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Implicatures and Discourse Structure
Nicholas Asher
To cite this version:
Nicholas Asher. Implicatures and Discourse Structure. Lingua, Elsevier, 2013, vol. 132, pp. 13-28.
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Implicatures and Discourse
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Implicatures
and
discourse
structure
Nicholas
Asher
Abstract
OneofthecharacteristicmarksofGriceanimplicaturesingeneral,andscalarimplicaturesinparticular,examplesofwhicharegiven in(1),isthattheyaretheresultofadefeasibleinference.
(1a) Johnhadsomeofthecookies
(1b) Johnhadsomeofthecookies.Infacthehadthemall.
(1a)invitestheinferencethatJohndidn’thaveallthecookies,aninferencethatcanbedefeatedbyadditionalinformation,asin(1b). Scalarinferenceslikethatin(1a)thusdependuponsomesortofnonmonotonicreasoningoversemanticcontents.Theysharethis characteristicofdefeasiblilitywithinferencesthatresultinthepresenceofdiscourserelationsthatlinkdiscoursesegmentstogetherintoa discoursestructureforacoherenttextordialogue---calltheseinferencesdiscourseorDinferences.Ihavestudiedtheseinferencesabout discoursestructure,theireffectsoncontentandhowtheyarecomputedinthetheoryknownasSegmentedDiscourseRepresentation TheoryorSDRT.InthispaperIinvestigatehowthetoolsusedtoinferdiscourserelationsapplytowhatGriceansandotherscallscalaror quantityimplicatures.Thebenefitsofthisinvestigationarethreefold:atthetheoreticallevel,wehaveaunifiedandrelativelysimple frameworkforcomputingdefeasibleinferencesbothofthequantityanddiscoursestructurevarieties;further,wecancapturewhat’sright about the intuitionsof socalled ‘‘localist’’views aboutscalarimplicatures; finally, this frameworkpermits usto investigate how D-inferencesandscalarinferencesmightinteract,inparticularhowdiscoursestructuremighttriggerscalarinferences,thusexplaining thevariability(Chemla,2008)orevennon-existenceofembeddedimplicaturesnotedrecently(e.g.,GeurtsandPouscoulous,2009),and theiroccasionalnoncancellability.Theviewofscalarinferencesthatemergesfromthisstudyisalsoratherdifferentfromthewayboth localistsandNeo-Griceansconceiveofthem.BothlocalistsandNeo-Griceansviewimplicaturesasemergingfrompragmaticreasoning processesthatarestrictlyseparatedfromthecalculationofsemanticvalues;wheretheydifferisatwhatlevelthepragmaticimplicatures arecalculated.Localiststakethemtobecalculatedinparallelwithsemanticcomposition,whereasNeo-Griceanstakethemtohaveas inputthecompletesemanticcontentoftheassertion.Myviewisthatscalarinferencesdependondiscoursestructureandlargeviewof semanticcontentinwhichsemanticsandpragmaticsinteractinacomplexwaytoproduceaninterpretationofanutteranceoradiscourse.
Keywords: Embeddedimplicatures;Discoursestructure;Defeasiblereasoning
1. Introduction
AcharacteristicmarkofGriceanimplicaturesingeneral,andscalarorquantityimplicaturesinparticularisthattheyare theresultofadefeasibleinference.1(1)illustratesanexampleofascalarimplicatureanditsdefeasibility.
(1) a. Johnhadsomeofthecookies
b. Johnhadsomeofthecookies.Infacthehadthemall.
E-mailaddresses:Nicholas.Asher@irit.fr,asher@irit.fr.
1AnearlierversionofthispaperwillappearinAsher(inpress).
