Menal Models Theory and Anaphora Guido Boella and Leonardo Leso Diparieno di Inforaica and Cenro di Scienza Cogniiva Universià di Torino eail: guido, leso @di.unio.i Absrac We argue ha anaphora canno be resolved a he level of he foral language represening eaning, bu, raher, by aking direc reference o he exension of he senences. Johnson-Laird s enal odels heory provide he ool for coping wih exensional represenaions in a cogniively plausible way. Inroducion Anaphoric expressions are radiionally viewed as subsiues for ore coplex linguisic expressions which have already occurred earlier in he ex. Anaphora has proven difficul o analyze a a purely synacic level, so ha srucural approaches like DRT [10] or seanic ones like Dynaic Seanics [4] cope wih his proble by enriching he foral language used o build or o represen he eaning of senences. We believe ha he lii of hese approaches is ha hey have chosen he wrong level of represenaion for dealing wih anaphora: we will show ha i is necessary o ake direc reference o exensional represenaions of eaning. In paricular, he represenaion of he conex should pu a disposal he eleens of he siuaion, which anaphors can refer o, insead of hiding he behind quanified expressions. However, exensions can possibly be infinie or oo large o be deal wih direcly. Bu here is a proposal which uses exensional represenaions of finie and liied size, and which has been sh o be cogniively plausible, i.e., he enal odels heory of [9]. Johnson- Laird has used enal odels in order o explain how people reason wihou having o resor o foral logic. Inferences are perfored by anipulaing exensional represenaions of senences which are coposed of a finie nuber of eleens and relaions: a enal odel represens he exension of an asserion, i.e., he siuaion i describes, and he recursive achinery for revising he odel represens he inension of he asserion, i.e., he se of all possible siuaions i describes. (p.100) In [8] s words: enal odels heory is a psychological heory of language processing and reasoning. The heory provides a fraework wihin which ore deailed accouns of he coponen processes of coprehension [...] such as anaphora inerpreaion [...] and reasoning can be developed, [...] Menal odels heory assues ha coprehension resuls in he consrucion of represenaions of siuaions in he real world [...] These odels are finie and copuable, and hey are consruced increenally, wih he odel so far acing as par of he conex for inerpreing he curren ex. (p.20) A siple preliinary exaple illusraes our soluion. In he following senences, he accepabiliy is guaraneed jus for he pair where he (inended) aneceden (a donkey) and he pronoun (hey) do no agree in heir synacic nuber: (1) Every farer s a donkey. *I is pink. (2) Every farer s a donkey. They are pink. When he second senence in each discourse is inerpreed, i produces a enal odel which us be inegraed wih he preceding one: a referen us be found for he anaphoric expressions. If we exaine in he Figure below how he firs senences of he wo pairs are represened in enal odels heory, we see ha he proble is easily solved. The enal odel conains f d a finie nuber of okens f d (placeholders f d for individuals, here farers and donkeys ) and relaions aong okens (he arrows labeled wih ). Given he odel above, which donkey, ou of he represened ones, can we relae o he singular i, appearing in he second senence of (1)? The proble of idenifying he referen appears o be he sae as in: (3) I have hree sisers. *She is blonde where we have o choose one referen ou of hree candidaes. One is given no (or no enough) inforaion o idenify he aneceden (aong he hree sisers) denoed by she. On he conrary, he hey pronoun in (2) can be inerpreed as referring o he se of donkeys appearing in he odel, due o is plural synacic nuber. The enal odel building algorih Firs of all, he senence undergoes a synacic and seanic inerpreaion process ha produces a seanic nework (see [6], [11] and [2] for deails on he nework represenaion). Then, following he proposal by [9], ha a proposiional represenaion can be used as he inpu o a procedural seanics ha consrucs enal od-
