Anaphora and Discourse Semantics

ScholarlyCommons

IRCS Technical Reports Series

Institute for Research in Cognitive Science

1-1-2001

Anaphora and Discourse Semantics

Bonnie L. Webber

University of Pennsylvania

, [email protected]

Matthew Stone

Rutgers University

, [email protected]

Aravind Joshi

University of Pennsylvania

, [email protected]

Alistair Knott

University of Otago

, [email protected]

Follow this and additional works at:

http://repository.upenn.edu/ircs_reports

University of Pennsylvania Institute for Research in Cognitive Science Technical Report No. IRCS-01-13.

At the time of publication, the author, Bonnie L. Webber, was affiliated with the University of Edinburgh. Currently, July 2007, she is a faculty member

in the Department of Engineering at the University of Pennsylvania.

Webber, Bonnie L.; Stone, Matthew; Joshi, Aravind; and Knott, Alistair, "Anaphora and Discourse Semantics" (2001).

IRCS Technical

Reports Series

. 30.

Abstract

We argue in this paper that many common adverbial phrases generally taken to be discourse connectives

signalling discourse relations between adjacent discourse units are instead anaphors. We do this by (i)

demonstrating their behavioral similarity with more common anaphors (pronouns and definite NPs); (ii)

presenting a general framework for understanding anaphora into which they nicely fit; (iii) showing the

interpretational benefits of understanding discourse adverbials as anaphors; and (iv) sketching out a

lexicalised grammar that facilitates discourse interpretation as a product of compositional rules, anaphor

resolution and inference.

Comments

University of Pennsylvania Institute for Research in Cognitive Science Technical Report No. IRCS-01-13.

At the time of publication, the author, Bonnie L. Webber, was affiliated with the University of Edinburgh.

Currently, July 2007, she is a faculty member in the Department of Engineering at the University of

Pennsylvania.

Bonnie Webber

Matthew Stone

EdinburghUniversity RutgersUniversity

AravindJoshi AlistairKnott

Universityof Pennsylvania UniversityofOtago

We argue in this paper that many common adverbial phrases generally taken to be dis-course connectives signalling discourse relations between adjacent discourse units are insteadanaphors. Wedothis by (i)demonstratingtheir behavioral similarity withmore commonanaphors(pronounsanddeniteNPs); (ii)presenting ageneral framework for understandinganaphoraintowhichtheynicelyt;(iii)showing theinterpretational ben-ets of understanding discourse adverbials as anaphors; and (iv) sketching out a lexi-calised grammar that facilitates discourse interpretation as a product of compositional rules, anaphorresolution andinference.

Introduction

Severalyearsago,inanACLworkshoppaper,JanyceWiebe(1993)cited Example1to questiontheadequacyoftreestructuresfordiscourse.

(1) a.Thecarwasnally comingtowardhim. b. He[Chee]nishedhisdiagnostictests, c.feelingrelief.

d. Butthenthecarstartedtoturn right.

The problem shenotedwas that thediscourse connectivesbut andthen appear to link clause (1d) totwodierentthings: \then"to clause(1b) {i.e., thecarstarting toturn right being the next relevant event after Chee's nishing his tests { and \but" to a combinationofclauses(1a)and(1c){i.e., thecar turningrightfailing theexpectation of its continuing in the same direction and being the car that Chee is awaiting. (The formerlink iscommonlycalledasequencerelation,andthelatter,aformofcontrast.)

These relations are usually taken to be the basis for low-level discourse structure, leadingtosomethinglikeFigure1forExample1.Thisstructuremightseemadvantageous in allowingthesemanticsoftheexampletobecomputeddirectlybycompositionalrules and defeasibleinference. However, this structure is in fact aDAG {adirected acyclic graph.

1

Viewed syntactically, arbitrary DAGS are completely unconstrained systems. Theysubstantiallycomplicateinterpretiverulesfordiscourse,inorderforthoserulesto account for therelativescope of unrelatedoperatorsand the contribution of syntactic nodeswitharbitrarilymanyparents.

Whilewearenotcommittedto discoursestructurebeingatree(e.g.Figure2from (Bateman,1999)),wefeelthatthecosttodiscoursetheoryofmovingtoarbitraryDAGs for discourse structure is too great to be taken lightly. Sowewant to suggest another explanationfortheseandotherexamplesofapparentcomplexandcrossingdependencies

DivisionofInformatics,UniversityofEdinburgh,2BuccleuchPlace,EdinburghUKEH89LW. E-mail:[email protected]

1ThestructureinFigure1islabelledwiththetypeofrelationtakentoholdandits\support"from eitheraconnective(\but")oradverbial(\then").Thereareotherpossiblestructuresfor

c

b

d

a

elaboration

contrast

seq

seq

PossiblediscoursestructureforExample1.

9

8

6

succession

manner

Figure2

Simplemulti-parentstructure

indiscourse:whilestructural connectivessuchascoordinating(e.g.,\but")and subordi-nating(e.g., \although")conjunctionsdoindeed signaldiscourserelationsbetween(the interpretationof)theirconjuncts,discourse adverbialssuch as\then",\otherwise",and \nevertheless"are insteadsimply anaphors, signalling arelation between the interpre-tation of their matrix clause and the discourse context. We argue that understanding discourse adverbialsas anaphorsaccomplishesfourimportantgoals:

1.It recognisestheirbehavioral similaritywiththepronounsanddenitenoun phrases(NPs)thatarethe\breadandbutter"ofpreviousworkonanaphora (Section1).

2.It contributessubstance totheview,expressedforexamplebyCarter(1987) that anaphoracomprisesmorethanjust pronounsanddenite NPs:

Anaphoraisthespecialcaseofcohesionwhere themeaning(sense and/orreference)ofoneitemin acohesiverelationship(theanaphor) is,in isolation,somehowvagueandincomplete,andcanonlybe properlyinterpretedbyconsideringthemeaningsoftheotheritem(s) in therelationship(theantecedent(s)).(Carter,1987,page33)

This isexplored inSection2.

3.It supportsthedirect computationofdiscoursesemanticsthrough

compositional rulesand defeasibleinference.Thisisagoalthat researchers havebeenstrugglingafterforsometime(AsherandLascarides,1999;Gardent, 1997;Kehler,1995;Polanyiand vanden Berg,1996;SchaandPolanyi,1988; Schilder,1997a;Schilder,1997b;vandenBerg,1996),andthatWiebe essentiallyrecognisesinherconcernabouttheconsequences fordiscourse structureofexamplessuch as(1).Enabling anaphorresolutiontocontributeto meaningsimpliestheprocessofcompositionalsemantics

2

anddirects

2Thereisananalogoussituationatthesentencelevel,wheretherelationshipbetweensyntactic structureandcompositionalsemanticsissimpliedbyfactoringawayinter-sententialanaphoric relations.Herethefactorisationissoobviousthatonedoesnoteventhinkaboutanyother possibility.

attentiontohowthemeaningofdiscourseadverbialssupportsand complementsotheraspectsofdiscoursesemantics(Section3).

4.It allowsustosee moreclearlyhowalexicalised approachtothecomputation ofclausalsyntaxandsemanticsextends naturallytothecomputationof discourse syntaxandsemantics,providingasinglesemanticmatrixwithwhich to associatespeakerintentionsandotheraspectsofpragmatics.(Section4)

Theaccountweprovidehereismeantto becompatible withcurrentapproachesto discoursesemanticssuchasDRT(KampandReyle,1993;vanEijckandKamp,1997)and Dynamic Semantics(Stokhof and Groenendijk, 1999) and with moredetailed analyses of the meaning anduse of individual discourse adverbials, such as(Jayez andRossari, 1998a; Traugott,1997):it provides whatwebelieveto be asimplerandmorecoherent account of how discourse meaning is computed, rather than an alternative account of what thatmeaningisorwhat speakerintentionsitisbeingusedtoachieve.

1 Discourse Adverbials as Anaphors

1.1 Discourse Adverbials do not behave like Structural Connectives

Wetakethebuilding blocksof themostbasiclevelof discoursestructure tobeexplicit structural connectives betweenadjacentdiscourse units (i.e., coordinating and subordi-natingconjunctions, and\paired"conjunctions such as\notonly... but also",\on the onehand...ontheother(hand)",etc.)andinferredrelationsbetweenadjacentdiscourse units(intheabsenseofanexplicitstructuralconnective).Here,adjacencyiswhattriggers theinference.Considerthefollowingexample:

(2) Youshouldn'ttrustJohn.Heneverreturnswhatheborrows.

Adjacency leadsthe hearer to hypothesize that the second clause is relatedto its left-adjacentneighbor{andmorespecically,thataformofrhetoricalrelationholdsbetween thetwo.(Wediscussthismorein Section 4.)Ourgoalinthissectionis toconvincethe reader that many discourse adverbials {including \then", \also", \otherwise", \never-theless",\instead"{behavenotlikestructuralconnectives,but insteadlikeanaphors.

Structuralconnectivesanddiscourse adverbialsdohaveonethingin common:Like verbs,theycanbothbeseenasheadingapredicate-argumentconstruction;unlikeverbs, theirargumentsareindependentclauses.Forexample,boththesubordinateconjunction \after"andtheadverbial\then"(initstemporalsense)canbeseenasbinarypredicates (sequenceorafter)whoseargumentsareclausally-derivedevents.

Butthatistheonlythingthat discourseadverbialsandstructuralconnectiveshave in common.As wehavepointedoutinearlierpapers(Webber,Knott,andJoshi,1999; Webber et al., 1999a; Webber et al., 1999b), structural connectives havetwo relevant properties: while they admit stretching of predicate-argument dependencies, they do not tolerate their crossing. This is most obvious in the case of preposed subordinate conjunctions (Example3) or\paired"coordinateconjunctions (Example4). With such connectives,theinitial predicatesignalsthatitstwoargumentswillfollow.

(3) Although Johnisgenerous,heishardtond.

(4) On theone hand,Fredlikesbeans.Onthe other hand,he'sallergictothem.