(1a)invitestheinferencethatJohndidn’thaveallthecookies,aninferencethatcanbedefeatedbyadditionalinformation, asin(1b).Scalarinferenceslikethatin(1a)thusdependuponsomesortofnonmonotonicreasoningoversemantic contents.Theysharethischaracteristicofdefeasiblilitywithinferencesthatresultinthepresenceofdiscourserelations thatlinkdiscoursesegmentstogetherintoadiscoursestructureforacoherenttextordialogue---calltheseinferences
discourseorD-inferences.IndevelopingthetheoryknownasSegmentedDiscourseRepresentationTheoryorSDRT,I havestudiedtheeffectsofD-inferencesoncontentandhowtheyarecomputed.InthispaperIapplythetoolsusedtoinfer discourserelationstothederivationofquantityimplicaturesThisyieldsathreeadvantages:atthetheoreticallevel,we haveaunifiedandrelativelysimpleframeworkforcomputingdefeasibleinferencesbothofthequantityanddiscourse structurevarieties;wecancapturewhat’srightabouttheintuitionsofsocalled‘‘localist’’viewsaboutscalarimplicatures; finally,thisframeworkpermitsus todemonstratehowD-inferences and scalarinferencesinteract, in particularhow discoursestructuretriggerscalarinferences.Inturnthisleadstoanaturalexplanationofthevariability(Chemla,2008)or evennon-existenceofembeddedimplicaturesnotedrecently(e.g.,GeurtsandPouscoulous,2009),aswellastheir occasionalnon-cancellability.Theviewofscalarinferencesthatemergesfromthisstudyisquitedifferentfromtheway bothlocalistsandNeo-Griceansconceiveofthem.BothlocalistsandNeo-Griceansviewimplicaturesasemergingfrom pragmaticreasoningprocessesthatarestrictlyseparatedfromthecalculationofsemanticvalues;wheretheydifferisat what level the pragmatic implicaturesare calculated. Localiststake themto becalculated in parallelwith semantic composition,whereasNeo-Griceanstakethemtohaveasinputthecompletesemanticcontentoftheassertion.Myview isthatscalarinferencesdependondiscourse structureandaninclusive notionofsemantic content; semanticsand pragmaticsinteractinacomplexway,subsententiallyandsupra-sententially,toproduceaninterpretationofanutterance oradiscourseinwhichbothscalarorquantityimplicaturesanddiscoursestructure.
2. D-inferences
Scalarinferencesarefamiliartomostlinguistswhoworkonpragmatics,butD-inferencesarelessso.Letuslookat someexamplesofthemintexts.
(2) a. Johnwalkedin./Hepouredhimselfacupofcoffee. b. Johnfell./Marypushedhim.
c. Weboughttheapartment,/butwe’verentedit.
d. Ilcommenceàdessineretpeindreen1943,/fréquentelesateliersdesculpture/puisdepeinturedel’école desBeaux-Artsd’Oran,/oùilrencontreGuermaz(ANNODIScorpus).
e. Juliehadanexcellentmeal,/beginningwithanelegantandinventivetruffesduPérigordenpremièrecuisson commeunpetitdéjeuner,/followedbysomewonderfulscallops,/thensweetbreads,/asumptuouscheese plate,/andendingwithascrumptiousdessert.
A presumption of relevance leads us to infer some link between elementary discourse units or EDUs (clausesor subclausalunitswhoseboundariesareeithersentenceinitialormarkedby/intheexamplesabove).Theselinksinvolve relationsthatarefamiliareventothenon-linguist:someunitselaborateorgointomoredetailconcerning something introducedinanotherconstituents(theseareElaborationtyperelations)asin(2e);someunitsformaparalleloracontrast withotherunits(suchunitsarelinkedbyParallelorContrast),asin(2c);someunitsfurnishexplanationswhysomething describedinanotherunithappened(Explanation)asin(2b);andsomeunitsconstituteanarrativesequenceofevents (Narration)(2a)or(2d).Otherdiscourserelationsofinterestforourpurposesareindirectquestionanswerpairs(IQAP), whichlinkresponsestoapriorquestion,Correction,whereaseconddiscoursemoverevisesthecontentofafirst,and Alternation,whichislinkedtocertainusesofdisjunction.
SomeD-inferencesareencodedgrammaticallythroughtheuseofcertaingrammaticalconstructions(likeadverbialor purposiveclauses,orleftfrontedtemporalorspatialadverbials)2orthroughdiscourseconnectorslikeasaresult,puisor
thechoiceandsequencingoflexicalitems.Anexampleofasetofdiscourserelationstriggeredbythechoiceofverband complementcomesin(2e),withtheuseofbeginningwith,followedbyandendingwith.Sometimes,itislessclearwhat linguisticsourcetriggerstheinferenceofthediscourserelationasin(2a--b)---mostlikely,anasyetnotfullyunderstoodmix oflexicalsemanticsandworldknowledge.Thediscourserelationsimplicatedbythesedeviceshaveimposestructural constraintsonthediscoursecontextandhavetruthconditionaleffectsthatanumberofresearchershaveexplored.3
ToseethedefeasibilityofD-inferencesincontext,considerthisvariantof(2b) (3) Johnfell.Marypushedhim.Herolledofftheedgeofthecliff.
2Foradiscussionofthese,seeforinstance,Vieuetal.(2005).
3Withregardstotemporalstructure,seeLascaridesandAsher(1993);onpronominalanaphora,seeAsher(1993),AsherandLascarides
Although(2b)ispartofthediscoursegivenin(3),theinferencetoExplanationbetweenthetwoclausesof(2)isnotso readilyavailablein(3).Rather,wetendtoreadthefirsttwoclausesin(3)asprovidinganarrativesequencethatresultsin hisrollingoffthecliff.