els, a enal odel represening he eaning of he senence is buil. The nework represenaion For he presen purposes, we will describe briefly only he echanis of Disribuiviy Abiguiy Spaces (DAS) which deals wih he possible disribuive readings of an NP (see [11] for deails). The nodes of he nework can be siple or DASs. The laer correspond o plural NPs, and hey were inroduced o deal wih he disincion beween collecive and disribuive readings of predicaes: each DAS includes wo subnodes Se and Indiv. In case of (4) Three en lifed hree ables, if he subjec NP is given a reading as a se, he en are seen as being joinly involved in he ac of lifing ables. Viceversa in he individual reading of he subjec, each an execued a separae lifing ac. If he ables are inerpreed as a se oo, hey were lifed all ogeher (perhaps hey were sacked). On he conrary, if hey are inerpreed as individuals, he en lifed he one a a ie. The four cobinaions of Se, Indiv readings for he subjec and he ec do no cover all possibiliies. In fac, i ay happen ha, for he Indiv reading of he subjec, here exis jus hree ables, and each an lifed one of he (hree individual lifing acs); or ha each an lifed hree ables (possibly, bu no necessarily, he sae hree ables; 9 differen ables could be involved), so ha nine individual lifing acs have been execued. Or, in he Se reading of he ec, he hree en lifed hree differen sacks of ables (so, we have wo ore readings, for a oal of 6) The exra readings (see Figure 1) are accouned for by eans of a echanis oher han he DAS described above (bu independenly oivaed, see [11]), i.e. by he presence of DEP-ON (dependen on) arcs. They are siilar o Skole funcions in firs order logic, and were inroduced for represening quanifier scoping. Each node which is no universally quanified can be specified o be dependen on anoher plural node. For insance, in Every farer s a donkey, he os naural reading is where each farer s a differen donkey, so ha he paricular donkey depends on he paricular farer. Menal odels In order o use a ore unabiguous version of he fraework wih respec o he diagraaic original version of [9], we refer o he foralizaion of enal odels provided by [1]. According o [1], a odel is riple T, R, A, where T is a (non-epy) bi-diensional arix of okens, R is a se of relaions on T, and A is a se of annoaions. For dealing wih soe inerpreaions, ore han one odel can be required. A oken is eiher a odel or an eleen. An eleen is a pair S, A where S is a sybol fro a given vocabulary and A is a se of annoaions; he vocabulary consiss of naed individual eniies (john for he proper nae John) and generic eniies belonging o soe caegory (c for cars, f for farers, ec.). 1) 2) 3) 4) 5) 6) SEMANTIC INTERPRETATION ag se ind ag se ind ag se ind ag se ind ag se ind ag se ind acion acion acion acion DEP-ON acion acion DEP-ON se ind se ind se ind se ind se ind se ind MENTAL MODELS... Figure 1: Six readings of (4).... A relaion is an ordered sequence r, x,..., x, A where r is a relaion sybol, x,..., x are okens in T and A is a se of annoaions. Annoaions are he proposiional enrichen of he analogical srucure of he odel [1]. In paricular, he no annoaion applies o any feaure of he odels. For odels and relaions, a negaion eans ha hey are no he case; for eniies, ha hey are absen in a odel. The... annoaion eans ha he odel can be furher exended. [1] consider relaions such as above, faser and wo special relaions conneced wih (CW) and never conneced wih (NCW). The CW relaion fors an individual by connecing wo of is properies. The NCW one saes ha wo properies canno hold for he sae individual. Usually he wo relaions are used o represen he eaning of, respecively, all huans are orals and os lawyers are no poor. Wih respec o [1] s fraework, we inroduce an exension for wha concerns he NCW relaion. In fac, NCW is originally ean o apply only o unary predicaes such as being huans or oral. We inroduce a version of he NCW relaion relaivized o a predicae rel, NCW(rel). In fac, he no annoaion of a relaion eans ha he relaion is no rue of he given eniies involved in he relaion. In faser, john, bill, no, he negaion does no concern he exisence or no of he wo individuals John and Bill, which are inroduced as exising eniies. Bu his is no sufficien o represen he eaning of a senence like John does no have a car: since he phrase a car inside a negaion does no inroduce or refer o an eniy in he odel, he eaning of he senence canno be represened by he negaion of he have relaion: in fac, a relaion as have, john, c, no does no express he fac ha fro he odel i is no possible o infer ha here is a car. Raher, his annoaed relaion expresses he fac ha here is a car in he odel and John is no is er. Wha we need is soehing siilar o he inerpreaion of he senence no lawyer is a crook fro which is no possible o infer ha here is soe crook in he odel. The odel of his senence in [1] is no represened by a negaion of soe predicae is bu wih he NCW rela-
