impler TAG semanics hrough snchronizaion The Harvard communi has made his aricle openl available. Please share how his access benefis ou. Your sor maers. Ciaion Published Version Accessed Ciable Link Terms of Use Rebecca Nesson and uar M. hieber. impler TAG semanics hrough snchronizaion. In Proceedings of he h Conference on Formal Grammar, Malaga, pain, 9-0 Jul 006. hp://cslipublicaions.sanford.edu/fg/006/nesson.pdf Februar 9, 08 :4:59 AM ET hp://nrs.harvard.edu/urn-:hul.insrepos:5595 This aricle was downloaded from Harvard Universi's DAH reposior, and is made available under he erms and condiions applicable o Oher Posed Maerial, as se forh a hp://nrs.harvard.edu/urn-:hul.insrepos:dash.curren.erms-ofuse#laa (Aricle begins on nex page)
Rebecca Nesson and uar M. hieber. 006. impler TAG emanics hrough nchronizaion. In Proceedings of he h Conference on Formal Grammar, Malaga, pain, 9 0 Jul. FG 006: The h conference on Formal Grammar Malaga, pain Jul 9-0, 006 Organizing Commiee: Paola Monachesi Gerald Penn Giorgio aa hul Winner CENTER FOR THE TUDY OF LANGUAGE AND INFORMATION
Conens impler TAG emanics hrough nchronizaion Rebecca Nesson and uar hieber iii
impler TAG emanics hrough nchronizaion Rebecca Nesson and uar hieber Kewords nchronous Tree-Adjoining Grammar, TAG semanics, quanifier scope, long-disance WH-movemen, raising verbs, aiude verbs, adverbs, relaive clauses, preposiional phrases. Absrac In recen ears Laura Kallmeer, Maribel Romero, and heir collaboraors have led research on TAG semanics hrough a series of papers refining a ssem of TAG semanics compuaion. Kallmeer and Romero bring ogeher he lessons of hese aemps wih a se of desirable properies ha such a ssem should have. Firs, compuaion of he semanics of a senence should rel onl on he relaionships expressed in he TAG derivaion ree. econd, he generaed semanics should compacl represen all valid inerpreaions of he inpu senence, in paricular wih respec o quanifier scope. Third, he formalism should no, if possible, increase he expressivi of he TAG formalism. We revive he proposal of using snchronous TAG (TAG) o simulaneousl generae snacic and semanic represenaions for an inpu senence. Alhough TAG mees he hree requiremens above, no serious aemp had previousl been made o deermine wheher i can model he semanic consrucions ha have proved difficul for oher approaches. In his paper we begin exploraion of his quesion b proposing TAG analses of man of he hard cases ha have spurred he research in his area. We reframe he TAG semanics problem in he conex of he TAG formalism and in he process presen a simple, inuiive base for furher exploraion of TAG semanics. We provide analses ha demonsrae how TAG can handle quanifier scope, long-disance WH-movemen, ineracion of raising verbs and adverbs, aiude verbs and quanifiers, relaive clauses, and quanifiers wihin preposiional phrases. FG-006. Organizing Commiee:, Paola Monachesi, Gerald Penn, Giorgio aa, hul Winner. Coprigh c 006, CLI Publicaions.