Likeverbs,structuralconnectivesallowthedistancebetweenthepredicateandits argu-mentstobe\stretched"overembeddedmaterial,withoutlossofthedependencybetween them.Fortheverb\like"andanobjectargument\apples",suchstretchingwithoutloss of dependencyisillustratedinExample5b.

(i)

(ii)

a

b

d

contrast[one/other]

elaboration

comparison[not only/but also]

a

b

d

elaboration

concession[although]

c

c

condition[if]

Discoursestructuresassociatedwith(i)Example6and(ii)Example7.

b. ApplesBillthinks heheardFredsayJohnlikes.

That this also happens with structural connectivesand theirarguments, is illustrated in Example6(inwhichtherstclauseofExample3iselaboratedbyanotherpreposed subordinate-mainclauseconstructionembeddedwithinit)andExample7(inwhichthe rstconjunctofExample4iselaboratedbyanotherpaired-conjunctionconstruction em-beddedwithinit).PossiblediscoursestructuresfortheseexamplesaregiveninFigure3.

(6) a.AlthoughJohnisverygenerous{ b. ifyouneedsomemoney,

c.youonlyhavetoaskhimforit{ d. he'sveryhardtond.

(7) a.Ontheonehand,Fredlikesbeans. b. Notonlydoesheeatthemfordinner.

c.Buthealsoeatsthem forbreakfastandsnacks. d. Ontheotherhand,he'sallergictothem.

But, as already noted, another property of structural connectives is that they do not admit crossingofpredicate-argumentdependencies.Ifwedothis withExamples6and 7,weget

(8) a.AlthoughJohnisverygenerous{ b. ifyouneedsomemoney{ c.he'sveryhardtond{

d. youonlyhaveto askhimforit.

(9) a.Ontheonehand,Fredlikesbeans. b. Notonlydoesheeatthemfordinner. c.Ontheotherhand,he'sallergictothem. d. Buthealsoeatsthemforbreakfastandsnacks.

Possiblediscoursestructuresforthese(impossible)discoursesaregiveninFigure4.Even ifthereaderndsnoproblemwiththese crossedversions,theyclearlydonotmeanthe samethingastheiruncrossedcounterparts:In(9),\but"nowappearsto link(9d)with (9c), conveying that despite being allergic to beans,Fred eats them for breakfast and snacks.Andwhile thismightbeinferred from(7), itis certainlynotconveyeddirectly. Asaconsequence,westipulatethatstructuralconnectivesdonotadmitcrossingoftheir predicate-argumentdependencies.

That is notall. Since wetake the basiclevel of discourse structure to be a conse-quence of(a) relationsassociatedwith explicitstructural connectivesand (b) relations

a

b

c

concession[although]

condition[if]

elaboration

a

b

elaboration

contrast[one/other]

comparison[not only...]

(i)

(ii)

d

c

d

Figure4

(Impossible)discoursestructuresthatwouldhavetobeassociatedwithExample8(i)and withExample9(ii).

a

b

c

d

conseq[so]

explanation[because]

seq[then]

contrast[but]

Figure5

Example10,withstructuralrealisationofall dependencies

whosedefeasibleinferenceistriggeredbyadjacency,westipulatethatlow-leveldiscourse structureitself does notadmitcrossingstructuraldependencies.(In thissense,discourse structure maybetruly simplerthansentencestructure. Toverifythis, itmightbe use-ful to carefullyexamine thediscourse structure of languagessuch asDutch that allow crossingdependenciesin sentence-levelsyntax.Initialcursoryexaminationdoesnotgive anyevidenceofcrossingdependenciesinDutchdiscourse.)

Ifwenowconsiderthecorrespondingpropertiesofdiscourseadverbials,weseethat they do admit crossing of predicate-argument dependencies. Example 10 shows this clearly. Clause 10(d) contains the discourse adverbial\then". For it to get is rst ar-gument from (b){i.e., theeventthat the discoveryin (d) is\after",it mustcross the structural connection between clauses (c) and (d) associated \because". This crossing dependencyisillustratedin Figure5.

(10) a.JohnlovesBarolo.

b. Soheorderedthree casesofthe'97. c.Buthehadtocanceltheorder

d. becausethenhediscoveredhewasbroke.

But ofcoursecrossingdependenciesarenotunusualin discourse becauseanaphors (e.g., pronounsanddeniteNPs)doitallthetime,forexample:

(11) Everyman i

tellseverywoman j

he i

meetsthatshe j remindshim i ofhis i mother.

This suggests that in Example 10, the relationship between \then" and the previous discourse mightusefullybetakento beanaphoricaswell.

1.2 Discourse Adverbials do behave likeAnaphors

There is additional evidence to suggest that \otherwise", \then" and other discourse adverbialsareanaphors.First,anaphorsin theform ofdeniteand demonstrativeNPs cantakeimplicitmaterialasarguments.Forexample,in

(12) Stack veblocks ontopof oneanother.Nowclose youreyesand tryknocking fthe tower,thistowergoverwithyournose.

bothNPs referto thestructurewhichis theimplicitresultoftheblockstacking. (Fur-ther discussionofsuch examplescanbefoundin (Isard, 1975;Dale,1992; Webberand Baldwin,1992).)Thesameistrueofdiscourseadverbials.In

(13) Doyouwantanapple?Otherwiseyoucanhaveapear.

thesituationinwhichyoucanhaveapearisoneinwhichyoudon'twantanapple{i.e., where youranswertothequestionis\no".Butthisanswerisn'ttherestructurally:itis onlyinferred.Whileitappearsnaturaltoresolveananaphortoaninferredentity,itwould bemuchmorediÆculttoestablishsuchlinksthroughpurelystructuralconnections:todo sowouldinvolveasubstantialcommitmenttocovertconstituentsindiscoursestructure.

Secondly,attempts toparaphrase\otherwise"in termsofthestructuralconnective \or"demonstratethat \otherwise"hasawider rangeofoptions.

3

Thisis illustratedby thefollowingpairofexamples:

(14) a. Ifthelightisred,stop.Otherwiseyou'llgetaticket. (Ifyou dosomething other thanstop,you'llgetaticket.)

b. Ifthelightisred,stop.Otherwisegostraighton. (Ifthe lightisnot red, go straighton.)

Only one of these two ways of resolving \otherwise" in the context of a preceding if-constructioncan beparaphrased with \or" {that is, only the case where \otherwise" resolvestoanalternativeto theconsequenceclause,asin (14a){cf.

Ifthelightisred,stoporyou'llgetaticket.

Paraphrasing(14b)with\or",asin

Ifthelightisred,stoporgostraighton.

produces somethingwhose meaning is quite dierent. Thus, \otherwise"has access to materialthatisnotavailabletoastructuralconnective.(Actually,inSection4,weposit twoseparatelexico-syntacticentriesfor\or"as astructuralconnective{oneforpurely logical\or"andtheotherfor\or"conveyinganindependentsemanticrelationbetween itsarguments,asisthecasehere.)

Our nal piece of evidence is that, like pronouns, these discourse adverbials can appearin ananalogueofdonkey sentences. Donkeysentences such asExample 15have beenusedtoarguetheintrinsicdiscoursenatureofpronominalanaphors:thatpronouns are notmerelyareexofasyntacticbindingoperation.

(15) Everyfarmerwhoownsadonkeyfeedsitrutabagas.

In donkey sentences, anaphors appear in astructural and interpretive environment in whichadirectsyntacticrelationshipbetweenanaphorandantecedentisnormally impos-sible. Therefore,donkeysentencesareevidence forinterpretingananaphorbyaccessing adiscourseentityinsteadofbysyntacticbinding.

While no one hasever argued that discourse adverbials are areex of asyntactic bindingoperation{theyhavealwaysbeentreatedaselementsofdiscourseinterpretation, signalling relationsbetweenadjacent clauses{it is signicantthat they canappear in theirownversionofdonkeysentences,asin

(16) a. Anyonewhohasdevelopednetworksoftware, hasthenhadto hire alaywer toprotecthis/herinterests.(i.e.,after developingnetwork software)

b. Manypeoplewhohavedevelopednetworksoftware,haveneverthelessnever gottenveryrich.(i.e.,despite havingdevelopednetworksoftware)

c. Everyperson selling \The Big Issue" might otherwise be asking for spare change.(i.e.,if s/he weren'tselling\TheBig Issue")

This suggests that discourse adverbials are accessing discourse entities (in particular, eventualities)ratherthansignallingastructuralconnectionbetweenadjacentclauses.

4

3ThiswaspointedoutindependentlybyNataliaModjeska,LauriKarttunen,MarkSteedman,Robin CooperandDavidTraum,onpresentationofthisworkatESSLLI'01inHelsinki,August2001. 4WhileRhetoricalStructureTheory(RST)(MannandThompson,1988)wasdevelopedasan

accountoftherelationbetweenadjacentunitswithinatext,Marcu'sguidetoRSTannotation (Marcu,1999)hasaddedan\embedded"versionofeachRSTrelationinordertohandexamples suchasin(16c)andothers,inwhichthematerialinanembeddedclause(here,arelativeclause) bearsasemanticrelationtoitsmatrixclause.Whilethisimportantlyrecognisesthephenomenon,it doesnotcontributetounderstandingitsnature.

These argumentshavebeendirectedat thebehavioralsimilaritybetweendiscourse adverbialsand whatwenormallytaketo bediscourseanaphors.Butthisisn't theonly reason to recognise themas anaphors:In thenext section,wesuggestaframework for anaphorain whichdiscourse adverbialstasneatly

5

aspronounsanddenite NPs.

2 A Frameworkfor Anaphora

2.1 Discourse referents and anaphor interpretation

If wewanttotakediscourseadverbialstobeanaphors,wehavetoask whatkind,since on thesurface,adverbialsneitherwalknortalk likethe anaphorswearemustfamiliar with {pronounsand deniteNPs.All discourseanaphors involve,at theveryleast, an anaphoric expressionandoneormoreentitiese

r

fromthediscoursecontextorcontext of utterance

6

that contributeinsomewaytotheinterpretationof,e

.