ion discussed above: NCW, lawyer, crook. Analogously, for inerpreing John does no have a car we inroduce a NCW(have) predicae, which no only expresses he negaion of he have predicae, bu which also does no asser he exisence of any car (see he Figure below). In NCW(have), john, c,, cars, as in NCW, bicycle, c, (no bicycle john is a car), are kep separae fro he oher eniies in he odel: hey canno play he role of anecedens of pronouns. For wha concerns he reaen of logical connecives, we sick o he proposal of [1]. Fro he nework o he enal odel The odel consrucing procedure akes as inpu an exising enal odel (represening he conex) and he nework represenaion of he new senence (sill associaed wih he synacic ree): he newly consruced odel is inegraed wih he exising ones by overlapping idenical okens and finding referen okens for anaphoric expressions. The process sars fro he non-dependen eniy nodes of he nework which derive fro he inerpreaion of NPs (i.e. NPs wihou exiing DEP-ON arcs), and proceeds wih he oher NPs, according o he (parial) order iposed by (reversed) DEP-ON arcs. Afer ha, all co-references are solved. For insance, in (5) Every farer who s a donkey beas i, every farer is processed firs, hen a donkey and, he pronoun i which depend on he subjec NP. More precisely, given a conex M coposed by a odel T, R, A, we have ha a nework W is inerpreed as a new odel T, R, A, in he following way: 1. Each non-dependen eniy node in he nework W deriving fro he inerpreaion of an NP is reaed separaely: (a) If he eniy node is represens an NP which is a proper noun (e.g., John), an individual oken (e.g., john) is inroduced in he arix T of he odel M; if ha oken is already presen in he odel, he wo okens are idenified. (b) If he NP is a quanified Noun (e.g., every farer), a se of disinc okens F = x,..., x represening he denoaion of he noun is added o he conex arix T; depending on he quanifier Q, a subse of he, Q(F), will be seleced for linking o oher okens by he relaion where he NP occurs as an arguen (selecing he whole se in case of every and all, a proporioned subse of i in case of os, ec). The annoaion A of he odel can be augened wih a, since, depending on he quanifier, ore okens could be added o he arix T or he se! #"%$ could be revised (e.g., if = soe, &'! #"%$(& could be iniially 2 or 3, bu i can be increased in case of necessiy, as in he sandard c reaen of syllogis in [9]). A special case, as in he enal odels heory of [9], is represened by he quanifier no: is eaning is represened by selecing all he okens F represening he denoaion of he noun i quanifies (Q(F)=F); bu when he relaion rel involving he NP is inroduced, i is inerpreed as negaed eiher in he sense of a NCW(rel) relaion or in he sense of being annoaed as negaed. As an exaple, in no farer s a donkey he ing relaion, is ransfored in a NCW() relaion which keeps apar all he farers fro he se of donkeys. (c) If he NP is an indefinie such as a car, wo cases are possible according o he presence of a negaion and he role played by he NP in he ain predicae: 1 ) If he NP is he subjec of he verb or i appears in a non-negaed relaion, a single new oken represening a car is added o he arix T of he odel and annoaed as..., since i does no convey any uniqueness presupposiion. ) If he NP appears in a negaed predicae and i is no he subjec of he predicae rel, soe okens represening he denoaion of he noun F = x,..., x are inroduced in T and appear in a NCW(rel) relaion o keep he separae fro he oher okens of he odel. 2 (d) If he eniy in he nework W is he inerpreaion of a definie NP or a definie pronoun, hen an aneceden us be searched for in he enal odel consruced so far; according o he nuber, one or ore okens exising in he odel are sough in T o ac as he poenial referens: furher, he se of relaions R us saisfy he descripion provided by he NP. This kind of unificaion, however, canno be accoplished wih ies which are linked o oher ones only by a NCW(rel) relaion in which