/ Rebecca Nesson and uar hieber. Inroducion In recen ears Laura Kallmeer, Maribel Romero, and heir collaboraors have led research on TAG semanics hrough a series of papers refining a ssem of TAG semanics compuaion using evolving echniques including enriched derivaion ree srucure (Kallmeer, 00a,b), flexible composiion of feaure-based TAG wih a semanic represenaion associaed wih each elemenar ree (Kallmeer and Joshi, 00, Joshi e al., 00, Kallmeer, 00), semanic feaures in a more expressive exension of feaure-based TAG (Garden and Kallmeer, 00), and, mos recenl, semanic feaures on he derivaion ree iself (Kallmeer and Romero, 004, Romero e al., 004). Kallmeer and Romero (004) bring ogeher he lessons of hese aemps wih a se of desirable properies ha such a ssem should have. Firs, compuaion of he semanics of a senence should rel onl on he relaionships expressed in he TAG derivaion ree. Because TAG elemenar rees represen minimal semanic unis, he onl informaion necessar for semanic compuaion should be he informaion encoded in he derivaion ree: which elemenar rees have combined and he address a which he combining operaion ook place. econd, he generaed semanics should compacl represen all valid inerpreaions of he inpu senence, in paricular wih respec o quanifier scope. Third, he formalism should no, if possible, increase he expressivi of he TAG formalism. We revive he proposal of using snchronous TAG (TAG) o simulaneousl generae snacic and semanic represenaions for an inpu senence (hieber and chabes, 990). Alhough TAG mees he hree requiremens above, no serious aemp had previousl been made o deermine wheher i can model he semanic consrucions ha have proved difficul for oher approaches. In his paper we begin exploraion of his quesion b proposing TAG analses of man of he hard cases ha have spurred he research in his area. We reframe he TAG semanics problem in he conex of he TAG formalism and in he process presen a simple, inuiive base for furher exploraion of TAG semanics. Afer reviewing TAG in ecion., we provide analses in ecions.. hrough..4 for senences ha exemplif several hard cases for TAG semanics ha have been raised b Kallmeer and ohers in recen papers: quanifier scope (as exemplified b senences () and (5), presened below along wih he desired semanic inerpreaions), longdisance WH-movemen (), ineracion of raising verbs and adverbs, aiude verbs and quanifiers (,4,5), relaive clauses (6), and quan-
impler TAG emanics hrough nchronizaion / ifiers wihin preposiional phrases (7) (Kallmeer and Romero, 004, Romero e al., 004, Joshi e al., 00, Kallmeer, 00, Kallmeer and Joshi, 00). () Everone someone. ever(x, person(x), some(z, person(z), like(x, z))) some(z, person(z), ever(x, person(x), like(x, z))) () Who does Bill hink Paul said John? who(, hink(bill, sa(paul, like(john, )))) () Bill hinks John apparenl Mar. hink(bill, apparenl(like(john, mar))) (4) John someimes everone. ever(x, person(x), someimes(like(john, x))) someimes(ever(x, person(x), like(john, x))) (5) Bill hinks everone someone. hink(bill, ever(x, person(x), some(z, person(z), (x, z)))) hink(bill, some(z, person(z), ever(x, person(x), (x, z)))) (6) A problem whose soluion is difficul sumped Bill. a(x, and( problem(x), he(, and(soluion(), poss(x, )), isdifficul())), sumped(bill, x)) (7) Two poliicians sp on someone from ever ci. wo(x, poliician(x), ever(z, ci(z), some(, person() f rom(z, ), spon(x, )))) ever(z, ci(z), some(, person() f rom(z, ), wo(x, polician(x), spon(x, )))) wo(x, poliician(x), some(, ever(z, ci(z), person() f rom(z, )) spon(x, ))) some(, ever(z, ci(z), person() f rom(z, )) wo(x, poliician(x), spon(x, ))). Inroducion o nchronous TAG A ree-adjoining grammar (TAG) consiss of a se of elemenar ree srucures and wo operaions, subsiuion and adjuncion, used We noae curried wo-place relaions P(x)() as P(, x) for readabili.
4 / Rebecca Nesson and uar hieber NP V P = NP V P NP V NP John V NP John V P NP V P = Adv V P V NP NP V P Adv V P apparenl apparenl V NP FIGURE Example TAG subsiuion and adjucion operaions. o combine hese srucures. The elemenar rees can be of arbirar deph. Each inernal node is labeled wih a nonerminal smbol. Fronier nodes ma be labeled wih eiher erminal smbols or nonerminal smbols and one of he diacriics or. Use of he diacriic on a fronier node indicaes ha i is a subsiuion node. The subsiuion operaion occurs when an elemenar ree rooed in he nonerminal smbol A is subsiued for a subsiuion node labeled wih he nonerminal smbol A. Auxiliar rees are elemenar rees in which he roo and a fronier node, called he foo node and disinguished b he diacriic, are labeled wih he same nonerminal. The adjuncion operaion involves splicing an auxiliar ree wih roo and designaed foo node labeled wih a nonerminal A a a node in an elemenar ree also labeled wih nonerminal A. Examples of he subsiuion and adjuncion operaions on sample elemenar rees are shown in Figure. nchronous TAG (TAG) exends TAG b aking he elemenar srucures o be pairs of TAG rees wih links beween paricular nodes in hose rees. An TAG is a se of riples, L, R, where L and R are elemenar TAG rees and is a linking relaion beween nodes in L and nodes in R (hieber, 994, hieber and chabes, 990). Derivaion proceeds as in TAG excep ha all operaions mus be paired. Tha is, a ree can onl be subsiued or adjoined a a node if is pair is simulaneousl subsiued or adjoined a a linked node. We noae he links b using boxed indices i marking linked nodes. Figure conains a sample English snax/semanics grammar frag-