One thing we want to point out, although it is not critical to our discussion of discourseadverbialsasanaphors,isthat notallthematerialin theexpressionmaybe anaphoric{i.e.,interpretedwithrespecttoe

r

.Forexample,onetypeofexpressionthat wetaketobeanaphoricis \otherNPs"

7 ,asin:

(17) a.ThenewmayorofLondonhasdeclaredwaronpigeons. b1.Other birdshavenotincurredhiswrath.

b2.Other birdsthatinhabit thecityyearroundhavenotincurredhis wrath. b3.Other birdswithmoresanitaryhabitshavenotincurredhiswrath. b4.Other moresanitarybirdshavenotincurredhis wrath.

In (b1),onewould obviouslytaketheanaphoric expressionto betheentire NP \other birds". Its interpretation involvesthe entitye

r

evoked by \pigeons"in (17a), which is excludedfromthesetofbirdsunderconsideration,whichhavenot(wearetold)incurred themayor'swrath.Similarly,in(b2),onewouldtaketheanaphoricexpressiontobethe entireNP\otherbirdsthatinhabitthecityyearround",withitsinterpretationinvolving the exclusionof e

r

(pigeons) from that set. In (b3) and (b4), however, if we take the anaphoric expressionto betheentireNP,then itisnotthecasethat e

r

(pigeons)isto beexcludedfromthesetofbirdswithmoresanitaryhabits(b3)ormoresanitarybirds (b4),sincetheydon't belong toeither set:theyare simplybeingexcludedfrom theset ofbirds.Soonemaywanttoallowforananaphoricexpressiontocompriseonlypartofa constituent, thoughtheinterpretation oftheentire constituentwill,asaresult,depend onhowtheanaphorisresolved.

8

Now,besidese r

(theentityorentitiesfromcontext d=u

)ande

(theinterpretationof theanaphoricexpression ),wehavebeenmotivatedto introduceathirdentitye

i into theprocessofanaphorinterpretation,whichwecallacontextualparameter:e

i

isderived from e

r

andsupplied to the interpretationof .The motivation relatesto thefamiliar phenomenon variously calledtextual ellipsis(Hahn, Markert,andStrube, 1996),partial anaphora (Luperfoy,1992),indirect anaphora(Hellman andFraurud, 1996),associative anaphora (Cosse, 1996), and bridging anaphora (Not, Tovena, and Zancanaro, 1999), illustratedin Example18.

(18) Myradarted toaphoneandpickedupthe receiver.

5totheextentthatanythinginhumanlanguagecanbeconsidered\neat" 6Sincewerefertothisdisjunctionsooften,weabbreviateitsimplycontext

d=u 7Thereismorediscussionof\otherNPs"laterinthissection.

8ThatthisoccursevenwithdeniteNPswasobservedovertwentyyearsagobyoneofthe co-authors(Joshi,1978),whoconsideredthequestionofwhetheradeniteNPcould simultaneouslyco-referandprovidenewinformationaboutitsreferent.

Here, the receiver is taken to be the one associated with the phone Myra darted to. Examplessuchasthiscanbemodelledwiththetwoentitieswealreadyhave,bysaying that e

canbederivedfrom e r

byassociation.However,relatedexamplessuchas

(19) She liftedthereceiverasMyradartedto the otherphone....

discoveredby Modjeska(2001)in the British NationalCorpus, requiremore,since the anaphoric expression (the other phone) is interpreted as the (contextually relevant) phone that is notthe one associated withthe receiverthat has just belifted. That is, getting from e

r to e

in this case requires both association (as in Example 18) and exclusion fromacontextuallyrelevantset.

Wecandealwiththisbyintroducinganotherentity{acontextualparameter{and computinge intwosteps: 1.e r !e i

(e.g.,[receiver]![phone(e r )]) 2.e i !e (e.g.,[phone(e r

)]![fcontextuallyrelevantphonesg-fphone(e r

)g]).

That is, in Example 19, \the receiver" evokesa discourse entity e r that is areceiver; from e r , we derive e i

, the phone associated with it; and from e i

, we compute e

, the interpretationof\theotherphone"is thephonein context

d=u

thatisnote i

. Moregenerally,wedistinguishpossiblerelationshipsbetweene

r ande i andbetween e i and e asfollows: e i maybeidenticaltoe r orsomeassociateofe r

.Thisdierencebetween coreference andmediated referenceisapropertyofoccurrencesof anaphors.Thatis,exceptfordemonstrativeNPs, whichcannotbeusedfor mediated reference, thesametypeofanaphoricexpressioncanbeusedfor both. e maybeidenticaltoe i orcomputedfrome i

in somemorecomplexwaythat isidiosyncratictotheparticularanaphor.This dierencebetweenan

interpretation thatisspecifiedbythecontextualparameterandonethat is computed fromit,isapropertyofthetypeofanaphoricexpression.

Thesepossiblerelationsbetweene r ande i andbetweene i ande

giveusthefamiliar caseofcoreferencewhene

=e

i =e

r

.ThisisshowninExamples20{23,usingavariety of anaphoricexpressions:

(20) pronoun:Theterrierdowntheblockbitmeyesterday.It'saviciouslittlebeast.

(21) denite NP: Johnused to havebothaterrierand aschnauzer.However,one daytheterrier gotlooseandranaway.

(22) demonstrative pronoun: The terrier down the block bit me yesterday. My sister foundthis amusing.

(23) demonstrativeNP:Someofthewomeninthewardareover30.Ifanyofthese primagravidaerequestsanurse,please attendtothemrightaway.

Example 22 also illustrates identitywith the discourse entity associated with an even-tuality, while Example 23 illustrates our earlier point that not all the material in an anaphoric expression may be anaphoric,with \primagravidae"(applied to womenover 30 who are giving birth for the rst time) being new information provided about the entitythat thedemonstrativeNPco-refersto.

9

9Accountingforhowcoreferenceisresolvedisprobablythemostpersistenttopicintheliteratureon anaphora,bothfromapsycholinguisticandfromanengineeringperspective.However,itisnotone wewilladdressinthispaper,thoughitisrelevanttoallformsofanaphorawediscusshere.

Distinguishingtherelationbetweene r

ande i

fromthatbetweene i

ande

alsogives thefamiliarcaseofassociative reference(aka\textualellipsis",\partialanaphora", \in-directanaphora",\associativeanaphora"and\bridginganaphora")whene

i =assoc(e r ), and either e =e i or e e i

.This is shownin Examples24{26.The onlyconstraintis that the association be licensed by the domain. (Notice that in the case of (24) and (26),e

=e

i

(i.e.,theinterpretationisspecifiedbythecontextualparameter),whilein (25), e

is an element of e i

(i.e., the interpretation is computed from the contextual parameter).

10

(24) denite NP: Johnforgotto put the picnic suppliesin his cooler.So whenhe gottothepicnic,the beerwastoowarmtodrink.

e r =[picnic supplies] e =e i =[beer(e i )]

(25) indenite NP: TheNumber26bushadtodetour totheWesternGeneral be-causeapassengerfell unconscious.

e r

=[theNumber26bus] e i =passengers(e r ) e e i

(26) demonstrative pronoun:Multiply 14times51,andthendividethatby17. e r =[actofmultiplying14*51] e =e i =[result(e r )] Bute

mayalsobecomputedfrome i

inwaysthatareidiosyncratictotheparticular anaphor, where either e

i =e r ore i = assoc(e r

). Anaphors of this type wecall lexical anaphors. Some are referringexpressions: The mostcommon may be NPs of the form \(the)otherX",whichrefertotheresultofexcludinge

i

fromacontextually-relevantset (Bierner, 2001a;Bierner, 2001b;Bierner and Webber, 2000; Modjeska, 2001). Here,e

i maybeanindividual (Example27)orasetderivedfromapluralNP orthrough\split reference"(Example28).

(27) Q:What'sthedrinkingageinAfganistan? A: :::

Q:What'sitinother countries? e i =e r =[Afganistan] e =fcountriesg-fe i g

(28) Q:What'sthedrinkingageinAfganistan? A: :::

Q:What'sitinBolivia? A: :::

Q:What'sitinother countries? e i =e r =f[Afganistan],[Bolivia]g e =fcountriesg-e i

As wehavealready seenin Example 19 (repeatedhere), thecontextual parameter maybeassociatedwithe

r

(mediated reference), ratherthanidenticalwithit:

(19)Shelifted thereceiverasMyradartedtothe other phone.... e r =[receiver] e i =[phone(e r )] e

=[fcontextuallyrelevantphonesg- fe i

g]

10Againhere,themainproblemnotedintheliteratureisthatofspecifyingeectiveresolution proceduresthattakeadvantageofboththecontext

d=u

andworldknowledge{thelatterto characteriselicencedassociations.

What istobeexcludedcanalsocome fromthecontextofutterance,asinExample29, askedbyoroftherstauthor,

(29) Arethereother shortpeopleworking on discourse? e i =e r =[BLW] e

=fshortpeopleworkingondiscourseg-fe i

g

ortheexcludedentitymaybeaneventualityassociatedwithoneormoreclauses, asin thefollowingfrom (Modjeska,2001):

(30) If the patientis veryheavy orthecarercannot manage for some other reason ::: [BNC]

e i

=e r

=kthepatientisveryheavyk e

=freasonswhythecarercannotmanageg-fe i

g

Note that \other X" also presupposes that theexcluded entities belong to the set under consideration (Bierner and Webber, 2000; Bierner, 2001a; Bierner, 2001b). For example,in (31),\otherrug-makingcountries"presupposesthat Chinaisarug-making country, and \otherartisticdisciplines" presupposesthat rug-makingisan artistic dis-cipline.