hey appear in a NCW(rel), non-subjec role &+* rel, x,..., x ( x,...,,..., x, (-, R. i 0/ 1 ), i.e., hese ies are iplicily assued as non exising in he odel. Moreover, if he se of possible referens X =,..., 1 is coposed of a subse of okens which occur in relaions wih oher okens and a subse of okens which are unrelaed: 2&3* rel, A, x,..., x ( rel, x,...,,..., x, A, R) 541 67&98:* rel, A, x,..., x ( rel, x,..., 6,..., x, A;, R) hen only he forer se can be considered by he uni- 1 Noe ha John does no love a girl in his office where he indefinie is a specific one (see [10]) and he speaker could idenify a unique referen for i, is no covered by his rule. 2 This reaen of indefinies is jusified also fro a linguisic poin of view. As [10] noice, he negaion of a verb us be inerpreed as having an inner scope which does no include he subjec of he verb, oherwise senences as soeone does no like a Porsche would be rue in case here is no people a all. And i finds a siilariy in DRT where indefinies inside he scope of a negaion are inerpreed in a subordinae DRT srucure which will no be accessible for he resoluion of anaphoric expressions.
F ficaion process (e.g., in he inerpreaion of John has any donkeys. They are pink where he odel includes a nuber of donkeys bu only a subse of he is relaed wih John: he pronoun hey refers only o his subse). Noe ha he se of annoaions is no consrained o be epy: in fac, i is possible o ake reference o a se of eniies which is involved in a negaed relaion as in: (6) he soldier didn see soe of he eneies. They were hiding in he rees. Finally, since a definie pronoun is a definie reference, he found referen us be non-abiguous: if differen possibiliies exis, hen, for pragaics reasons, he reference fails (see exaple (3)). 2. If he eniy node of he NP np< is dependen on anoher node which is buil fro he NP np=, is inerpreaion depends on he one of np= : his eans ha, for each oken buil in correspondence wih np= he inerpreaion of np< us be repeaed according o he rules in 1 described above for non-dependen NPs. In paricular, if np< is a singular indefinie and he corresponding relaion is no negaed, a new oken is inroduced for each oken associaed wih np= ; if np< is plural, a differen se of exaple okens is added o he odel for each oken associaed wih np=. For exaple in he disribuive inerpreaion of Every farer has a donkey. They bea i, hey is unified wih he okens f<,..., f> represening farers, bu he inerpreaion of i (which in his reading canno bu be dependen on he) is perfored for each f? (1@ i @ n) relaively o he se of okens A B7CED rel, x<,..., x> (F rel, x<,..., f?,..., B,..., x>, GIHKJ R) L. In he exaple, for each i, i is unified wih he d? such ha F bea, f?, d?, GMH. 3. Finally, he okens are linked by he relaions described by he predicaes. The nuber of relaions which are inroduced depends on he se or individual inerpreaion of he DAS of he NPs involved: if an NP is considered as a se, he okens resuling fro is inerpreaion are included as a whole in he role hey play in he relaion. Oherwise, each eleen of he se is inroduced in differen insance of he relaion. 4. As we discuss in he following Secion, he inerpreaion of a senence which includes logical connecives can resul in ore han one odel. The rule 1 is ieraed for each of he clauses in he coplex senence. During he inerpreaion process soe of he possible odels us be discharged as inconsisen. This is a correc ove bu i can lead o he refecion of he senence for pragaic reasons (as in exaple (11) below). In fac, if he inerpreaion of a senence resuls in a reduced se of odels which can be beer described by anoher senence (ha is, is inerpreaion does no discard any odel), hen by he Gricean principle of cooperaion, he speaker should have used i insead of he one he chose. 