impler TAG emanics hrough nchronizaion / 5 (a) NP e V P John john Adv V P, NP V P e, e NP e apparenl apparenl V NP 4 e 4 Mar mar (b) NP Adv V P V, V P apparenl e, NP e e john (c) john 4 mar apparenl John apparenl Mar mar FIGURE An English snax/semanics TAG fragmen (a), derived ree pair (b), and derivaion ree (c) for he senence John apparenl Mar. men ha can be used o parse he senence John apparenl Mar. The node labels we use in he semanics correspond o he semanic pes of he phrases he dominae. Variables such as x in he semanic ree in Figure are aken o be bound in he obvious wa, so ha in muliple uses of he ree he can be presumed o be renamed apar. Figure (c) shows he derivaion ree for he senence. ubsiuions are noaed wih a solid line and adjuncions are noaed wih a dashed line. Noe ha each link in he derivaion ree specifies a link number in he elemenar ree pair. The links provide he locaion of he operaions in he snax ree and in he semanics ree. These operaions mus occur a linked nodes in he arge elemenar ree pair. In his case, he noun phrases John and Mar subsiue ino a links and 4 respecivel. The word apparenl adjoins a link. The resuling semanic represenaion can be read off he derived ree b reaing he lefmos child of a node as a funcor and is siblings as is argumens. Our sample senence hus resuls in he semanic represenaion apparenl((john, mar)). This represenaion is for he sake of readabili. The labels could be replaced using an well-chosen finie se of nonerminal smbols.
6 / Rebecca Nesson and uar hieber N e, (a) NP ever x De N ever e, x e x NP De N some e, some e one person NP V P 4 e, e 4 ever some (b) V NP 4 e 4 person person (c) NP V P ever x some De N V NP e, x some e, De N person e, e, e person ever one some one person e x ever x e, x e, person e e x FIGURE The elemenar ree pairs (a), derivaion ree (b), and derived snacic and semanic rees (c) for he senence Everone someone. Noe ha he derivaion ree is a scope neural represenaion: depending on wheher ever or some adjoins higher, differen semanic derived rees and scope orderings are obained.. TAG Analses of he Phenomena.. Quanifier cope and Wh-Words For senence (), we would like o generae a scope-neural semanic represenaion ha allows boh he reading where some akes scope over ever and he reading where ever akes scope over some. We propose a soluion in which a derivaion ree wih muliple adjuncion nondeerminisicall deermines muliple derived rees each manifesing explici scope (chabes and hieber, 99); he derivaion ree iself is herefore he scope neural represenaion. The muli-componen quanifier approach followed b Joshi e al. (00) suggess a naural implemenaion of quanifiers in TAG. In his approach he snacic ree for quanifiers has wo pars, one ha The muli-componen approach o quanifiers in TAG was firs suggesed b hieber and chabes (990) under he rewriing definiion of TAG derivaion where he order of rewriing produced he scope ambigui. Williford (99) explored he use of muliple adjuncion o achieve scope ambigui.
impler TAG emanics hrough nchronizaion / 7 WH 4 NP V P V NP wh ǫ WH who who e e, 4 e e 4 NP V P V hink 5 who wh 4 john e, hinks sa e paul hinks bill FIGURE 4 elecion of elemenar rees and full derivaion ree for he senence Who does Bill hink Paul said John?. corresponds o he scope of he quanifier and aaches a he poin where he quanifier akes scope, and he oher ha conains he quanifier iself and is resricion and aaches where snacicall expeced a a noun phrase. In heir work, a single-node auxiliar ree is used for he scope par of he snax in order o ge he desired relaionship beween he quanifier and he quanified expression in feaures hreaded hrough he derivaion ree and hence in he semanics. Using TAG, we do no need he single-node auxiliar ree in he snax because we can pair he usual snacic represenaion for quanified NPs wih a muli-componen semanic represenaion ha expresses he same idea (Figure ). In order o use hese quanifiers, we change he links in he elemenar rees for verbs o allow a single link o indicae wo posiions in he semanics where a ree pair can adjoin, as shown in Figure. 4 Given his represenaion of quanifiers we ge he derivaion ree shown in Figure for senence (). 5 Noe ha he resuling derivaion ree necessaril incorporaes muliple adjuncion (chabes and hieber, 99), ha is, muliple auxiliar rees are adjoined a he same node 4 We have chosen here o add he hree-wa links in addiion o he exising links in he ree for unquanified noun phrases such as proper nouns (hough we suppress he wo-wa NP links in he figures for readabili). Anoher possibili would be o remove he wo-wa links. In his case, all noun phrases would be lifed à la Monague. Tha is, even unquanified noun phrases would have a scope par, which could be a single-node auxiliar ree. 5 We noae muli-componen inserions ha involve boh a subsiuion and an adjuncion wih a combinaion dashed and doed line.