Whilescalarinferencesoccurembeddedunderquantifiersandotheroperators,manypeoplehavenotedthatthese implicaturesarelessrobustthanunembeddedcasesofscalarimplicatureslike(1a).D-inferences,ontheotherhand, robustlyembedunderquantifiersandotheroperators(aswellasotherdiscourserelations).
(4) a. Ifitwaslate,Johntookoffhisshoesandwenttobed. b. Ifitwaslate,Johnwenttobedandtookoffhisshoes. c. IfJohndrankanddrove,heputhispassengersindanger.
d. TheCEOofWidgets&Co.doubtsthatthecompanywillmakeaprofitthisyearandthat(asaresult) therewillbemuchinthewayofdividendsforshareholdersthisyear.
Inboth(4a--b),theD-implicaturethatthereisanarrativesequencebetweenthetwoclausesintheconsequentofthe conditionalsurvivesunderembedding,and(4c)showsthatthisholdsintheantecedentofaconditionalaswell.(4d)shows thatthecausalrelationofresultholdswhenembeddedunderadownwardentailingattitudeverb.
So D-inferences andS-implicatures share atleastone feature---defeasibility. Below,Isketchthe accountofhow D-inferencesareinferred.Ithentrytoanswertwoquestions:howdoesthemechanismforinferringD-inferencesapplyto S-implicatures?HowdoD-inferencesandS-implicaturesinteract?IarguethatthemechanismforinferringD-inferences readilyadaptstothecomputationofS-implicatures,regardlessofwhatexactviewofS-implicaturesoneadopts.Ialso showthatthereisatightinteractionbetweenD-inferencesandS-implicatures.IshowhowtoderiveS-implicaturesfrom D-inferencesandIshowwhysometimestheS-implicaturesaren’tdefeasible.ThemechanismforderivingD-inferences showsthatallS-implicaturesdependondiscoursestructure,whichmaybeimplicitorinferredinoutofthebluecontexts. Thus,IofferawayofunderstandingS-implicaturesthatisdifferentbothfromthelocalistone(e.g.,Chierchia,2004,inter alia)andaGriceanone(e.g.,vanRooijandSchulz,2004,interalia).
3. SDRT,atheoryaboutD-inferences
ToaddressthequestionsIhavesetmyself,ImustsaymoreaboutD-inferencesandthetheoryforinvestigatingthem. AtheoryofD-inferencesmustprovidealogicormeansforcomputingtheseinferencesanddetailhowtheyinteractwith semanticcontent.Whilethereareseveraltheoriesofdiscoursestructurethatresearchersinlinguisticsandcomputer scienceinvestigate,SDRTisanappropriatetheorytouseherebecauseitspellsoutaveryclearpictureofthestructure, theconstructionandthesemanticsofdiscoursestructureswithanemphasisonthecomputationofD-inferencesandtheir interactionwithsemanticcontent.Thetheoryanswerstothreetasks:
!itsegmentsatextintoEDUs;
!itcomputesattachmentpointsofEDUsinadiscoursestructure;
!itcomputesoneormorediscourserelationsbetweenanEDUanditsattachmentpoint(s).
EDUsarediscourseunitscontainingelementarypredicationsinvolvingsomesortofeventuality(eventorstate).All clauses giveriseto EDUs,butappositives,parentheticals,non-restrictiverelativeclauses,andadverbials thatare detachedtotheleftofthemainsyntacticstructureofaclausealsointroduceEDUs.Coordinatedverbphrasesthatuse recognizeddiscourseconnectorslikebutinJohnwenttothestorebutdidn’tgetanymilkalsogiverisetotwoEDUs.The other elementinvolved in thetasksabove thatisperhaps unfamiliarto linguists whoworkprimarily onsentential semanticsandsyntaxarediscourserelations.Ingeneralallresearchersworkingondiscourseagreethatthereare relationsthatarecausal,thematic(e.g.,elaborationorbackground)andnarrative.Thephilosophicalbackgroundforthis workgoesbacktoHume’staxonomyofideasandtoKant’scategoriesofrelation.Withinthesegeneralcategories, researchersanddifferenttheoriesofdiscoursestructuredifferastothenumberoffiner-grainedrelations.SDRTdefines relationsasdistinctjustincasetheymakeadifferencetothecontentofthediscourse(butnotdistinguishrelationsbased on,e.g.,speakerintentions).
An SDRT discoursestructureorSDRSisthe result ofthe computationsoutlinedabove. Itmay containcomplex constituents where several EDUscombine togetherto makeone largerconstituent. An SDRS is a logicalform for discourse withawell-defined dynamicsemanticsthat hasmanyequivalentformulations---asa first ordermodel like structureconsistingofasetoflabelsandassignmentsofformulastolabels(AsherandLascarides,2003),asaDRSlike structure(Asher,1993)orasalterminintensionallogic(AsherandPogodalla,2010).