5. On he oher hand, if he inerpreaion of he senence leads feliciously o a se of odels, hese odels becoe par of he conex. When a subsequen senence is inerpreed, is inerpreaion us be copaible wih all he odels in he conex. In paricular, if he inerpreaion of he subsequen senence produces ore han one odel, for each odel in he conex, a leas one of he newly consruced odels us be copaible (even if no he sae one for all he odel in he conex). Oherwise, he senence will be rejeced (as in exaple (14) below). Logical connecives According o [10] he inerplay of anaphora and logical connecives is a fundaenal esbed for any heory of language inerpreaion. Here, he eaning of connecives is expressed by heir possible odels in [9] s syle. Firs he iplici odels are consruced and if necessary he explici ones are fleshed ou. Le s sar wih a siple exaple involving negaion: (7) *John does no a car. He washes i. Since, according o he represenaion oulined in he previous secion, cars are included in NCW() relaions, no referen can be found in he odel for he pronoun i: T=A+ANG, c<ol, A john, GPL,L+L, R= A'F NCW(), john, c<, GMH, A= GML(H So, he senence is no inerpreable according o ha reading. An exaple a bi ore coplex is: (8) No farer has a car. *I is red. A senence like no farer is rich is represened by a NCW relaion beween farers and rich people see rule 1.b. In our odel, his relaion is exended o arbirary predicaes. Hence, he firs senence produces a odel where cars appear in he se of never conneced wih eniies, so ha he inerpreaion (and failure in inegraion) is exacly he sae as in he previous exaple: F T=A5A+ANG,c<3L+ANG,c=OL+ANG,cQ9L+L, A+A f<, GPL, A f=, GPL, A fq, GPL+L L, R= A'F NCW(), f<, c<nh, GRH, F NCW(), f=, c=eh, GMH, F NCW(), fq, cqeh, GMH7L, A= A...LSL On he conrary: (9) No farer has a car. They prefer donkeys. is accepable, in spie of he negaion appearing in he subjec NP and of is singular nuber. In fac, he farers (appearing as exising eniies) are available for inegraion. If we now consider conjuncions and disjuncions, anoher ineresing anoaly arises: (10) John s a car? and Fred washes i? (11) *John s a car? or Fred washes i? The synacic srucures are idenical bu he accepabiliy is no. In order o explain his fac, [10] inroduced an accessibiliy consrain a he srucural level: no disjunc of a disjuncive condiion is accessible fro any oher. The enal odel represenaion of a conjuncion involves he inclusion in he sae odel of he conjoined senences. So, no proble arises wih (10), since he referen for i can be found in he sae odel where he second conjunc us be inegraed. Copare he unaccepabiliy of *John does no have a Porsche and Fred washes i.
On he conrary, a disjuncion A T B requires he consrucion of wo separae odels (one wih A and one wih B). So, in he second odel of (11) here is no available referen for he pronoun (B, i.e., Fred washes i). Bu when a difficuly (such as he ipossibiliy of undersanding a senence) occurs in a enal odel, he odel can be anipulaed and fleshed ou; in principle, when applied o he second odel (B), his process could produce wo alernaives. In he firs one John s a car (A and B), while in he second one he does no (no A and B, i.e., John does no have a car and Fred washes i). So, i sees ha he firs exension could solve he proble: John, in fac, s a car and Fred washes i: J J A c... * F wash? B J F wash wash? c... J c... F c A A B no A B The lower par of he figure shows he hree resuling odels: he second one (A and B) includes he firs (A) and he hird (no A and B) is discharged since Fred canno wash a car which does no exis (see he * in he hird box). However, i sees ha fro any disjuncion a leas wo disinc odels us be consruced, and ha none of he us be included in he oher: oherwise, he coon par of he wo odels would be necessarily rue and according o Grice, he speaker should no have used a disjuncion o express such a eaning (see rule 4 of he inerpreaion algorih). An exaple ha suppors he previous analysis is he accepabiliy of he following senence, as he reader can easily es: (12) John does no a car or he washes i. The second odel (he one of he washes i) can be fleshed ou wih he negaion of he firs disjunc (no A and B, i.e., John does a car and Fred washes i): afer his exension, he resuling odel pus a disposal he required referen for he pronoun. We are lef wih wo differen odels, equivalen o he [10] s inerpreaion of he exaple, i.e John does no a car or John s a car and he washes i. In [10] his resul is obained by copying he negaion of he firs conjunc in he second DRS: such a rule, however, presupposes ha disjuncions in naural language are always inerpreed a exclusive disjuncions. I is ineresing o noe ha Dynaic Seanics [4], in order o explain his kind of exaples, has o inroduce a new class of anaphora, E-ype. The las connecive o be considered is iplicaion: (13) If John s a car, he washes i. This senence involves wo odels (A