8 / Rebecca Nesson and uar hieber ( a ) ( b ) ( c ) hinks bill 4 4 john apparenl mar john someimes ever person hinks bill 4 ever some person person FIGURE 5 Derivaion rees for (a) Bill hinks John apparenl Mar, (b) John someimes everone, and (c) Bill hinks everone someone. in an auxiliar ree. In paricular, he scope pars of boh ever and some aach a he roo of he semanic ree of. uch cases of muliple adjuncion induce ambigui; he derivaion ree represens muliple derived rees. In he case a hand, he derivaion is ambiguous as o which quanifier scopes higher han he oher. This ambigui in he derivaion ree hus models he se of valid scopings for he senence. In essence, his mehod uses muliple adjuncion o model scope-neurali. This same mehod can be used o obain he correc scope relaions for senences wih long-disance WH-movemen such as senence () using he muli-componen elemenar ree pair for who and he elemenar ree pairs for hinks (he ree pair for sas is similar) and in he WH conex given in Figure 4. Kallmeer and Romero (004) highligh his case as difficul because in he usual snacic analsis here is no link in he derivaion ree beween who and hinks or beween hinks and, bu in he desired semanics who akes scope over he hinks proposiion and he proposiion is an argumen o hinks. In our analsis, b conras, he semanics follows quie naurall from he sandard snacic analsis of he srucure of he elemenar ree in he WH conex and he elemenar ree pair for hinks given in Figure 4. The derivaion of his senence is also given in Figure 4. Noe ha i is required b he srucure of he rees ha who ake scope over hinks... The Ineracion Beween Aiude Verbs, Raising Verbs, Adverbs and Quanifiers The ineracion beween aiude verbs and raising verbs or adverbs as in senences (), (4), and (5) has been problemaic for TAG semanics (Kallmeer and Romero, 004). A successful analsis mus be flexible enough o produce he correc semanics for senence () even hough here is no link beween hinks and apparenl in he derivaion ree. I mus also be flexible enough o allow all scope orderings beween
impler TAG emanics hrough nchronizaion / 9 NP V P 4 V NP 4 e, e e 4 FIGURE 6 Modified ree for ha enforces a resricion on quanifiers scoping ouside of he finie clause. VP modifiers and quanifiers as in senence (4). In fac, given he elemenar rees we have alread presened and he ones for aiude verbs demonsraed b Figure 4, our analsis alread allows for scope ineracions among all hese elemens. Indeed, because he semanic componens of aiude verbs, VP modifiers, and quanifiers all adjoin a he same node in he semanic ree of he verb, our analsis allows all scope orderings among hem. This is clearl oo permissive, because i allows quanifiers o scope ou of he finie clause in which he appear and would allow a reading of senence () in which apparenl scopes over hinks. To preven quanifiers from scoping ou of he finie clause in which he appear, as in senences () and (5), we can add an addiional adjuncion sie o he semanic rees for verbs above he curren roo node. This is shown in Figure 6 in he ree pair. The link configuraion ensures ha aiude verbs (adjoining a link ) will now scope higher han all VP modifiers (adjoining a ) and quanifiers (adjoining a links and 4). VP modifiers and quanifiers will sill be able o ake all scope orderings relaive o each oher. Using he modified verb rees, TAG produces he correc semanics for senences (), (4), and (5) wih he derivaions given in Figure 5... Relaive Clauses Relaive clauses provide anoher puaivel difficul case for TAG semanics because boh he main verb and he relaive clause need access o he variable inroduced b he deerminer as in senence (6) (Kallmeer, 00). We overcome his difficul and compue he desired semanics b inroducing higher-order funcions ino he semanic rees using lambda-calculus noaion. This modificaion allows us o mainain ree-locali. The snacic analsis we use is similar o ha of Kallmeer (00) in ha i mainains he Condiion on Elemenar Tree Minimali (Frank, 99) and uses he relaive pronoun o inroduce he relaive clause. However, i reas
