Grammatical Functions, Discourse, Referents, and Quantification

ABSTRACI'

A new algorlthm is proposed which trsnsfoms f-structures into discrurse representatian structures (IRSs) · Its pri!IBry festures are that it woiks l:ottan up, that it is capable of translating f-structures witrout preinposing sny arbl.trary onler an the attributes occurring in it, snd that it harxll.es inietenninacy of scoping by using sets of trsnslations. The approach sheds light on h:Jw' an efficient interaction of different canponents of a natural 1.anguage processing mxlel can be achieved.

I INJ:roDUCITOO *)

1be infoiiDStional content of a sentence is detennined rot only by its linguistic fonn, but also by a IJJDi>er of contextual factors. Thus within sny canpositional approach to SEmllltics the control structure for the functional canpositian DliSt rot be detennired exclusively by the syntactic structure of the phrase. The present approach is bised an two 1evela of representatian, that 'mediate' between the linguistic fonn of a sentence snd ita deootation(s) (in a mxlel).

F-structures constitute the first level. They have the property that the unraveling of the granmatical roles of a sentence is already achieved, l>hl.l.e the qusntifier scope relations are rot yet represented. This is bisically due to the use of granmatical functions as theoretical primitives ([1],[3]).

The secoo:i level accounts for the dependency of ( the construction of the interpretstian) of a sentence on factors which are not purely syntactic. It consists of IRSs in v.hlch the scope relations will be treated. The central property of IRSs is that the part of sentence or text fran v.hlch they derive acts as a context wtdch guides the interpretstion of the parts foll.OO.ng it. This property of DRSs is based DBinly on their containing discourse referents ( [ 4]). It l.esds to a dynamic creation of interpretations of sentences.

We will sh:Jw' h:Jw' to foiiilllate a trsnslatian mechanism ~.nich al.lcMI for arbl.trary scope relations rot only within the limit of a clause tUJciaJs but also w.f.thin the various cl.ause ruclei in which an NP can play a role by ueans of functional control. Possible ~tactic scope restrictions can thus be licensed by additional constraints derived fran various other features of the surface string, the SEmllltics, or pragoatics.

The central feature of the trsnslation algoritlm is, loosely speaking, to replace the granmatical functions in the f-structure by the discourse referents v.hlch have been made available (for subsequent reference) by the values of the granmatical functions, i.e. the f-structures representing NPs. These f-structures themselves are translated into IRSs v.hlch are partial in the sense that there are (in general) still

*) This work has been supported in psrt by DFG mder grant R0245/13 snd ESPRIT mder grant AroRD.

l.Jiole Reyle Department of Linguistica University of Stuttgart r,.eg t Geiiii!Il;Y

conditions or sub-IRSs mi.ssing in order to be interpretable. We w.f.ll define SODe principles for the trsnslation into snd caq>letian of partial DRSs.

II EXAMPLE

But before stating the exact definitions let us illustrate the algoritlm by

(1) Evecy boy loves a girl

In order to give a graphic representatian of · the interplay between syntax snd semantics -we will represent f-structures as directed acyclic graphs (dag), the oodes Ci of v.hlch are associated with the translations of the f-structures rooted in Ci. The procedure works l:ottan-up (i.e. fran inside the f-structures out). First, -we associate with every 1eaf node a partial IRS as follows (mald.ng use of sane >,-notation):

After ordinary >.-conversian of the SPEC-PRID canbinations in the sub-dags of SUBJ snd OBJ -we get

TransfoiiDStian of this dag into a tree is achieved by splitting the oodes wtdch are the values of the granmatical functions snd ARGi so that the discourse referents occurring in the partial DRSs are associated w.f.th the new oodes of the ARGi attributes snd the partial IRSs themselves with the oodes of the granmatical functions:

After pnming the attributes -we get the following set of expressions which is to be associated with the root rode of the tree.

This set allows for tw different sequences of >.-conversion, yielding the tw desired readings

The example srows that ~ have to foilllllate tw principles, one for the transduction of the dag into a tree, the other for calculating the partial translation of an arb:l.trary non-terminal tree node given the partial translations associated with its daughter nodes. Both principles will be local in the sense that only local trees and dags are used in their foilllllation.

III THE AiroRITilM

First ~ have to give the precise definition of partial DRSs. The usual definition of a DRS K as a pair consisting of a set of discourse referents U(K) and a set of conditions CXJN(K), tagether with Kamp's accessiblility relation (cf. [4]), allows for the abstraction of discourse referents, predicates and (sets of) conditions. We therefore define partial DRSs inductively as follows.

Def. (a) Every DRS K = <U(K),CXJN(K)) is a partial DRS (b) If u is a discourse referent occurring in oonditions cl, ··· ,cn of CXJN(K) b.Jt not in any of the universes that are

accessible fran K, then

,\uK = <U(K),,\umN(K)> is a partial DRS, "1\lhere

,\uOON(K) = {,\ucili=l, ··· n} u ffiN(K)\{cili=l, ··· ,n}.

(c) If P is a variable over partial DRSs of the form ,\uK' with u and cl, ··· ,cn as under (b), then ,\PK = AP<lJ(K), mN(K) u P(u)> is a partial DRS.

(d) If Q is a variable over DRSs, then

AQ = ,\Q<U(K),aN(K) u Q> isapartial DRS.