(31) Unlikeotherrug-makingcountries,Chinamainlydrawsitsdesignrepertoirefrom other artisticdisciplines (painting,etc),:::

e i1 =e r1 =[China] e 1 =frug-makingcountriesg-fe i1 g presupposed:e r1 frug-makingcountriesg e i2 =e r2 =[rug-making] e 2 =fartistic disciplinesg-fe i2 g presupposed:e r2 fartisticdisciplinesg

A hearer for whom this is new information must either accommodate it or refuse to do so. Certain relational anaphors such as\nevertheless"also have a presuppositional component to their meaning (Section 2.2). This will be relevant to our discussion in Section 3of relationsbetween thesemanticcontributions ofanaphoric connectivesand those ofstructuralconnectivesandadjacency-triggeredinferences.

Other expressionsdiscussedin (Bierner,2001b)that incorporateinanidiosyncratic way, an individual or set from the discourse context orcontext of utterance are noun phrasesheaded by\other" (Example32), \such NPs"(Example33), comparativeNPs (Example 34),andthepronoun\elsewhere"(Example35).

(32) Somedogsareconstantlyonthemove.Othersliearounduntilyoucallthem.

(33) Isawa2kglobsterintheshstoreyesterday.Theshmongersaidittakesabout 5yearstogrowtosuchasize.

(34) Terriersareverynervous.Larger dogstendto havecalmerdispositions.

(35) I don'tlikesittinginthisroom.Canwemoveelsewhere?

As Bierner(2001b)notes, thesehavesimilarpresuppositionsaboutmembershipofe i

in thesetunderconsideration.Inaddition,allofthemalsoappearinconstructionsthatare not anaphoric {e.g.,Xs otherthan Y, Xs such as Y, <comparative> Xsthan Y, etc., wherewhatistobeexcludedorcomparedtoisprovidedstructurally.Butignoringthese non-anaphoric versions,the same problem of how to resolve lexical function anaphors against the discourse context orcontext of utteranceremains to be solved (Modjeska, 2001; Salmon-Alt,2000).

11

11Ourdiscussionhereofrelationsbetweene r

,e i

ande

2.2 Discourse Adverbials as Lexical Anaphors

Wewanttoclaimthatlexicalanaphorsdonothavetobereferringexpressions.Instead,a lexicalanaphorcanexpressabinaryrelationbetweenananaphorically-derivedargument (thecontextualparametere

i

)andtheinterpretationoftheanaphor'smatrixsentenceor clause. Theresultisanadditionalpropositioncontributedto thediscourse.

Thisisthewayinwhichweclaimthatavarietyofdiscourseadverbialsareanaphoric {forexample,\then"inExample36and\instead"in Example37.

12

(36) JohnlovesBarolo.Soheorderedthreecasesofthe'97.Buthehadtocancelthe order becausehe thendiscoveredhewasbroke.(i.e.,after heorderedthewine, hediscoveredhewasbroke.)

(37) John didn't have enoughmoney to buy a mango.Instead, he boughta guava. (i.e.,heboughtaguavaasanalternativetobuyingamango)

These paraphrasesareonlymeantto conveyroughapproximationsof theactual mean-ing of \then" and \instead". Our concern here is only with the mechanism by which these adverbialsget theirmeaning. For a detailed analysis of themeaningof discourse adverbials and connectives, see (Jayez and Rossari, 1998a; Jayez and Rossari, 1998b; Lagerwerf,1998;Traugott,1995;Traugott,1997)andothers.

Formally,wemodelsuchlexicalanaphors{whichwecallrelational anaphors{asa functionthatmapsthecontextualparametere

i

(eithercoreferentialwithe r

orassociated with it)to anexpressionthat isidiosyncraticto theanaphor

:e i !x:R (x;e i )

Thatfunction thenappliestotheeventualitythatcorrespondstotheinterpretationof theanaphor'smatrixclauseS,yieldingaproposition

S:[x:R (x;e i )]=R (;e i )

The two dierent function notations (!, ) and the explicit step of derivation here indicate that the contextual parameter e

i

serves as an argument to R

but that is supplied compositionallyfromsyntax.

Wewill nowuse thisto explainwhat is going onin arangeof examplesinvolving discourse adverbials.Butto doso, weneed to introduce and justifythe representation wewilluseforclausal interpretations.

Therearetwocommonwaysofrepresentingpredicate-argumentrelationsin sentence-level interpretations. For example, themeaning of Example 38a canbe roughly repre-sentedeitheras(b)or(c).

(38) a.Johnlikessomeapples.

b. likes'(e,j,a)^john'(j)^some-apples'(a) c.likes'(john',some-apples')

discourseadverbials.Butotherlinguisticphenomenahavebeenconsideredanaphoric,includingVP ellipsis(Hardt,1999;Kehler,1995),\doso"anaphora(and,wesuggest,\dootherwise").Certain modiersmightalsobeconsideredanaphors(e.g.,\dierent",\dierently",\similar",\similarly", etc.).Soitwouldbeworthwhiletoconsiderwhat,ifanything,canbegainedbyanalysingsuch anaphorsintermsofthesetwostagesofer!eiandei!e.

12Wordsandphrasesthatfunctionasdiscourseadverbialsmayhaveotherfunctionsaswell{e.g., \otherwise"canbeusedasanadjectivalmodier,asin\Iwasotherwiseoccupiedwithgrading exams."and\ontheotherhand"mayserveasonehalfofthestructuralconnective\Ontheone hand,::: Ontheother(hand),:::"(cf.Section4).Overloadingclosed-classlexico-syntacticitems isnotunusualinEnglish,andmustjustbehandledaspartofthenormalambiguityresolution process.

(38b)makesexplicittheroleofindividuals,eventualitiesandrelationshipsamongthemin interpretation.Ithelpsthereaderunderstandthekindofmeaningsthatlexicalitemscan have,orthewaylexicalmeaningscontributeto utterancemeaning.Butrepresentations like(38b)arelessgeneralthanrepresentationslike(38c),asExample39illustrates.

(39) a.Thepresidentopposestaxincreases.

b. oppose'(e,p,i)^president'(p)^taxincreases'(i) c.oppose'(president',taxincreases')

Wecaneasily understand (39a) as a compactdescriptionof many dierent people (Reagan, Bush, Clinton, Bush) fullling a common role over time, and the attitudes they have taken to a number of purely hypothetical objects (planned increases that wereneverrealized).Representationslike(39b)accommodate thisonly by somerather extremeassumptionsaboutwhatindividualsandeventualitiescancountasvaluesfore, pori.Representationslike(38c)and(39c)aremoregeneral,whileaordinglessspecic semanticintuitions.

We nd the same tradeo with predicate-argument structures in discourse. (For ease of reading later on, we will switch here to a minor syntactic variant of the \b" representation, in which the eventualityargumentindexes thepredicate{for example, e:likes(j,a)ratherthanlikes(e,j,a).)

(40) a.JohnleftbecauseMaryleft. b. e 1 :left'(j) ^john'(j)^e 2 :left'(m)^mary'(m)^e 3 :because(e 1 ,e 2 ) c.because'(left'(john'),left'(mary')

While(40b)givesgoodintuitionsabouttheindividuals andeventualitiesdescribed in discourseand the compositionalityinvolvedin discourse interpretation, representing \because"this wayrequiresunderstanding eventualitiesin arichand potentially prob-lematic way.Ontheotherhand,while(40c)isunproblematic,itsnotationdoesnothelp usrememberthemanyconstraintson\because"{inparticular,thatJohnandMarydid in factleave!

Anaphoraandanaphorresolutioncomplicatethepicture:Theb-representations rep-resent resolved anaphors by reuse of a discourse referent, while the c-representations requiretheconstructionofE-typedescriptions(Evans,1980;Neale, 1990)that drawon material frompreviousdiscourse.WecanseethisbycontinuingExample38asfollows:

(41) a.::: [but]Billhatesthem. b. ::: e

2

:hates'(b,a)^bill'(b)

c.hates'(bill',the'(apples',x.likes'(john',x)))

(41b) reuses thediscourse referenta introduced by \some apples" in (38b). For(38c), there is no such discourse referent, sowe haveto construct adescription: \the apples Johnlikes".

In this paper, we follow Hobbs (1985)in using b-style representations,becausewe wanttomakeintuitionsaboutindividuals,eventualities,lexicalmeaningandanaphoraas clearaspossible.Butthischoiceisnottheoreticallynecessary.Usingthisrepresentation, wetreatourfamilarExample10,repeatedhereas(42),asfollows:

(42) JohnlovesBarolo.Soheorderedthreecasesofthe'97.Buthehadtocancelthe order becausehethendiscoveredhewasbroke.

then:e i

!x.after(x, e i

)

S =he[John]discoveredhewasbroke =e 4 ,wheree 4 :discover(j,e 5 )ande 5 :broke(j) e i =e r =e 2 ,wheree 2 :order(j,c 1 ) thenS:[x.after(x,e 2 )]e 4 after(e 4 ,e 2 ) That is, e 4

(the interpretation ofS as an eventuality)is the eventof John discovering that he wasbroke,while e

2

Resolvingtheanaphor\then"toe 2

leadstothepropositionafter(e 4

,e 2

)beingaddedto thediscoursecontext.

Similarly, in Example 43, \then" picks up a culminated event from the discourse context and maps it to an expression that applies to the interpretation of its matrix sentence,addingapropositiontothediscoursecontext.

(43) Go westonLancasterAvenue.Thenturn rightonCountyLine. then:e

i

!x.after(x, e i

) S =turnrightonCountyLine =e 3 ,wheree 3 :turn-right(you,cl) e r =e 1 ,wheree 1 :go-west(you,la) e i =e 2 ,where e 2 :culmination(e r ) thenS:[x.after(x,e 2 )]e 3 after(e 3 ,e 2 ) That is,e 3

istheeventofthehearer(h) turningrightonCountyLine(cl),whichisthe interpretationofS asaneventuality,whilee

r

resolvesto e 1

, theeventofthehearer go-ingwestonLancasterAvenue.Butsince\then"requiresaculminatedeventualityasits secondargument,e

i

isitsassociatedculmination,e 2

.Butofcourse,theintended culmina-tionisnottheendofLancasterAvenue(about75mileswestofdowntownPhiladelphia), but itsintersection withCounty Line(about 4mileswest ofdowntown). Thismust be derivedthroughfurther inferencethatwedonotdiscuss here.Finally,resolving\then" leadstotheproposition after(e

3 , e

2

)beingaddedto thediscoursecontext.