0 / Rebecca Nesson and uar hieber N e, N e, N N and e, e, N /NP se e, e, who N NP De N a a e, e N e, problem/ soluion problem/ soluion se N /NP e, λ z NP V P e, z ǫ is difficul isdifficul sumped 4 a bill problem who se soluion isdifficul FIGURE 7 Ke elemenar rees and derivaion for A problem whose soluion is difficul sumped Bill. he relaive pronoun as a noun modifier raher han a noun phrase modifier. We also posi he exisence of lifed versions of he elemenar rees for verbs in which heir argumen posiions have been absraced over. We use a higher-order conjuncion and ha relaes wo properies: λpqx.p(x) Q(x), and a higher-order se funcion ha relaes wo properies and makes use of he higher-order conjuncion: λp Qx.he(, and(p, λz.poss(x, z))(), Q()). The elemenar ree pairs and resuling derivaion ree for senence (6) are given in Figure 7. The derived ree is given in Figure 8. When reduced, he resuling semanics is a(z, λx.(problem(x) he(, soluion() poss(x, ),isdifficul())), sumped(bill, z))...4 Nesed Quanifiers and Inverse Linking Quanifiers in preposiional phrases such as in senence (7) pose anoher challenge for TAG semanics (Joshi e al., 00). Alhough a nesed quanifier ma ake scope over he quanifier wihin which i is nesed (so-called inverse linking ) no all permuaions of scope orderings of he quanifiers are available (Joshi e al., 00). In paricular, readings in which a quanifier inervenes beween a nesing quanifier and is nesed quanifier are no valid. In our example senence (7), his predics ha he readings some > wo > ever and ever > wo > some should no be valid. Joshi e al. (00) inroduce a special device allowing nesing and nesed quanifiers o form an indivisible quanifier
impler TAG emanics hrough nchronizaion / a e, e, e and e, e, sumped e problem se e, e, soluion λ z e, z isdifficul bill FIGURE 8 Derived ree for A problem whose soluion is difficul sumped Bill. se during he derivaion, which prevens oher quanifiers from inervening beween hem. In our soluion, because he nesed quanifier is inroduced hrough he preposiional phrase, which in urn modifies he noun phrase conaining he nesing quanifier, he wo quanifiers alread naurall form a se ha operaes as a uni wih respec o he res of he derivaion. 6 The elemenar ree pairs and derivaion rees for our analsis of (7) are shown in Figure 9. One noable feaure of his analsis is ha he four differen scope readings ha resul are no he produc of a single derivaion ree. The alernae scope orderings for he nesed and nesing quanifier exis because here are wo available adjuncion sies for he scope of quanifiers in he preposiional phrase o aach. This resuls in wo disinc derivaion rees. The alernae scope orderings for his quanifier se and he remaining quanifier are obained b muliple adjuncion a he roo of he verb ree. The se of valid derivaion rees for a senence hus consiues he scope neural represenaion. This se of rees ma be compacl represened, for insance as a shared fores. 7 6 We make use of ree-se-local TAG in he semanics where he ree se for ever adjoins ino he ree se for from. Alhough ree-se-local TAG is more powerful han TAG, his paricular use is benign because i canno be ieraed. More concreel, we could convenionall make he grammar ree-local b including all combinaions of preposiions wih quanifiers as elemenar rees in he grammar. 7 This analsis, like ha of Joshi e al. (00), makes several predicions abou quanifier scope ha migh be dispued. Firs, some argue ha more han four scope orderings should be available for senences like senence (7) (VanLehn, 978, Hobbs and hieber, 987). This analsis canno generae addiional scope orderings wihou breaking ree se locali. econd, he scope readings in which he nesing