TogetanideaofwhatSDRSslooklikeconsiderthefollowingtext(5)discussedatlengthin(AsherandLascarides, 2003).Themodel-likeSDRSisgivenin(50)
(5) p1 Johnhadagreateveninglastnight.
p2 Hehadagreatmeal.
p3 Heate salmon.
p4 Hedevouredlotsofcheese.
p5 Hethenwonadancingcompetition.
(50) hA;F;Lasti,where:
A={p0,p1,p2,p3,p4,p5,p6,p7}
Thatis,inadditiontotheEDUsp1,...,p5,wehavethecomplexconstituentsp0,p6andp7.
F ðp0Þ¼Elaborationðp1;p6Þ
F ðp6Þ¼Narrationðp2;p5Þ^Elaborationðp2;p7Þ F ðp7Þ¼Narrationðp3;p4Þ
InSDRTweabstractawayfromthedetailsofthestructuretogetagraphrepresentationrelevanttocomputingdiscourse accessibilityforanaphoricantecedentsandsites forpresuppositionaccommodationorbinding(againfordetails see
AsherandLascarides,2003andAsher,2008).
3.1. InferringD-inferences
Inferring D-inferences is a matter of defeasible and uncertain inference. Many of the features used to infer discourserelationsareonlygoodindicationsofaparticulardiscourserelationorparticulardiscoursestructure;very fewareinandofthemselvessufficienttodeductivelyinfertherelationorstructure.Manydiscourseconnectivesare forexampleambiguous.Inaddition,manysegmentsmaybeardiscourserelationstoothersegmentsdespitethelack ofdiscourseconnectivesorknownstructuralorlexicalcues,asin(2a,b)or(5).Tosolvethisproblem,mycolleagues andIdeveloped anonmonotonic logic,a logicfordefeasibleinference,tailoredto inferringD-inferences.
Thetaskofbuildingsuchalogicisnotcompletelytrivial.Integratingnonmonotonicityindiscourseinterpretationis problematic,especiallyifthisintegrationoccursatthelevelofcontentsorwhatissaid.Reasoningovercontents non-monotonicallyrequiresfindingaclassPofpreferredmodels,thosewiththeintendeddiscourserelations,andcomputing validityorlogicalconsequencewithrespecttoP.Giventhatthelanguageofinformationcontentisatleastthatoffirstorder logic,wherethecomplexityofthecomputationofvalidityandlogicalconsequenceisonlyrecursivelyenumerableandthat almostallnonmonotoniclogicsrequiresomesortofconsistencytestovertheformulasoneisusingfortheinference,the complexity of computing logical consequence with respect to the class P of preferred models is not recursively enumerable---i.e.,computationallyhopeless.Thisisnotjustamatterofimplementationbutoneofprinciple.Wecannot assumethatagents,withtheirlimitedcomputationalcapacities,areabletosolveaproblemreliablywhichwecanshow mathematicallytobeincapableofhavinganythinglikewhatwewouldcallanalgorithm.Attributingsuchcomputational capacitiestoagentsshowsthatwehavemischaracterizedtheproblem:theyarenotcomputinglogicalconsequenceover formulasofinformationcontent;eitherthelanguageinwhichthecomputationisdoneissomehowasimplificationofthe languageofinformationcontent,ortheyarecomputingsomethingotherthanlogicalconsequence,perhapsusingsome sortofheuristic.
OnecoulddevelopaheuristicforcomputingD-inferences.Infact,Fox(2007)aswellasothershaveproceededtodo thisforscalarandfreechoiceimplicatures.Theproblemwithtakingthistack,however,liesinitsverification.Inorderto makesurethattheheuristicisdoingwhatitissupposedto,wemustcheckitinthewaythatcomputerprogramsare checked,viaprogramverification.Inmostifnotallinstances,thismeanstranslatingtheproblemintoalogicandthen checkingthattheresultdesiredisinfactalogicalconsequenceoftheprogram’stranslationandtheinputdata.Thisleads usbacktothetaskofbuildinganonmonotoniclogicforD-inferences.
SDRT’ssolution tothisproblem istolookat non-monotonicreasoning notover contents but overlogicalforms. Roughly,insteadoftryingtocomputethenonmonotonicconsequencesofabunchoffactsabouttheworld,factswhich maybequantificationallycomplex, wetrytocomputethenonmonotonicconsequencesofa discourselogicalform’s havingacertainshapeandofasegment’shavingthelexicalchoicesandstructurethatitdoes.Thismeansthatweare tryingtosolvealogicalconsequenceproblem,notinthelanguageofinformationcontent,butinalanguagefordescribing discourselogicalformsandfeaturesofdiscourseconstituents.AsherandLascarides(2003)developsuchalanguage, whichthey callthe glue language. Thenonmonotonic logic adaptedto thislanguageisknownas the gluelogic or
GL.AsherandLascarides(2003)showthattheproblemoflogicalconsequenceforformulasofthislanguageisinfact decidable.