It isimportanttostressherethat thelevelofrepresentationweare concernedwith is essentially alogical form (LF) for discourse { propositions of the form after(e

3 , e 2 ) and if(e 4 , e 5

). Any reasoningthat mightthen haveto bedone on their content might then require makingexplicit thedierentmodal and temporal contexts involved, their accessibilityrelations,etc.Butasourgoalhereisprimarilytocapturethemechanismin which discourse adverbialsare involvedin discourse structure and discoursesemantics, wewillcontinuetoassumeforaslongaspossiblethataLF representationwill suÆce.

Nowitmayappearasifthereisnodierencebetweentreatingadverbialsasanaphors and treatingthemasstructural connectives{that is,asevidencefor relationsbetween adjacent discourse units. However, we claim that a relation conveyed by an anaphor canbedistinctfromanyrelationassociatedwithstructure.Infact,wewilldemonstrate in Section 3 avariety of waysin which discourse adverbials caninteract with inferred relationsandexplicitstructuralrelations.

One particular relational anaphor {\otherwise" { that wediscussed previously in (Webberetal.,1999a)deservesmorecommenthere.Roughlyspeaking,\otherwise" con-veysthatthecomplementofitsanaphorically-derivedcontextualparametere

i

servesasa conditionunderwhichtheinterpretationofitsstructuralmatrixholds.(Thiscomplement mustbewithrespecttosomecontextuallyrelevantset.

13 )

13Kruij-KorbayovaandWebber(2001)demonstratethattheInformationStructureofsentencesin thepreviousdiscourse(theme-rhemepartitioning,aswellasfocuswithinthemeandwithinrheme (Steedman,2000a))caninuencewhateventualitieser,andthuswhatcontextualparameterse

i , areavailableforresolvingtheanaphoricallyderivedargumentof\otherwise".Thisthencorrectly predictsdierentinterpretationsfor\otherwise"in(i)and(ii):

(i)Q:HowshouldItransportthedog?

A:Youshouldcarrythedog.Otherwiseyoumightgethurt.

(ii)Q.WhatshouldIcarry?

A.Youshouldcarrythedog.Otherwiseyoumightgethurt.

Inboth(i)and(ii),thequestionsconstrainthetheme/rhemepartitionoftheanswer,whilesmall capitalsconveyfocuswithintherheme.In(i),the\otherwise"clausewillbeinterpretedaswarning thehearer(H)thatHmightgethurtifs/hetransportsthedoginsomewayotherthancarryingit (e.g.,Hmightgettangledupinitslead).In(ii),the\otherwise"clausewarnsHthats/hemight

Ifwerepresentaconditionalrelationalbetweentwoeventualitiessimplyasif(e 1 ,e 2 ), where e 1

is the antecedent and e 2

, the consequent, and we approximate the contextu-ally relevant alternatives e

2

to an eventuality e 1

using a complement predicte { e.g., complement(e

1 ;e

2

){thenwecanrepresenttheinterpretationof\otherwise"as

otherwise:e i !x.if(e gi , x),where complement(e i ;e gi )

and index gi is heretoforeunused. That is, \otherwise"presupposes acontextually rel-evantcomplementto e

i

andasserts that ifany memberof that complement holds, the argmentto the-expression will. Theresulting -expression applies to the interpreta-tion ofthematrixclause of\otherwise",resultingin theboththecomplementand the conditional beingaddedtothediscoursecontext:

otherwise S:[x.if(e gi ,x)],where complement(e i ,e gi ) if(e gi ,),wherecomplement(e i , e gi )

AsweshowedinSection1.2,dierentwaysofresolvingtheanaphoricargumentlead to dierentinterpretations:

(44) Ifthelightisred, stop.Otherwiseyou'llgetaticket. otherwise:e i !x.if(e gi ,x),wherecomplement(e i ;e gi ) S =yougetaticket

=e 3 ,wheree 3 :get ticket(you) e i =e r =e 2 ,wheree 2 :stop(you) otherwise S:if(e gi ,e 3 ),wherecomplement(e 2 ,e gi )

i.e., Ifyoudosomethingotherthanstop,you'll getaticket.

(45) Ifthelightisred,stop.Otherwisegostraighton. otherwise:e i !x.if(e gi ,x),wherecomplement(e i ;e gi ) S =gostraighton =e 3 ,wheree 3 :go straight(you) e i =e r =e 2 ,where e 2 :red(light1) otherwise S:if(e gi ,e 3 ),wherecomplement(e 2 ,e gi )

i.e., ifthelightisnotred,gostraighton.

Likepluralpronouns,deniteNPsand\otherNPs"(cf.Example28),\otherwise"toocan exploit \splitantecedents", which are thenexcluded from thecontext ofinterpretation of thematrixclause,as in:

(46) Ifthelightisred, youshouldstop.

Ifit'sashingyellow,youshouldslowdown. Otherwiseyoucancontinueonyourway.

Here, the lightbeing red and it beingyellow are both excluded from the contextually relevantsituations(i.e.,ones relatedtothestateofthelight).

Andasalreadynoted(Section 1.2),limitedforms ofinferencemayalsoberequired to resolve\otherwise"and otherrelationalanaphors,asin:

(47) Doyouwantanapple?Otherwiseyoucanhaveapear.

Here thesituationsin which youcanhaveapearareonesalternativeto thosein which youwantanapple{i.e., inwhichtheanswertothequestionis \yes".

gethurtifwhatsheiscarryingisnotthedog(e.g.,Hmightbewalkingpastfanaticalmembersof theRoyalKennelClub).

To close, we wantto point to a nal type of lexical anaphor which contributes to the discoursecontextneither anentity(by virtueofbeingareferringexpression)nora proposition(asabove).Instead,itsidiosyncraticcontributiontothediscoursecontexthas theformofarule{thesamekindofpresupposeddefeasiblerule(PDR )thatLagerwerf (1998)in his PhDdissertationattributes tothesemanticsof thestructural connectives \although"and \but" {arulewhoseapplicabilityis denied in thecurrentcase.

14 This is thecontributionofthediscourseadverbials\nevertheless"and\though"

Stretchingourpreviousnotationsomewhat,wecanrepresentthedefeasiblerulethey contributeto thediscourseas

nevertheless:e i

!x :e i

> :x

Applyingthisto theinterpretation ofthematrixclauseoftheadverbialyields

neverthelessS:[x: e i

>:x] e i

> :

where >isAsher&Morreau'scommonsense entailmentoperator(1991).(Thatis, nor-mally iftheanaphoricallyderivedsituationholds, doesn't.)Forexample,

(48) Johngraduatedwithhonors.Nevertheless hewasdepressed. S =Johnwasdepressed

=e 2 ,wheree 2 :depressed(john) e i =e r =e 1 ,wheree 1

:graduatecum laude(john) neverthelessS:[x:e 1 >:x]e 2 e 1 > :e 2

i.e.,Normally if John graduates with honors, he is not depressed. Thisrule is then de-nied by the matrix clause {he was depressed. While we recognize that the defeasible rule that isaccommodated(or conventionallyimplicated) hereis morelikelyto involve generalisations ofbothe

i

and { somethinglike\normallyifsomeone graduateswith honors,theyarenotdepressed",ratherthansomethingparticulartoJohn{theprocess ofabstractingtoanappropriatelevelseemsseparablefromthatofresolvingtheanaphor and formulatingtherulewhoseapplicabilityisbeingdenied.

2.3 Summary

Thegeneralframeworkwehavepresentedforanaphorahastwomain features:

It posits athirdentitye i

{acontextual parameter{involvedin theresolution process, inordertoallowalltypesofanaphoratomakeuseofthestepfrom a discourse referentto oneassociatedwithit,andthenasubsequentstepthat maysimplybeequivalenceorsomethingidiosyncraticto thetypeofanaphor.

It allowsanaphorstousee i

in idiosyncraticwaysthat maylead,notonlyto newreferringexpressions(andthusnewentities), butalsotoadditional propositionsandpresuppositionsin thediscoursecontext.

Wehave shown e r

and e i

beingused systematicallyin avarietyof waysin computing theinterpretatione

ofanaphoricexpressions,andhavetherebyenlargedtherangeof expressionsusefullythoughtofasanaphoric.

14Earlier,bothGeorgeLako(1971a)andRobinLako(1971b)calledattentiontosucha presupposition.

3 Inferred,Structural and Anaphoric Relations

Prior to the current work, accounts have treated both explicit structural connectives (coordinatingandsubordinatingconjunctions,and\paired"conjunctions)anddiscourse adverbialssimplyasevidenceforaparticularstructuralrelationholdingbetweenadjacent units.Forexample,Kehler(1995)takes\but"asevidenceofacontrastrelationbetween adjacentunits,\ingeneral"asevidenceofageneralizationrelation,\inotherwords"as evidenceofaelaborationrelation,\therefore"asevidenceofaresultrelation,\because"as evidenceofaexplanationrelation,and\eventhough"asevidenceofadenialofpreventer relation(Kehler,1995,Chapter2.1),andMarcu(1999),followingMannandThompson (1988),appearstotake\otherwise"asevidenceforanotherwiserelation.

Because wetakediscourse adverbialsto contributemeaninginadierentwaythan explicitstructuralconnectives,wepredictthattheycaninteractinavarietyofwayswith relations conveyedstructurally and inferred relationstriggeredbyadjacency. Belowwe showthatthispredictioniscorrect.