/ Rebecca Nesson and uar hieber NP De N wo/ some/ ever wo/ some/ e, ever e, e N N PP P NP from e, and e, e, from e wo spon 4 some poliicians person from ever ci FIGURE 9 Ke elemenar rees and derivaions for Two poliicians sp on someone from ever ci..4 Comparison o he Kallmeer and Romero Approach As menioned above, research on TAG semanics has been led b Laura Kallmeer, Maribel Romero, and heir collaboraors hrough a series of papers refining a ssem of TAG semanics compuaion using feaure unificaion and oher formal devices (Kallmeer and Romero, 004, Romero e al., 004, Kallmeer, 00, Kallmeer and Joshi, 00, Joshi e al., 00, Garden and Kallmeer, 00). Alhough heir approach has evolved over ime, he underling principles of using he relaionships expressed in he derivaion ree as he basis for he compuaion and generaing underspecified semanic represenaions have been consan. In is curren formulaion, he perform semanic compuaion b aaching semanic feaure srucures direcl o he nodes in he derivaion ree. When carefull chosen, hese feaures unif o produce an underspecified represenaion of he semanics of a senence ha, when furher disambiguaed, generaes he se of valid inerpreaions. In one or anoher of heir recen papers he have provided successful analses of each of he hard cases ha we have addressed here, hough some of heir analses migh have o be resaed o bring hem up o dae wih he newes formulaion of heir mehod. Our work owes much o heirs boh for he clear formulaion of he problems and he progress in formulaing analses for some of he hard cases. The primar advanage of our approach is is concepual simplici. The clear separaion of snax and semanics, he direcness of he link inerface, and he familiari of he TAG operaions used in our approach make i ver simple. The semanic-feaure-unificaion-based approach has become cleaner and easier o undersand as Kallmeer quanifier akes scope over he nesed quanifier resul in he nesed quanifier having scope over he resricion of he nesing quanifier bu no over is scope. Donke senence consrucions such as Ever man wih wo books loves hem call his predicion ino quesion.
impler TAG emanics hrough nchronizaion / and ohers have refined i over he ears. Noneheless, i is safe o sa ha he amoun of formal machiner including proposiional labels, separae individual and proposiional variables, semanic represenaions consising of a se of formulas and a se of scope consrains, feaures on he derived ree and he derivaion ree, each semanic feaure srucure conaining a nesed feaure srucure for each address in he elemenar snax ree, each of hese feaure srucures conaining feaures o handle binding of proposiional and individual variables, feaure unificaion, flexible composiion, and quanifier ses necessar o solve he range of problems ha we have addressed here, is qualiaivel more complex. In fac, we use no formal machiner ha had no been inroduced b 994 in he TAG lieraure. An addiional advanage of our approach is ha i does no increase he expressivi of he TAG formalism. One migh hink ha he inclusion of muliple adjuncion would lead o an increase in expressivi (Dras, 999). However, because links can onl be used once in an TAG derivaion, onl a finie number of muliple adjuncions ma occur a a single adjuncion sie. This rules ou problemaic uses of muliple adjuncion. Kallmeer and Romero mainain he semanic feaures on he derivaion ree raher han in he feaure srucures alread used in he feaure-based TAGs (FTAG) of heir snax in par because he se of semanic feaure srucures is no finie, poeniall increasing he expressivi of he FTAG formalism (Kallmeer and Romero, 004). Alhough moving he feaures o he derivaion ree avoids increasing he expressivi of he formalism used for snax when aken alone, he addiional expressivi in he feaures of he semanics could be used o block operaions in he snax hereb filering he snax o produce non-ree-adjoining languages. I remains o be seen wheher his addiional expressivi will be required for TAG semanics. Advanages and disadvanages of he differen mehods aside, in his sill nascen area of research i is desirable o have several quie differen approaches a our disposal as we explore he hard problems presened b generaing naural language semanics in he TAG framework. Our approach revives an old idea wih he aim of opening a new avenue for research ino semanics in he TAG framework..5 Conclusion We have presened he snchronous TAG formalism as a mehod for compuing semanics in he TAG framework, and have shown ha i enables simple, naural analses for all of he cases ha have exercised recen aemps a formulaing formal semanics for TAG. I saisfies