GL uses axioms exploiting variousresourcesto get the intended discourse relations to holdbetween discourse constituents.Thegeneralformofsuchaxiomsisthis:
!GeneralForm:(?(a,b,l)^some stuff)>R(a,b,l)
Inthisgeneralform,‘?’representsanunderspecifiedrelationlinkingbtolwithintheconstituenta,while>isaweak conditionalwhosesemanticssuppliesthenonmonotonicconsequencerelation;‘‘somestuff’’isinformationabouta,b and l that’s transferredinto the glue language from more expressivelanguagesfor other information sourceslike: compositionalsemantics,lexicalsemantics,pragmaticmaximsofconversation,generalizationsaboutagentbehaviourin conversation, anddomainknowledge. Tothe righthandsideof the> isa formula thatspecifiesthe underspecified discourserelationtotheleft.
Themainitemofinterestinthisgeneralformisthesemanticsof>andthenotionofdefeasibleconsequencethat issuesfromit.Thesemanticsof>wasdevelopedbyAsherandMorreau(1991)inafirstordernon-monotoniclogic known as commonsense entailment. Thisis a logicfor nonmonotonicor defeasible reasoningbased ona weak conditional>.Originallydevisedtotreatgenerics,Ihaveusedaversionofitrestrictedtoaquantifierfreedescription language, the gluelanguage, nowfor many years to calculate D-inferences, andit isa relativelyadaptable non monotonic logic. It has two parts: a basic, monotonic, conditional logic with a standard proof theory ⊢ and consequencerelation⊨,andthenadefeasibleinferencerelation andanonmonotonicconsequencerelation that make useof thebasic logic.Iwill usethe gluelogic versionof commonsense entailmentto model bothD- and S-implicatures.
Letmebrieflyrecapitulatethebasicsofcommonsenseentailmentrestrictedtoapropositionallanguage.
!AmodalgenericframeF¼hW;*iwhereWisanonemptysetofworldsand*:W+PðWÞ!PðWÞisaselection function.AmodelAisconstructedbyaddingavaluationfunction.
!A;w⊨A>Biff*ðw;kAkÞ.kBk
!thestandardclausesforthequantifiersandconnectives,thoughthegluelanguageitselfhasonlyaquantifierfreelogical structure.
Thissemanticsfor>willbefamiliartothoseaccustomedtoconditionallogics;itcomeswithastandardmonotonic validitypredicateandcompleteaxiomatization.4
4Itvalidatesthefollowingaxiomsandrules,someofwhichdependonframeconstraintsthatIgivebelow.
! classicaltautologies ! closureontheright
((ϕ>ψ)^(ϕ>x))!(ϕ>(ψ^x)) ! rightweakening:
‘f!c x>f‘x>c ! idempotence:
followswiththeframeconstraint*ðw;pÞ.p
! supraclassicality: ‘A!B
‘A>B
! substitutionoflogicallyequivalentformulaeintheantecedentofa>formula. ‘A$B
‘ðA>CÞ$ðB>CÞ
! the‘‘or’’principle:*ðw;p[qÞ.*ðw;pÞ[*ðw;qÞ
A>B,C>B⊢(A_C)>B
! the‘‘specificity’’principle:ðp.q^*ðw;pÞ\*ðw;qÞ¼0Þ!*ðw;qÞ\p¼0 ‘A!B
Howdowepassfromanotionofmonotonicconsequencetoanonmonotonicone?Theideaofthenonmonotonic consequencerelationistoassumethatmattersareasnormalas‘‘possible’’giventheinformationinthepremisesandto thenseewhatfollows.Assumingmattersareasnormalaspossiblemeansmaking>asmuchlikethematerialconditional as‘‘possible’’---movingfromifp thennormally qto ifp thenq.Thereisbotha‘‘prooftheoretic method’’fordefining nonmonotonicconsequence( )andamodeltheoreticmethod( )forwhichacorrespondencetheoremisgiveninAsher (1995).5Fortheprooftheoreticmethod,wedefinefirstanA!extensionof
G,GA!: !GA!=G[{A!ϕ:G⊢A>ϕ},ifconsistent.