and B, and no A o be furher exended): in he firs one, John s a car and washes i, while in he second one he does no any car. Bu, if he senence is followed by (14) *I is a Porsche, he pronoun of he second senence can find a referen only in he firs odel in he conex, while no aneceden is accessible in he second one (where he * car, in fac, is conneced wih a NCW relaion). As prescribed by rule 4 of he algorih, a new senence us be inegraed wih all he pre-exising odels in he conex, oherwise i is unaccepable. An analogous reasoning explains he oddiy of *If John does no a car, Fred washes i. Moreover, so called exainaion senences as (15) no sudens will be adied o he exa unless hey have regisered four weeks in advance can be deal wih by inerpreing he conjuncion unless as an if no or a sronger exclusive or. Plurals A nuber of ineresing anaphoric phenoena are relaed o plurals. The firs siuaion concerns a plural pronoun referring o a se of singular anecedens which occur in he odel: (16) Mary e John. They alked. Even if in enal odels he firs senence inroduces separaely wo okens, he rule 1.d can cope wih hese case as if hey were inroduced siulaneously as by he NP wo people. So i can resolve he anaphora wihou explicily suing he anecedens o for a plural discourse referen, as DRT does. Quanifier phrases such as any of he farers do no always inroduce he referens wih which subsequen pronouns will be co-referenial. For exaple, hose pronouns refer o ses ha have o be consruced fro explici inforaion in he ex. Here, quanifiers inroduce in he odel a se of okens which pronouns can refer o in he subsequen discourse: (17) Susan has found every book which Bill needs. They are on his desk. To resolve hey we need only he se of okens inroduced in he odel by he analysis of he firs senence. The righ subse of books is idenified in he odel hanks o rule 1.d (see discussion below). In DRT, in conras, a new discourse referen is consruced via an absracion rule which copies he conen of he DRSs inroduced by he previous senence. In soe approaches, definie NPs and pronouns inside he scope of a quanifier are considered like bound variables in a logical syse. In (18) every waier wans cusoers o give hi large ips he pronoun does no see o refer o any paricular eniy, while i does in (19) John wans cusoers o give hi large ips. DRT in order o deal wih boh cases in a unifor way inroduces he noion of discourse referen which does no correspond direcly o any individual in he world, while providing anecedens for he pronouns. In conras, enal odels heory allows unifying boh cases, since quanifier phrases, in an exensional represenaion inroduce ses of eniies in he odel. No all definie pronouns following quanifiers behave like bound variables, in paricular, if hey appear in a following clause, i.e., ouside he quanifier scope: (20) few congressen adire Kennedy and hey are very junior. They refers o hose (few) congressen who adire Kennedy, even if here is no such an expression referring o he. If he pronoun were inerpreed as a variable, he senence would be equivalen o (21) Few congressen adire Kennedy and are very junior. In [5] s ers, here
is an aneceden rigger, a linguisic expression which inroduces he aneceden of he pronoun bu i does no have he sae referen of he pronoun. In our odel, afer he inerpreaion of he firs clause he enal odel conains he se of congressen and a (sall) subse of he which are in an adire relaion wih Kennedy. For rule 1.d above, he definie pronoun hey can be resolved wih his subse. Bu as i igh be expeced, quanifiers focus on he subse of he se specified by he head noun. Hence, he unificaion process us be suiably consrained. In: (22) Soe farers of his valley a donkey. They don like cars, he pronoun hey can in principle refer eiher o he farers of his valley who a donkey or o he copleen se; according o rule 1.d in he inerpreaion algorih, if he se of candidae referens can be pariioned in differen ses, he pronoun is unified only wih he eniies which are involved in a relaion (of ing a donkey). The possibiliy of a plural anaphor resolved agains referens described by a singular indefinie is explained by rule 1.d which deals wih he inerpreaion of dependen NPs in disribuive readings (see he Figure on firs page). In (23) Every farer s a donkey. They are pink he disribuive reading expresses explicily he