Westartfrom the ideathat {in the absenceof anexplicitstructural connective{ defeasibleinferencecorrelateswithstructuralattachmentofadjacentdiscoursesegments in discoursestructure,relatingtheirinterpretations.Themostbasicrelationisthat the following segmentin somewaydescribes thesame generalisedobjectoreventualityas theoneitabuts(elaboration). Butevidencein thesegmentscanlead(viadefeasible in-ference)toamorespecicrelation,suchasoneoftheresemblencerelations(e.g.,parallel, contrast,exemplication,generalisation),orcause-eectrelations(result,explanation, vi-olatedexpectation),orcontiguityrelations(narration)describedin(Hobbs,1990;Kehler, 1995). Ifnothingmorespecic canbeinferred,therelation willremain simply elabora-tion.Whatexplicitstructuralconnectivescandoisconveyrelationsthatarenoteasyto conveybydefeasibleinference (e.g., \if",conveyingcondition, and\or",conveying dis-junction) orprovidenon-defeasibleevidence foran inferrablerelation (e.g., \yet",\so" and \because").

Thisisnot,weclaim,whatdiscourseadverbialsdo.Rather,theyinteractinavariety of ways with structural connectives, with adjacency-triggered defeasible inference and witheachother.Thissectiondescribesthekindsofinteractionswehaveobservedsofar, using thesamenotationusedintheprevioussection:

=discourseadverbial;

S =thematrixclause/sentenceof;

=thelogicalform (LF)interpretationof S;

e i

=thecontextualparametersuppliedtotheinterpretationof;

R

=thenameof therelationassociatedwith.

But because we will be considering how the relation between discourse-adjacent units can interact with the interpretation of a discourse adverbial, weneed some additional notationaswell.

D =theimmediately left-adjacentdiscourse unitthat S relatestoviaan adjacency-triggeredinferenceoranexplicitstructuralconnective;

Æ =theLFinterpretationofD;

Case 1:R

(;e i

) isdistinctfrom R (;Æ)because e i

6=Æ .

As before, westartwithourfamiliar Example10,repeatedearlieras(42)andhere as(49):

(49) JohnlovesBarolo.Soheorderedthreecasesofthe'97.Buthehadtocancelthe order becausehethendiscoveredhewasbroke.

then:e i

!x.after(x, e i

)

S =he[John]discoveredhewasbroke =e 4 ,wheree 4 :discover(j,e 5 ) D =he[John]hadtocanceltheorder Æ=e 3 ,wheree 3 :cancel(j,o 1 ) R (;Æ)explanation(e 4 ,e 3 ) e i =e r =e 2 ,wheree 2 :order(j,c 1 ) R (;e i )[x.after(x, e 2 )]e 4 after(e 4 ,e 2 )

Thatis,afterrelatesthediscovery(e 4

)totheordering(e 2

),whileexplanation(conveyed by\because")relatesittothecancelling(e

3 ). 15 Case 2:R incorporatesR (;e i

)as oneargument. Whentheanaphor\otherwise" isresolved,theresultingconditionalrelationservesasoneargumenttoR ,andÆservesas theother.ThisholdswhetherRisconveyedstructurally(cf.Example50awith\because", Example51awith\but")orabyadjacency-triggeredinference,asshownintheparallel \b" examples,repeatedherefrom(44)and(45).

(50) a. Ifthelightisred,stop,becauseotherwiseyou'llgetaticket.

b. Ifthelightisred,stop.Otherwiseyou'llgetaticket. otherwise:e i !.if(e gi ,x)],wherecomplement(e i ;e gi ) S =yougetaticket

=e 3 ,wheree 3 :get ticket(you) D=stop Æ=e 2 ,where e 2 :stop(you) e i =e r =e 2 ,wheree 2 :stop(you) R (;e i )e 4 :if(e gi ;e 3 ),wherecomplement(e 2 ;e gi ) R (;Æ)explanation(e 4 , e 2 )

i.e.,Ifyoudosomethingotherthanstop,you'll getaticket.

(51) a. Ifthelightisred,stop,but otherwisegostraighton.

b. Ifthelightisred,stop.Otherwisegostraighton. otherwise:e i !.if(e gi ,x)],wherecomplement(e i ;e gi ) S =gostraighton =e 3 ,wheree 3 :gostraight(you) D=ifthelightisred,stop Æ=e 4 ,wheree 4 :if(e 2 ,e 1 ),e 1 :red(light1),e 2 :stop(you) e i =e r =e 1 ,wheree 1 :red(light1) R (;e i )e 5 :if(e gi ;e 3 ),wherecomplement(e 2 ;e gi ) R (;Æ)contrast(e 5 ,e 4 )

15Becauseeventualitye2 hasboththepropertiesofexplainingthecancellingandofbeingafterthe ordering,itfollowsthatwhatexplainsthecancellingissomethingthatwasaftertheordering.

i.e., ifthelightisnotred,gostraighton.

Noticethattheabovetreatmentobviatestheneedforaseparateotherwiserelation. Mann and Thompson (1988) describe their proposed otherwise relation as having the eect:

R[thereader]recognizesthedependencyrelationofpreventionbetween therealizationofthesituationpresentedinN[thenucleus]andthe real-izationofthesituationpresentedinS[thesatellite](Mannand Thomp-son,1988,p.276)

and giveasanexample:

Anyonedesiringtoupdatetheirentryinthisbrochureshouldhavetheir copyin byDec.1.Otherwisetheexisting entrywillbeused.

ThisissimilartoExample50.Butgivenouroverallapproach,wherelexico-syntactic ma-terial cancontributetobothclause-levelanddiscourse-levelsemantics,itisnotdiÆcult to see howresolving\otherwise" andinferring explanation (or having explicitevidence forit,inthecaseofExample50a),isexactlywhatMannandThompsonwereafter.And, asdemonstrated,theaboveapproachaccountsforotherinstancesof\otherwise"aswell.

Case 3: The relation contributed by the adverbial is parasitic on R . Herewe depart fromourstraight\discourseadverbialasanaphor"storybecauseitappearsthat some adverbials{theclearest casesbeing\forexample" and \forinstance" {function in discourseneitherasconnectivesnorasanaphors.Rather,theyappearto derivetheir interpretation parasitically on the relation associated with a structural connective or discourseadverbialoronaninferredrelationtriggeredbyadjacency.Thewaytoseethis is toconsiderintra-clausaluseof\forexample",whereitfollowstheverb,asin

(52) Thecollectionincludes,for example,apiece ofhematite.

Interpreting\forexample"hereinvolvesabstractingthemeaningofitsmatrixstructure with respect to thematerial to itsright,and thenmakingan assertionwithrespectto this abstraction. That is, if the logicalform (LF) contributed by the matrix clause of Example 52is,roughly,

i.include(collection1,hematite1)

then theLFaddedby\forexample"is

ii.exampleof(hematite1,fXjinclude(collection1,X)g)

That is, \hematite" is an example of things included in the collection. 16

(Since with appropriate axioms,proposition (ii)implies proposition (i),onemight chooseto retain only (ii) andderive(i) when needed.Butthis is amatterof choice, notaclaim about whether bothoronlyoneistheinterpretationof(52).)

If welookat thecomparable situation in discourse,where \forexample"occurs to the rightof anexplicit structuralconnectivesuch as\so"(Example53a) or\because" (Example53b)orarelationalanaphorsuchas\then"(Example53c),itcanalsobeseen as abstracting theinterpretation ofits discourse-levelmatrixstructure, with respectto thematerialto itsright.

16Thematerialtotherightof\forexample"appearsabletobeanykindofCCGconstituent (Steedman,1996;Steedman,2000b),includingsuchstrangeonesas

Johngave,forexample,aowertoapoliceman.

Here,\aowertoapoliceman"wouldbeanexampleofthesetofobject-recipientpairswithin John'sgivings.

(53) a. Johnjustbrokehisarm.So,for example,hecan'tcycletoworknow.

b. You shouldn't trust John because, for example, he never returns what he borrows.

c. Shall we goto the Lincoln Memorial? Then, for example, wecango to the WhiteHouse.

In(53a),theinterpretation ofthe discourse-levelmatrixstructure headedbythe inter-pretationof\so"is:

result(,Æ)

whereistheinterpretationof\Johncan'tcycletoworknow",andÆistheinterpretation of \John just brokehis arm".\Forexample" then abstracts this matrixinterpretation with respecttothematerialtoitsright(i.e.,),therebycontributing:

exemplication(,fXjresult(X,Æ)g)

That is,\John can't cycle to work"is anexampleof the resultsof\John breaking his arm".Similarly,what isaddedbythematrixsentenceof(53b)is

explanation(,Æ)

where is theinterpretationof\heneverreturnswhatheborrows"and\forexample" adds

exemplication(,fXjexplanation(X,Æ)g)

i.e., that this is an example of the reasonsfor not trustingJohn. And the proposition contributedbytheresolveddiscourseadverbial\then"in (53c)is

after(,Æ)

whereistheinterpretationof\wecangototheWhiteHouse",and\forexample"adds

exemplication(,fXjafter(X,Æ)g)

i.e., that this is an example of the events that follow going to the Lincoln Memorial. (N.B.WeusetherelationR

=exemplicationhere,ratherthanexampleofusedinthe interpretationof(52),becauseitiswhatiscommonlyfoundintheliteratureondiscourse relations. We are also being fairly fastand loose regarding tense and modality, in the interestsofmakingastrongcaseforthebasicscaolding.)

Whatoccurswithstructuralconnectivescanalsooccurwithrelationsaddedthrough adjacency-triggereddefeasibleinference,asin

(54) Youshouldn'ttrustJohn.Forexample,heneverreturnswhatheborrows. explanation(,Æ)

exemplication(, fXjexplanation(X,Æ)g)

Here,asinExample53b,therelationprovidedbyadjacency-triggeredinferenceisR =explanation, whichisthenusedby\forexample".