! =G,ifnot
ForeachantecedentAofa>conditionalderivablefromG,defineanA!extensionofGinductivelyrelativetoanorderingr overantecedentsof>statementswithG!r,0=G.Everysuchsequencehasafixedpoint.Wenowhavethedefinition:
Definition1. G ϕiffforallorderingsrthefixedpointG*ofeachG!rextensionsequenceissuchthatG*⊢ϕ.
4. Griceanscalarimplicature
Withthissketchofcommonsenseentailment,letusnowturntoGrice’spictureaboutimplicatures.Grice’sviewof implicaturesisthattheyarecalculatedaftercompositionalsemanticshasfinisheditsjobviahisfamousgeneralmaximsof conversation,quality,quantityandrelevance.InprincipletheGriceanpicturetellsthebeginningofanattractivestoryfor computingscalarimplicatures(Horn,1972,2005;SchulzandvanRooij,2006;Schulz,2007;Spector,2006).Butthisis onlythebeginningofastory,sinceGrice’smaximsofqualityandquantityarenotpreciseenoughreallytolicenseany inferences.Inaddition,thesemaximsshouldclearlybeformalizedwithinanonmonotoniclogic.GLprovidesasimpleyet precisereconstruction.
Consider(6)anditsimplicaturesignaledby : (6) JohnorSusancametotheparty(j_s) :(j^s).
TheweakGriceanimplicaturethatthespeakerdoesnotbelievethatj^sfollowsinGLifweincorporatethedefeasible principleofSincerity---Sayf>Bf---togetherwithaprincipleofignoranceaboutmoreinformativealternativestowhatwas said.SinceGLworkswithdescriptionsoflogicalforms,wehavethemeanstowritedownthefactthatacertainrelation holdsbetweentwoformulas,namelythatψisanalternativethatcouldhavebeensaidinthegivendiscoursecontext insteadofϕandthatitisanalternative.Being abletoexpressand todefinethissetofalternatives iscrucial tothe enterpriseofformalizing S-implicatures.Topickthe rightalternatives,we needameasureof informativeness.Let’s supposeit’slogicalentailmentthatisprovidedfromthebackgroundlogicofinformationcontent(itisnotstateableinGL itself,sinceitsconsequencerelationismuchweakerthanthatofthebackgroundlogic).IwilldefineAlt(ϕ,ψ)iffψisa strictlymoreinformativeformulathatisanalternativetoϕ.Iassumethatthesetofrelevantalternativesisfiniteand abbreviatethefactthatAlt(ϕ,ψ1)^...^Alt(ϕ,ψn)asAlt(ϕ,C),therelevantaxiomtodrawignoranceimplicaturesisnow:
(7) Altðf;CÞ!ððSayf^:Sayc1^...^:SaycnÞ>ðBf^:Bc1^...^:BcnÞÞ
ProvidedAlt(j_s)={j,s,j^s},wegetignoranceimplicaturesfrom(6)thatthespeakerdoesn’tbelievethats,jorthat
j^s,bysimplyturningtherelevant>instanceoftheschema(7)intoa!statement.Using(7)alonewehaveonlyone fixedpointinwhichthespeakerbelievesj_sandthatshebelievesneitherj,snorj^s.
TogetthestrongerGriceanimplicature,thatthespeakerbelieves:(j^s),Iadoptthefollowingaxiom: (8) Altðf;cÞ!ð:Sayc>B:cÞ
5Defineanormalizationof
GrelativetoAforamodelA !kGkA
N;A¼\ððW7kAk
AÞ[S
w2jGkA*ðw;kAkÞÞifthisisnon0. !¼kGkA,otherwise.
ForeachantecedentAofa>conditionalderivablefromG,defineinductivelyaGnormalizationsequencerelativeamodelAandanorderingr overtheantecedentsof>statements.G ϕiffforeveryorderingrthefixpointsoftheGnormalizationsequencerelativetorandthecanonical modelprovidedbycompletenessverifyϕ.