Suppose now ~ have a sanantic interpretation schana with attrib.Jte naDES ATrRl, ··· ,ATIRn

"1\lhere the translations Cl', ··· ,Cn' are already given as sets of partial DRSs. Suppose further that Cl', ··· ,Cn' are singletons, i.e. contain exactly one partial DRS. Then (X)' is calculated fran than by the following principle.

F\mctional application principle for sets of partial DRSs Given a set KK = {Kl, ··· ,Kn} of partial DRSs, then the set FA(Kl, ··· ,Kn) consists of those eleDEIJ.ts "1\lhich belong to the

*) In cantrast to the set of at least tw s--structures "1\lhich Halvorsen's algorithm ([3]) ~ produce, ~ have still just one representation of the sentence. The reason is that in [3] the attributes (corresponding to the aigllllents of the verb) are linearly ordered in the s--structures, and therefore, a quantifying-in device is used.

transitive closure of KK under the operation of flmctional application fa defined by:

• (a) fa(l\uK, v) = fa(,\~(K), v) = K(v/u], "1\lhere u and v are discourse referents and K[v/u] is the result of replacing every occurrence of u in mN(K) by v.

(b) fa(,\PK,,\u'K') =

< U(K) u U(K'), CXJN(K)\P(u) u fa(,\u'OON(K'),u) >, Where Pis a variable over partial DRSs of the form ,\uK and u and u' are discourse referents.

(c) fa(,\~,K') = <U(K) u U(K'), (X)N(K) u aN(K')), "1\lhere Q is a variable over DRSs.

Def. (a) A DRS K is closed if a11 discourse referents occurring in CXJN(KD) for sane sub-:OOS KD of K are introduced in sane universe U(Kl) accessible form I<O.

This allows us to finish the interpretation of (SISl): ~ supposed that a11 Cl', ··· ,Cn' ~re singletons . If ~ na.r admit ~ingletons moong the Ci' then (X)' is calculated as the union of a11 FA( Cl", ··· ,Cn") with Ci" belanging to Ci'. fut we restriet the occurrence of non-singletons to such sets Ci' for "1\lhich a11 Ci" are closed.

What ~ have rot explained yet is how the semmtic predicate gets the correct discourse referent as its value.

Def. A DRS with distinguished discourse referent u is a pair (u,K>, "1\lhere u is a discourse referent introduced in K and K is a partial ms.

This allows us to foilllllate the second interpretation schema.. Its task is to disanbiguate the role of the nodes in the dag "1\lhich are values of IIXlre than one attribute. In every such configuration at least as many gramnatical ftmctions Fj occur as there are AR;!. ~ will restriet ourselves to the treat:m:nt of gramnatical functions and argtiiE!lt positions ( ( 2]) ·

Suppose first that the rode is the value of a subcategorizable function and is of NP-type, i.e. the associated translation is a partial DRS with distinguished discourse referent u. Then for m =< n and 1 =< k =< n ~ have

I

'

That is, every argument position is filled up by the distinguished discourse referent, and only one of the gramnatical functions gets the content of the NP, i.e. determines the position of the introduction of the discourse referent in the hierarchy of the "1\lhole ms. The edges of the other gramnatical flmctions are erased. This allows for the introduction of the content of the NP exactly in those c1ause nuclei in "1\lhich it plays a semmtic role by force of controlling an tmexpressed constituent in than. If the node 1s the value of a subcategorizable flmction the value of "1\lhich 1s a c1ause nucleus, then the corresponding node in the dag has been associated with a set of closed IRSs KK. In order to disambiguate this rode ~ take one K out of KK, associate it with the AR;! attribute, and prune the gramnatical function F.

Of course the translation of the PRED has to introduce a discrurse referent p specified by K. For the interpretation of (5) \ole tramlate the

1. Every boy expects an Auerican to win

Before \ole calculate the other b.lo readings for (5) l!l!! want to note that in the case of Equi verbs the requirement that only closed mss are accepted as a translation excludes the derivation just outlined. Remember that the l.exical entry for e.g. persuade also subcategorizes for the ORJ an:i hence yields the translation in 'Which the o t position would not have been bound by the discrurse referent v introduced by an American. Only the follawing 0;o calculations will be applicable to both types of verbs. If l!l!! had taken the ORJ in the application of (SIS2) above \ole would have got an:i then (6), if the value of the PRED is oonverted with the value of the SUBJ first; or, if one converts the value of the PRED first into the value of the ORJ one gets the third and last reading (7) of this sentence.

IV a:o:::uJSICN

It has been slnin b:Jw grllllll!ltical functions and discoorse referents can be used in the translation process fran linguistic fonn to discrurse representations. The algorittm described accrunts for the dynanics of the construction of interpretations of sentences, detemdned not only by syntactic configurations, but also by contextualllll811S, semmtics, or prag~~Btics.

• (1] Bresnan, J.W. (1982), The Mental Representation of Grllllll!ltical Relations, MIT Press, Caoi>ridge, Massachusetts.
• Frey, w. (1985), "Syntax and SaiBntics of Seme Noun Phrases", in: IBubsch, J. ( ed.) Proceedings of GWAI 1984, Springer, 1985.
• Halvorsen, P.-K. (1983), "SaiBntics for lexical-Functional Gramnar", in: Linguistic Inquiry 14.
• ~. H. (1981), "A Theory of Truth and SaiBntic Representation", in: Groenendijk, J.A., et al. (eds.), Formal SaiBntics in the Study of Natural I.anguage, Vol.I, Jmsterdam.