Butwhataboutthemanycaseswhereonlyexemplicationseemspresent,asin

(55) a. Insomerespectsthey[hypertextbooks]areclearlysuperiortonormalbooks, forexampletheyhavedatabasecross-referencingfacilitiesordinaryvolumes lack.[BritishNational Corpus,CBX1087]

b. The shows that top the ratings are soft, for examplewe make Rupert the Bearand that gets a60 per cent share of the kids' audience. [BNC, K5C 909]

There are at least two explanations: One is that \for example" simply provides directnon-defeasible evidenceforexemplication,which istheonlyrelationthat holds. Theotherexplanation followsthesamepattern asthe examplesgivenabove,but with no furtherrelation thanelaboration(,Æ).That is, weunderstand in (55a)that \having databasecross-referencingfacilities"elaboratestherespectsinwhichhypertextbooksare superior tonormalbooks,whilein(55b), weunderstandthat\RuperttheBeargetting a60%shareofthekids'audience"elaboratestheclaimthat\showsthattoptheratings are soft". Thiselaboration relationis thenabstracted(in response to\forexample")to produce:

exemplication(,fXjelaboration(X, Æ)g)

i.e.,thatthisisoneexampleofmanypossibleelaborations.Becausethisismorespecic thanelaborationandseemstomeanthesameasexemplication(,Æ),onemightassume that it istheonlyrelationthat holds.Giventhat somanynaturally-occuringinstances of \forexample" occurwith elaboration, it isprobably usefulto persist with theabove shorthand.Butitshouldn'tobscuretheregularpatternthat appearstobethecase.

Before going on to Case 4, we should comment on occurences of \for example" elsewherein asentenceorclause.Here itmaysimplycontributepropositional meaning intra-clausally asaparenthetical, illustratingan abstraction introduced by an NP, PP or clause,ratherthanbeingparasiticonanotherrelation,asin:

(56) a. In the case of the managed funds they will be denominated in a leading currency,forexampleUS dollar,::: [BNCCBX1590]

(i.e.,USdollar isanexampleof aleadingcurrency)

b. AndKuhnhimselfarguedthatideasthathavebeenrejectedbycontemporary science{thatheat,forexample,iscausedbyphlogiston::: [NYTimeson the Web21July2001,\ComingtoBlowsoverhowvalidSciencereallyis"] (i.e.,that heat iscaused byphlogiston isan example of ideas that have been rejectedbycontemporary science)

(In \English"English{incontrastwith\American"English,theBNCshowsmostsuch examplestooccurwith\suchas"{i.e., intheconstruction\suchasforexample".This paraphrasedoesnotworkwiththepredicate-abstracting\forexample"thatisofprimary concernhere,such asinExample 52.)

But there are also moresubtle casesof clause-medial \forexample". Consider Ex-ample 57.

(57) All thechildrenareill,soAndrew, forexample, can'thelpoutintheshop. Here, asin Example53a, \so"explicitly connectsthe twoclauses. But (57)cannot be paraphrasedas

Allthechildrenareill,soforexampleAndrewcan'thelpoutintheshop.

becauseitdescribesnotjustaexampleconsequenceofallthechildrenbeingill,aswould (58) All thechildrenareill,sofor exampleoneofushastobeathomeattimes. but aconsequencewithrespecttoanexampleinstancefromthesetofchildren.

WesuspectheretheinvolvementofInformationStructure(Steedman,2000a):While theinterpretationconveyedby\forexample"isparasiticontheadjacencyrelation(result in Example57),itspositionafter theNP in(57)mayindicateacontrastivethemewith respect to the previousclause. But morework needsto bedone on this to gain afull understanding ofwhatisgoingon.

Case4:R

isadefeasiblerulethatincorporatesR . Earlier(Section2.2),wenoted that therelationconveyedbycertaindiscourseadverbials{notably,\nevertheless"and \though"{hasthenatureofapresupposed(orconventionallyimplicated)defeasiblerule that failsto hold in the currentsituation.With discourseadverbials,theantecedentto the rulederivesanaphoricallyfromthepreviousdiscourse,while theconsequent derives from theadverbial'smatrixclause.

Here we illustrate this possibility with examplesin which \nevertheless"occurs in themain clauseofasentencecontainingapreposedsubordinateclause. WhereCase 2 showedR

incorporatedintoanargumentofR ,thispossibilityshowsanabstractionof R incorporatedintothedefeasiblerulethat manifestsR

.Forexample,

(59) WhileJohnshowers,heneverthelessthinksaboutchess. S =he[John]thinks::: =e

2

,where e 2

:thinkabout(john, chess) D =Johnshowers Æ=e 1 ,wheree 1 :shower(john) R :during(e 2 ;e 1 ) R :during(X;e 1 )>:(X =e 2 )

Paraphrase:Normally,whateveronedoesduring thetimeoneshowers,itisnot thinking aboutchess.

(60) Even after John hashad three glasses of wine, he isnevertheless able to solve diÆcultalgebraproblems.

S =heisableto solve::: =e 2

,wheree 2

:solve(john,hard-algebra-problems) D =Johnhasthreeglasses::: Æ=e

1 ,wheree 1 :drink(john,wine) R :after(e 2 ;e 1 ) R :after(X;e 1 )>:(X=e 2 )

Paraphrase:Normally,whateveroneisabletodoafteronehashadthreeglasses ofwine,itisnotsolvingdiÆcultalgebraproblems.

Wespeculatethatthereasonsuchexamplessound morenaturalwiththefocusparticle \even"appliedtothesubordinateclause,isthat\even"conveysanevengreaterlikelihood that thedefeasiblerulesholds, so\nevertheless"emphasisesitsfailuretodoso.

Summary

We have indicated four ways in which we have found the relation associated with a discourse adverbial(R

, inthecaseofarelationalanaphor,andR

, inthecaseof\for example")tointeractwitharelationRtriggeredbyadjacencyorconveyedbystructural connectivesor,insomecases,byanotherrelationalanaphor:

1.R (;e i )isdistinctfromR (;Æ); 2.R (;e i

)servesastherstargumenttoR .

3.R

contributedbytheadverbialisparasiticonR ;

4.R

isadefeasiblerulethat incorporatesR ;

Whilewedonotbelievethatthisisanexhaustivelist,andwedonotknowwhether adiscourseadverbialalwaysbehavesthesamewayvis-a-visotherrelations,nevertheless we believethat acknowledging somediscourse adverbialsto be anaphors (and at least oneto beneither anaphornorconnective) openssuchissues upfor explorationin ways theyhavenotbeenbefore.

4 LexicalisedGrammar for Discourse Syntax and Semantics

As wenotedin theIntroduction, wedonotbelievethat therelationbetweendiscourse and semanticsis intrinsically dierent from that betweenasentence and its semantics

{ i.e., that both are, at least in part, a projection from the lexicon and syntax. The alternative{ that discourse relatesto semantics in acompletely dierentway {seems strangewhen notonlycanaclausebepartofadiscourse,adiscoursecanbepartof a clause:

(61) Anyfarmerwhohasbeatenadonkeyandgonehomeregrettingitandhasthen returnedandapologisedtothebeast, deservesforgiveness.

(62) If they're drunk and they're meant to beon parade and yougo to their room andthey're lyinginapoolofpiss,thenyoulockthemupforaday.

[TheIndependent,17June1997]

Thatis,thesuccessiveconjunctswithintherelativeclauseof(61)andwithinthe condi-tionalantecedentof (62)exhibit thecohesiveand argumentativeconnectionswhich are characteristicof theinterpretationofdiscourse.

In theprevioussection, weshowedhowthe semantics ofdiscourseadverbialscould be resolved within the clause and projectedinto discourse. Now we take another step back,tosketchoutacouplingbetweendiscoursesyntaxandsemanticsthat isanatural outgrowthofthecouplingbetweenclause-levelsyntaxandsemantics.

BecauselexicalizedgrammarssuchasLexicalizedTree-AdjoiningGrammar(LTAG) (Joshi,1987;XTAG-Group,2001)andCombinatoryCategorialGrammar(CCG) (Steed-man,1996;Steedman,2000b)havebeenverysuccessfulinshowinghowclause-level syn-tax andsemanticsprojectfromthelexicon, LTAGisourgrammarof choicehere.

17 We havedescribedthis workin severalconferencepapers(Webber,Knott,and Joshi,1999; Webberet al.,1999a;Webberet al.,1999b), andthis hasled to theinitialversionof a discourseparser(Forbeset al.,2001)inwhichthesameparserthatbuildstreesfor indi-vidual clausesusing clause-levelLTAG trees, thencombinesthem using discourse-level LTAGtrees.Here wesimplyoutlinethe grammar,whichwecallDLTAG(Section4.1), and thenshowhowitsupportstheapproachtostructuralandanaphoricdiscourse con-nectivespresentedearlier(Section4.2).

4.1 DLTAG and Discourse Syntax

AlexicalizedTAGbeginswiththenotionofalexicalanchor,whichcanhaveoneormore associatedtreestructures.Forexample,theverblikesanchorsonetreecorrespondingto John likes apples, another corresponding to the topicalized Apples John likes, a third correspondingto thepassiveApplesare likedbyJohn,andothersaswell.Thatis,there is atree for each minimal syntacticconstructionin which likes canappear,all sharing thesamepredicate-argumentstructure.Thissyntactic/semanticencapsulationispossible becauseoftheextendeddomainoflocalityofLTAG.

A lexicalizedTAGcontains twokindsof elementary trees: initial treesthat reect basic functor-argument dependencies and auxiliary trees that introduce recursion and allow elementary trees to be modied and/or elaborated. Unlike the wide variety of trees needed at the clause level, we have found that extending a lexicalized TAG to discourse only requires a few elementary tree structures, possibly because clause-level syntaxexploits structuralvariationinwaysthatdiscourse doesn't.

4.1.1 Initial Trees Thegrammar hasinitial treesforthree typesof construction:(a) subordinate-main clauseconstructions; (b)parallel constructions; and(c) what wecall relational coordination.Wedescribeeachin turn.

