICK OF => ~. u, v: u[2] = v) The net result of these logical and descriptive trans- Note that different rules for one EFL constant can formations is the following expression: coexist without conflict, because of the assumption of lexical ambiguity in EFL. (In the general case, an EFL {x ~ {z • (SHIPS X READINESS-AREAS) expression will have several WML expansions for this X READINESS-VALUES reason; often, many rule-applications will be blocked / READINESS-OF(# 1]) ,, z[2]} by semantic type-checking.) / #1][1] ,, FREDERICK} This expression is then simplified to: This basic approach makes it possible to trans- form the EFL representation of any of the construc- {z G ({FREDERICK~ X READINESS-AREAS) tions shown in the examples in section 1 into reason- X READINESS-VALUES able World Model Language and Data Base Lan- / READINESS-OF(z[1]), z[2]} guago formulations of the intended query. We shall which in its turn can be transformed into a logically illustrate the process of applying the EFL-to-WML equivalent but more optimally evaluable expressions: translations and logical simplifications in a little more detail while showing how to extend this treatment to (for: {FREDERICK} X READINESF-AREAS, function nouns which can take more than one ar- apply: ~ x: )) gument. Such nouns interact with specific kinds of (The actual system may apply further transformations preposition phrases to pick up their arguments. For (from WML into DBL), if it has to account for dis- instance: "Frederick's distance to Hawaii; "the dis. crepancles between the database structure and the tance from Hawaii to Guam". As an example, we will canonical domain model, possibly followed by further now discuss the noun "readiness" as used in the U.S. optJmizations at the DBL leveL) Navy, which designates a two-argument function. Other restrictions on "readiness; as in "the readi- "Readiness; as used in the Navy baffle manage- ness o.n.npersonnel', "the personnel readiness, or "a merit domain, refers to the degree to which a vessel - c l readiness', are handled in an analogous manner: to be more precise, a unit - is prepared for combat or for a specific mission. This degree is indicated on a ON -> ~u,v: u[l][2],,v) five-point scale, using either c-codes (C1 to C5), if PREMOD ,,> (~ u,v: u[l][2] ,, v) referring to combat readiness, or m-codes (M1 to M5), PREMOD ,,> ~ u,v: u[2] - v) if referring to mission readiness. The readiness for where PREMOD is the EFL translation of the elided combat can furthermore be the overall readiness (the relation in a noun-noun compound. (Note that if the default case) or the readiness with respect to one of same preposition is used with different nouns to mark the four resource readiness areas: personnel, train- different argument places, we need a more elaborate ing, equipment or supplies. Therefore, notation which identifies the arguments of a function READINESS-OF is a function which maps two ar- by labels rather than by position.) guments, an element of SHIPS and an element of READINESS-AREAS, into READINESS-VALUES. Consider as an example the noun phrase "/he *MuIti-an:jumentfunc~ns are viewedas functions on n-tuplas. OF specifies, in this case, the first elementof the argument-n-tuple. readiness of Frederick: If we ignore for the moment the effect of the "singular the" operator (see section °Notation: (for: A. Iplldy: F) denotasthe beg contmningthe results 5), its initial translation is: of all applicationsof the functionF to elementsof the set A.

30 Because of the essentially local character of the 6 RELATION EXTENSIONS AS descriptive transformations on HAVE, OF, ON, ANSWERS. PREMOD, etc., and the completely general character The decision to treat relational nouns as denoting of the simplifications dealing with intersections of sets relation extensions has an immediate consequence, and tuples, a small number of transformations (a few of some practical importance for question-answering for each EFL relation) covers a wide variety of expres- systems, concerning the way in which wh-questions sions. involving relational nouns are answered. For example, the request "List the speeds of the ships in the Indian Ocean." could be answered in three ways, 5 IMPLICIT ARGUMENTS. of ascending informativeness: 1) with a set of speed One or more of the arguments of a relation may values (possibly of smaller cardinality then the set of be unspecified in the input sentence, while the intent ships in the Indian Ocean) 2) with a bag of speed of the utterance is nevertheless that a particular ar- values (of the same cardinality as the set of ships) gument should be filled in. The present section dis- and 3) with a set of ordered pairs, such cusses briefly how this issue can be dealt with during that each ship is paired off with its speed. a phase of semantic processing which follows the Clearly, 3) is most likely to be the desired EFL-to-WML translation. response (although it is possible to envision situations The most important case arises from the usa of where reponses 1) and 2) are desired). One cannot definite descriptions in the English input sentence. obtain this response, however, if the semantic trans- The phrase *the readiness of Frederick", for instance, lation of the noun phrase "the speeds of the ships in leads to an expression which has the operator "the" the Indian Ocean" does not retain the information of wrapped around the expression which represents which speed goes with which ship. An important ad- "readiness(as) of Frederick'. "the" is a pragmatic vantage of our approach to the relational noun operator, which selects the single most salient ele- problem is that it preserves this information, making 3) ment out of the set that it operates on. the normal reponse and 1 ) and 2) derivable from it. Where the expression representing "readiness of This may be compared to the "procedural Frederick on personnel" would denote a set contain- semantics" approach to this same problem, as found ing exactly one tuple, the expression representing in the work on LUNAR [14]. In this work, meaning is "readiness of Frederick" denotes a set containing a regarded as procedural in nature, and quantifications number of different tuples: ones with EQUIPMENT, are represented in terms of nested iterations. The PERSONNEL, OVERALL, etc., filled in as the second request "List the speeds of the ships in the In.an argument, l=timinating the "the" operator consists in Ocean'would be represented as: accessing a Discourse Model to find out which of the (FOIt ~.L X / slrrps fillers of the second argument place is contextually : (nl X ZNDT.3UI-OCLIkIB) most accessible. (We assume that available discourse ; (~RZa'Jr (s~mm x) ) ) referents are stored at every level of embedding in a recursive model of discourse surface structure, such where the action of this representation would be to as [9]). If none of the readiness areas were mentioned iterate over the class SHIPS, for each member in an accessible discourse constituent, the system checking to see if it is IN the INDIAN.OCEAN, and if defaults to the "unmarked" readiness area, i.e., so, printing its speed. The PRINT operator is made OVERALL "smart" enough to detect the occurrence of the free vadable in its argument and to add in a printout the Plural definite noun phrases are treated in a value of this variable for each iteration. similar fashion. For instance, "the readineesas of Frederick" leads to an expression in which a prag- Note that while this representation provides for the matic operator selects the contextually salient multiple tuple response (3), and perhaps, if the "smartness" is element subset of the tuples in the extension of made optional, for the bag response (2), the set READINESS-OF which have FREDERICK as a first response (1) would seem out of reach. In contrast, argument. In this case, if no particular subset of the the approach this paper presents allows for all three, readiness areas can be construed as a discourse by generating as a default response the tuple set, and referent, the system defaults to the assumption that then optionally "projecting" on its second column. here the overall readiness plus the four resource readinesses are intended. (Another possibility being the reference to the ship's readiness history:, a se- 7 CONCLUSION quence of past, current and projected future Relational nouns are of primary importance for readinesses.) 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

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