4 / Rebecca Nesson and uar hieber each of he desideraa laid ou a he beginning of his paper. Firs, i does no require an addiional informaion oher han ha available in he derivaion ree o generae he semanics. Because he snax and semanic represenaions are buil up snchronousl, he derivaion ree se is a complee specificaion of he relaionship beween hem. Nohing oher han he se of elemenar ree pairs and he snchronous TAG operaions are required o generae a semanic represenaion. econd, he derivaion ree se provides a compac represenaion for all valid semanic inerpreaions of he given senence. Using mulipladjoined quanifiers we ake advanage of he ambigui in he inerpreaion of he derivaion ree ha is inroduced b muliple adjuncion. We ake each possible ordering of mulipl-adjoined rees o be valid. We leave open he possibili of using an addiional mehod o prefer cerain scope orders and disprefer or eliminae ohers. Third, he TAG ssem, as used, does no increase he expressivi of he TAG formalism (hieber, 994). Finall, our analsis is a sraighforward expression of a simple idea: we use TAG for boh snax and semanics and use he derivaion ree and he links beween rees in elemenar ree pairs as he inerface beween hem..6 Acknowledgemens This work was suppored in par b gran II-09089 from he Naional cience Foundaion. We wish o hank Rani Nelken and he hree anonmous reviewers for valuable commens on earlier drafs. References Dras, Mark. 999. A mea-level grammar: Redefining snchronous TAG for ranslaion and paraphrase. In Proceedings of he Thir-evenh Annual Meeing of he Associaion for Compuaional Linguisics, pages 80 87. Marland, UA. Frank, Rober. 99. nacic locali and Tree Adjoining Grammar: Grammaical, acquisiion and processing perspecives. Ph.D. Thesis, Universi of Pennslvania. Garden, Claire and Laura Kallmeer. 00. emanic consrucion in feaure-based TAG. In Proceedings of he 0h Meeing of he European Chaper of he Associaion for Compuaional Linguisics. Budapes, Hungar. Hobbs, Jerr and uar M. hieber. 987. An algorihm for generaing quanifier scopings. Compuaional Linguisics (-):47 6. Joshi, Aravind K., Laura Kallmeer, and Maribel Romero. 00. Flexible composiion in LTAG: Quanifier scope and inverse linking. In I. v. d..
References / 5 Harr Bun and R. Morane, eds., Proceedings of he Fifh Inernaional Workshop on Compuaional emanics IWC-5, pages 79 94. Tilburg. Kallmeer, Laura. 00a. Enriching he TAG derivaion ree for semanics. In. Busemann, ed., KONVEN 00. 6. Konferenz zur Verarbeiung naürlicher prache., pages 67 74. aarbrücken. Kallmeer, Laura. 00b. Using an enriched ag derivaion srucure as basis for semanics. In Proceedings of he ixh Inernaional Workshop on Tree Adjoining Grammar and Relaed Frameworks (TAG+6), pages 7 6. Venice. Kallmeer, Laura. 00. LTAG semanics for relaive clauses. In I. v. d.. Harr Bun and R. Morane, eds., Proceedings of he Fifh Inernaional Workshop on Compuaional emanics IWC-5, pages 95 0. Tilburg. Kallmeer, Laura and Aravind K. Joshi. 00. Facoring predicae argumen and scope semanics: Underspecified semanics wih LTAG. Research on Language and Compuaion : 58. Kallmeer, Laura and Maribel Romero. 004. LTAG semanics wih semanic unificaion. In Proceedings of TAG+7, pages 55 6. Vancouver. Romero, Maribel, Laura Kallmeer, and Olga Babko-Malaa. 004. LTAG semanics for quesions. In Proceedings of TAG+7, pages 86 9. Vancouver. chabes, Yves and uar M. hieber. 99. An alernaive concepion of ree-adjoining derivaion. Compuaional Linguisics 0():9 4. hieber, uar M. 994. Resricing he weak-generaive capaci of snchronous ree-adjoining grammars. Compuaional Inelligence 0(4):7 85. hieber, uar M. and Yves chabes. 990. nchronous ree-adjoining grammars. In Proceedings of he h Inernaional Conference on Compuaional Linguisics, vol., pages 5 58. Helsinki. VanLehn, Kur. 978. Deermining he scope of English quanifiers. Tech. Rep. 48, MIT Arificial Inelligence Laboraor, Cambridge, MA. Williford, ean. 99. Applicaion of snchronous ree-adjoining grammar o quanifier scoping phenomena in English. Undergraduae Thesis, Harvard College.