Theformin(7)hasamorespecificantecedentthan(8)andsowilloverride(8)’sincompatibleconsequences.Let’ssee whathappenswhenwecomputethefixedpointof(7)and(8).Wehavetheatomicfacts:
(9) Say(j_s),:Sayj,Alt(j_s,{j,s,j^s}),:Says,:Say(j^s)
Allfixedpointsofthesetofpremisescontainthe!transformationsoftherelevantinstanceof(7): (10) ðSayðj_sÞ^Altðj_s;fj;s;j^sgÞ^:Sayðj^sÞÞ!ðBðj_sÞ^:Bðj^sÞ^:Bj^:BsÞ
(7)’s antecedent entails (8)’s antecedent, so in cases of conflicting defeasible consequences where Alt(ϕ, ψ), the specificityprincipleentails:
(11) :Sayψ>:(Sayϕ^:Sayψ1^...^:Sayψn)
Fromthe factsathand,weseethat(8)and(7)conflict whenψin(8)isjors(butnot j^s),because,forinstance, instantiatingψin(8)tojwewouldhaveB:j.ButsinceBisclosedunderlogicalconsequenceandBðj_sÞfollowsfrom (7),we wouldgetBs, whichcontradicts anotherconsequenceof (7).Thismeansthat Specificityaddsthe following additionalpremisesinthederivation:
(12) :Sayj>:(Say(j_s)^:Sayj^:Says^:Say(j^s));
(13) :Says>:(Say(j_s)^:Sayj^:Says^:Say(j^s));
Onceweadd(12)and(13)toourpremises,attemptingtotransformtheinstancesof(8)involvingjandsinto!statements fails,becauseintransformingtherelevantinstancesof(8),wemustturnall>statementsinvolvingtheantecedents:Sayj and:Saysinto!formulas.Andthisrendersoursetofformulasinconsistent.Ontheotherhand,thereisnoinconsistency between(7)andtheinstanceof(8)usingj^s;thedefeasibleconsequenceof(8)inthatcaseisBð:j_:sÞ.Sowegetin thefinalfixedpointforthecomputationusing(7)and(8)thedesiredimplicatures:6
(14) Bðj_sÞ^:Bðj^sÞ^B:ðj^sÞ
Likemanyotherderivationsofscalarimplicaturesfor(6),theGLderivationisvalidonlyifthealternativenessrelationAlt isrestrictedasabove.Ifthesetofalternativescontainsotherstrictlystrongerlogicalentailments,thenGLpredictsno implicaturecanbedrawn.7
TheGriceanprogrammeitself saysnothingaboutrelevant setsof alternatives(Block, 2009).Wewouldneedan additionalcomponentofthetheorytoaddthis.Alternativesmightbespecifiedlexicallyandbepartofthegrammar(see
FoxandKatzir,2011).Forexample,wemightsaythatalternativesaredefinedlexicallyforscalaritems,foradjectives
beautiful,stupendous,gorgeous,...,fornounsgenius,idiot,...,forconnectives(_,^)(hereitdependsastowhether>, !, etc. are also considered connectives),and for quantifiers (no, some, many, most, all). Suchlexically specified alternativesseemreasonablebut weneedtoknowhowalternativescomposetogether.Onemightalsotrytofixthe alternativesforanutteranceviaaquestionunderdiscussionapproach,butthishasmanydifficultiesofitsown,notthe leastofwhichisdeterminingwhatthequestionunderdiscussionis.8Anotherapproachistoreasondirectlyoverpreferred
6Inparticular
Sauerland’s(2004)prioritizationofdefaults(hisExpertnessassumption)isnotneeded;theunderlyinglogicandtheSpecificity Principleofcommonsenseentailmenthandlesthis.Thisisdesirable,sincethisallowsforastraightforwardcancellationoftheimplicaturesifthe explicitsemanticcontentcontainsforexampleanexplicitdenialofoneoftheimplicatures.Further,notethatbecauseGLcalculatesdefeasible implicaturesoveralanguagedescribinglogicalformsinwhichquantifiersareeliminable,theprocessisdecidable,infactPSPACE.
7Thisisaformalizationofthesocalledsymmetryproblem(Kroch,1972).
8Oneoptionistotakethequestionunderdiscussion(QUD)tobethepolarquestioninducedfromtheutterance,whichforwhich(6)is:
(15) DidJohnorSusangototheparty?
Unfortunately,theanswerstothisquestiondoesn’tspecifytherightalternatives.AlternativelywecouldtaketheQUDtobe (16) Whowenttotheparty?
modelsofinformationcontent(vanRooijandSchulz,2004;SchulzandvanRooij,2006),butthisgeneratesanothersetof problems,theproblemofsideeffects,whichleadsagaintoanintroductionofrelevantalternatives.9
5. Embeddedimplicaturesandthelocalistchallenge
Sofar,Ihavedetailedagenerallogic,GL,forcomputingD-inferencesthatalsoservestocaptureS-inferencesgivena setofalternatives.Weneedonlyaxioms(7)and(8),togetherwithaspecificationofalternatives.10Sowhatabouttheset ofalternatives?Itseemsreasonablethatthesetofalternativesisatleastpartiallyconventionallydetermined.Butatwhat level are thesealternatives computed? Griceans claim thatthe alternativesare computed pragmatically,after truth conditionalsemanticshasfinisheditsjob.Givenastandardviewofwhattruthconditionsareinsemantics(setsofpossible worlds),thismeansthatGriceansdonothaveaccesstothe‘‘finestructure’’ofasentence’smeaning;theparticularway thetruthconditionshavebeenderivedfrom lexicalmeaningshasbeenerasedinthe semanticvalue.Acontrasting, ‘‘localist’’ theory claims that implicatures are, like presuppositions in the theory of Karttunen and Peters (1979), conventionallydeterminedbythelexiconandcomputedinparalleltocompositionalsemanticinterpretation.Incontrastto Griceans, localists like (Chierchia, 2004) have access to the fine structure of meaning in computing implicatures, inparticularincomputingthesetofalternativesuponwhichthederivationofimplicaturesdepends.