InthelargeLTAGdevelopedbytheXTAGproject(XTAG-Group,2001), subordi-nate clausesareseenasadjuncts tosentencesorverbphrases{i.e.,asauxiliarytrees{

D

c

D

c

D

c

subconj

(a)

D

c

D

c

D

c

subconj

(b)

α:

subconj_mid

α:

subconj_pre

Initialtrees(a-b)forasubordinateconjunction.D c

standsfor\discourseclause",#indicatesa substitution site,while\subconj"standsfortheparticularsubordinateconjunctionthat anchorsthetree.

D

c

On the

one hand

On the

other

D

c

D

c

α:

contrast

Figure7

Aninitialtreeforparallelconstructions.Thisparticularoneisfor acontrastiveconstruction anchoredby\ontheonehand"and\ontheotherhand".

becausetheyareoutsidethedomainoflocalityoftheverb.Fromadiscourseperspective, however,itispredicatesonclausalarguments(suchascoordinateandsubordinate con-junctions) thatdenethedomainoflocality.Thus,atthislevel,thesepredicatesanchor initial treesintowhich clausessubstituteasarguments.Figure 6showstheinitial trees for postposed subordinate clauses(a) and preposed subordinate clauses (b).

18

Atboth leavesandrootisadiscourseclause(D

c

){aclauseorastructurecomposedofdiscourse clauses.

One reasonfortaking somethingtobean initialtree isthat itslocal dependencies canbestretchedlong-distance.Atthesentence-level,thedependencybetweenapplesand likes in apples John likes islocalized in allthe trees forlikes. This dependency canbe stretchedlong-distance,asinApples,BillthinksJohnmaylike.Indiscourse,aswenoted in Section1,localdependenciescan bestretchedlong-distanceaswell{asin

(63) a. AlthoughJohnisgenerous,he'shardtond.

b. AlthoughJohnisgenerous{forexample,hegivesmoneytoanyonewhoasks himforit{he'shardtond.

(64) a. Ontheonehand,Johnisgenerous.Ontheother hand,he'shardtond.

b. Ontheonehand,Johnisgenerous.Forexample,supposeyouneededsome money:You'd only haveto askhim forit. On theother hand,he's hardto nd.

Thus ourlexicalised discourse grammaralso containsinitial treesfor parallel construc-tions as in (64) and Figure 7. Like some initial trees in XTAG (XTAG-Group, 2001), such treescanhaveapair ofanchors.Since there aredierentwaysin whichdiscourse units canbeparallel,weassume adierentinitialtree forcontrast(\on theone hand" ::: \ontheotherhand"::: ),disjunction(\either"::: \or"::: ),addition(\notonly" ::: \butalso"::: ),andconcession(\admittedly"::: \but" ::: ).

Thethirdconstructionforwhichwehaveaninitialtreeisforstructuralconnectives thatconveyaparticularrelationbetweentheconnectedclauses.So,forexample,thereis aninitialtreeassociatedwith\so"conveyingresult{cf.Figure8a.Additionally,weposit initial trees for relational coordination, cases where \and" or\or" convey aparticular relation betweenconjuncts (disjuncts) besides simpletruth-functionality. For example, both\and"and\or"conveyresultin

(65) a. Throwanotherspit ballandyou'llregretit.

18Whileinanearlierpaper(WebberandJoshi,1998),wediscussreasonsfortakingthelexical anchorsoftheinitialtreesinFigures6and7tobefeaturestructures,followingtheanalysisin (Knott,1996;KnottandMellish,1996),herewejusttakethemtobespeciclexicalitems.

D

c

D

c

D

c

(b)

and

D

c

D

c

D

c

α:

so

α:

and_conseq

so

(a)

Initialtreesforcoordinateconjunction.Theseparticulartrees arefor(a)\so"and(b) relationalcoordinationon\and"expressingconsequence.

D

c

D

c

D

c

∗

.

D

c

D

c

D

c

∗

and

∗

S

S

then

(a)

(b)

(c)

β:

punct1

β:

and

β:

then

Auxiliarytreesforbasicelaboration.Theseparticulartreesareanchoredby(a)the punctuationmark\."and(b)\and".Thesymbolindicatesthefootnodeoftheauxiliary tree,whichhasthesamelabelasitsroot.(c)Auxiliarytreeforthediscourseadverbial\then".

b. Eatyourspinachoryouwon'tgetdessert.

while \and'canalsoconveypurpose,asin

(66) Go totheshopandgetmeaquartofmilk.

From a discourse perspective, relational coordination diers from what we are calling scopal coordination,inthatthelattersimplyconveysthatbothconjunctsbearthesame relation tothe immediatelyleft-adjacentdiscourse unit,whateverthat maybe.For ex-ample,in(67)therelationisexplanationandeachconjunctisaseparateexplanation for nottrustingJohn,whilein(68),therelationisresult.

(67) Youshouldn'ttrustJohn.Heneverreturnswhatheborrows,andhebad-mouths his associatesbehindtheirbacks.

(68) a.Johnwonthelottery.Sohiswifequit herjob, andheboughtayacht. b. John just won the lottery. So he will quit his job, or he will at least stop workingovertime.

In(68a),eachconjunctisaseparateresultofJohn'swinningthelottery,whilein(68b), eachdisjunctconveysanalternativeresultofJohn'sgood fortune.

We distinguish relational coordination and scopal coordination in the grammar by havinginitialtreesfortheformer(Figure8b){oneforeachcoordinatorwithits appro-priatesemantics{andauxiliarytreesforthelatter(Figure9b),sothatthecompositional rulescantreatthetwocasesdistinctly.Notethat thismeansthatthelexicalambiguity of \and" and\or"corresponds toastructural ambiguitywithrespectto this aspectof discourse grammar.

4.1.2AuxiliaryTrees Thegrammarusesauxiliarytreesintwoways:(a)fordiscourse units that continue adescription in someway;and (b)for discourse adverbials. Again wedescribeeachin turn.

First,auxiliarytreesanchoredbypunctuation(e.g.period,comma,semi-colon,etc.) (Figure9a)orbyscopalcoordination(Figure9b)areusedtoprovidefurtherdescription

β:

punct1

β:

punct1

0

τ1

3

τ2

*

.

T1

T2

T1

T2

.

ofasituation orofone ormoreentities (objects,events,situations, states,etc.) within thesituation

19

Theadditionalinformationisconveyedbythediscourse clausethat lls its substitutionsite.Suchauxiliarytreesareusedin thederivationof simplediscourses suchas:

(69) a.Johnwentto thezoo.

b. Hetook hiscellphonewithhim.

Figure 10 shows theTAG derivation of Example 69. Tothe left of ! are the ele-mentarytreestobecombined:T1standsfortheLTAGtreeforclause69a,T2forclause 69b,and:punct1,fortheauxiliarytree.Inthederivation,thefoot nodeof :punct1 isadjoinedtotherootofT1anditssubstitutionsitelledbyT2,resultinginthetreeto therightof!.(AstandardwayofindicatingTAGderivationsisshownunder!,where dashedlinesindicate adjunction,andsolidlines,substitution,witheachlinelabelledby theaddressoftheargumentatwhichtheoperationoccurs.1isthederivationtree for T1,and2,thederivationtreeforT2.)

The other auxiliary trees used in the lexicalised discourse grammar are those for discourse adverbials,whicharesimplyauxiliarytreesin asentence-levelLTAG (XTAG-Group, 2001), but with an interpretation that projects up to the discourse level. An exampleisshowninFigure9c.Adjoiningsuchanadverbialtoaclausal/sentential struc-ture contributesto howinformationconveyed by that structure relatesto theprevious discourse.

Obviously,this discourse grammarsuers from lexical ambiguity. First,as already noted, we havedierenttrees for \and" (and for \or"),depending on whether it con-tributes an independentrelation (in which case, it anchorsan initial tree), orwhether it merely extends the \scope" of the previous clause, so that the same relation holds with the previousdiscourse.Secondly, manyofthe adverbialsfound in secondposition in parallelconstructions(e.g., \ontheotherhand",\atthesametime",\nevertheless") can alsoserveassimpleadverbialdiscourse connectivesontheir own. Intherst case, theywillbeoneofthetwoanchorsofaninitialtree(Figure7),whileinthesecond,they will anchorasimpleauxiliarytree(Figure9c). Theselexical ambiguitiescorrelatewith semanticambiguity.

4.2 ExampleDerivations and Interpretations

Itshouldbeclearbynowthatourapproachaimstoexplaindiscoursesemanticsinterms of aproductof

compositionalrulesonsyntacticstructure

anaphorresolution

19Thelatteruseofanauxiliarytreeisrelatedtodominanttopicchainingin(SchaandPolanyi,1988) andentitychainsin(Knottetal.,2001).

α:

because_mid

α:

because_mid

3

1

T2

T1

τ1

τ2

because

because

T1

T2

DerivationofExample70a.Thederivationtreeisshownbelowthearrow,andthederived tree,toitsright.

inferencetriggeredbyadjacency

muchasclausalsemanticscanbeexplainedinthisway.Forthecompositionalpartof se-manticsinLTAG(inparticular,computinginterpretationsonderivationtrees),wefollow JoshiandVijay-Shanker(1999).Roughly,theycomputeinterpretationsonthederivation treebyabottom-upprocedure.Ateachlevel,function-applicationisusedtoassemblethe interpretationofthetreefromtheinterpretationofitsrootnodeanditssubtrees.Where multiplesubtreeshavefunctiontypes,theinterpretationprocedureispotentially nonde-terministic: Theresultingambiguitiesininterpretation maybeadmitted asgenuine, or theymaybeeliminatedbyalexicalspecication.

Here we tryto show rather informallyhow this lexicalised discourse grammarand an interpretation process on its derivations can explain the interpretations of several examples.Tostartwith,considerthefollowingvariantsonafamiliarexample:

(70) a. Youshouldn'ttrustJohnbecauseheneverreturnswhat heborrows.

b. Youshouldn'ttrustJohn.Heneverreturnswhatheborrows.

c. You shouldn't trust John because, for example, he never returns what he borrows.

d. Youshouldn'ttrustJohn.Forexample,heneverreturnswhatheborrows