pluraliy of donkeys so ha he correc referens are available for he plural pronoun. In conras, in (24) Every farer s a donkey. *He is a wise an, he singular definie pronoun he canno be resolved, since we do no have any inforaion o choose one of he farers (see rule 1.d). An exaple slighly ore coplex is: (25) Three farers a donkey. They bea he. The laer senence can be inerpreed only as far he second clause is inerpreed wih wo individual readings of he NP wihou DEP-ON arcs beween he (case 3 of Figure 1). In his case he donkeys who for he aneceden of he are relaed each by a differen relaion wih he farers. Which farer is seleced for relaing wih he beaing relaion o a given donkey? as in case of rule 2 he inerpreaion of an anaphor is perfored exacly wih respec o he oher okens which are linked o i by soe relaion. Indeed, in he conex is ainained he relaion beween each farer and he donkey he s: hence, he inerpreaion of he senence leads o a siuaion where each farer beas he donkey he s, and no a differen one (as i happens in soe foral odels of anaphora). Finally, plural and singular pronouns can be ixed: (26) Every farer s a donkey. They bea i. Since i in he second senence is dependen on he subjec hey, he inerpreaion of he second senence is parallel o he inerpreaion of he firs: he ec (i) can be resolved agains an aneceden only if i is inerpreed as dependen on he subjec; according o rule 1.d of he inerpreaion algorih, hey is unified wih he se of farers appearing in he odel and, again, since here is an explici relaion () linking each of he o a donkey, his link is followed o deerine he (singular) referen of i. Siilarly, he so called donkey senence, (27) Every farer who s a donkey beas i, is accepable: he procedure firs inerpres he subjec phrase, hus obaining, in he wide-scope reading of he universal, a represenaion where each farer has a leas a donkey; hen i exends he represenaion by searching for a referen hrough each relaion U, fv, dv, WYX ; so, in he disribuive reading he senence, as in he exaple above, for each farer, a differen referen for i is found, i.e. he donkey ed by hi. The possible aneceden us saisfy he resricion carried by he nuber of he singular pronoun (copare *Every farer who has wo donkeys beas i). Conclusion Since enal odels are a cogniively plausible heory of huan reasoning, hey can be also useful in finding an explanaion of linguisic phenoena. In [3], we exploied enal odels o provide an explanaion of lexically riggered presupposiions. In [2] ore coplex anaphorical phenoena relaed o he differen readings of donkey senences have been coped wih in he sae fraework. The lii of logical approaches in explaining anaphora is ha hey exploi represenaions ha are no isoorphic o our concepion of he described siuaion. The necessiy of resoring o a referenial level in explaining anaphora has been highlighed also by [7]. We followed his suggesion, bu going in a differen direcion, where enal odels replace he classical odelheoreic fraework o provide a cogniively plausible approach o language inerpreaion. References [1] B. Bara, M. Bucciarelli, and V. Lobardo. Model heory of deducion: A unified copuaional approach. Cogniive Science, 25(6), 2001. [2] G. Boella, R. Daiano, and L. Leso. Beaing a donkey: a enal odel approach o coplex anaphorical phenoena. In Proc. of European Congress of Cogniive Science of ECCS 99, Ponignano, 1999. [3] G. Boella, R. Daiano, and L. Leso. Menal odels and pragaics: he case of presupposiions. CogSci99 Conference, 1999. [4] G. Chierchia. Anaphora and dynaic binding. Linguisics and Philosophy, 15:111 183, 1992. [5] F. Cornish. Anecedenless anaphors: Deixis, anaphora or wha? Journal of Linguisics, (32):19 41, 1996. [6] B. DiEugenio and L. Leso. Represenaion and inerpreaion of deeriners in naural language. In Proc. 10h IJCAI, pages 648 653, Milano, 1987. [7] D. A. H. Elworhy. A heory of anaphoric inforaion. Linguisics and Philosophy, 18:207 332, 1995. [8] A. Garnha. Menal odels and he inerpreaion of anaphora. Psychology Press, Hove, 2001. [9] P.N. Johnson-Laird. Menal Models. Cabridge Universiy Press, Cabridge, 1983. [10] Hans Kap and Uwe Reyle, ediors. Fro Discourse o Logic. Kluwer, Dordrech, 1993. [11] L. Leso, M. Beri, and P. Terenziani. A nework foralis for represening naural language quanifiers. In Proceedings of ECAI-88, pages 473 478, 1988.