Theprincipal motivationfor the localist approachis the presence ofembedded implicatures,which can present problemsforNeo-Griceanapproaches.Anembeddedimplicatureisanimplicaturethatisgeneratedbyanexpression withinthescopeofatruthfunctional,modaloperatororquantifier.11
(18) Johndidthereadingorsomeofthehomework
Thisimplicates Johndidn’t dothereading and someof thehomework. Italsoimplicates thathedidn’t doallof the homework.Since Griceanscomputeimplicaturesonlyonwholeutterancesorfullsentences,it’snotclearhowtoget thesecondimplicature,whichisbasedonthemeaningofasubsententialcomponentof(18).(18)andsimilarexamples haveimpressedsomelinguistsasadecisiveargumentagainstaGriceanview(forexampleFox,2007).Nevertheless,the difficultyforGriceanswith(18)dependsonceagainonthesetofalternativeschosen(Spector,2007).InAsher(inpress)I showhowtoadaptthebasicrules(7)and(8)toexploittherecursivestructureofthelogicalformandlexicallybasedscales forscalarpredicates,disjunctionanddeterminers(thelatterhasbeenacknowledgetobeasourceofimplicaturessince the early workof Horn, 1972). Byreasoningover logical forms GLhasaccess to the alternatives of subsentential constituentsandthusallowsusderiveimplicaturesofthesortthatChierchiaclaimstohold,ifwewantthem,allwithina broadlyGriceanframework.
6. InteractionsbetweenS-implicaturesanddiscoursecontext
Thelocalistvision,however,isasflawedastheNeo-Grieanone.Theybothoverlooktheeffectsofdiscoursecontext. Theheart of the localistposition isthat implicaturesare calculated onthe basis of lexical semanticsand syntactic structure.IshowinthissectionthatsocalledembeddedS-implicaturesaresensitivetodiscoursestructure;infactthey are triggered by it. Sometimes theseembedded implicatures, when necessary for discourse coherence, losetheir characteristicasadefeasibleimplicature.Theyare,ifyouwill,stillpragmaticinferences,insofarasdiscoursestructureisa matterofpragmaticsaswellassemantics.Buttheseuncancellable‘‘S-inferences’’bearlittleresemblancetotheirintuitive characterizationasimplicaturesgivenatthe beginningofthispaper.First,Iwant toexaminehowS-inferencesand discoursestructureinteract.IwillthenproposeanaccountofthatinteractionthatmakesS-inferencesparasiticoratleast codependentupondiscoursestructure.Thisaccountwillopenthewaytoamoreradicalposition:eventhestandard examplesofS-implicaturesdependonassumptionsaboutimplicitdiscoursecontext,andineffect bothlocalists and Griceanshavegottenitwrongabouthowsuchinferencesaretobecomputed.
9
InAsher(inpress)Ilookatthissolutioninmoredetail.Toseetheproblemofsideeffectsconsider
(17) a. (Assumeaproblemsetwith10problemsonit.)HowmanyproblemsdidJohndoontheproblemset? b. Johndidsomeoftheproblemset :B(Johndidmorethan1problemoftheproblemset). But(17b)doesnothaveanysuchimplicature.
10Fox(2007),KratzerandShimoyama(2002)andAlfonso-Ovalle(2005)argue thatfreechoiceimplcaturesshouldbetreated withthe
mechanismforscalarimplicatures.Ihavearatherdifferenttakeonfreechoiceimplicatures,butthatwouldtakeustoofarafieldhere.SeeAsher andBonevac(2005).
Sometimes the discourse context canlicense S-inferencesthat aren’t normally considered by either localists or Griceans.Consider
(19) a. A:Doyoulikehim? b. B:Why,yes,Ido.
c. A:Imean,doyoulikehimordoyouLIKEhimlikehim? d. B:Ilikehim.
Inthe firstquestionanswerpairwitha yes/noquestion,thelexicalscaleassociatedwithlikeisn’treallyoperativeor neededtounderstandtheexchangetoanalternativequestionwhereascaleisexplicitlyinvoked,andwheretheresponse implies thenegation ofthestrongeremotion(likinghim likinghimisstrongerthanlikinghim).12Whatisgoingonin
these examples? While there are, most likely, scales lexically associated with adjectives like full, bald, etc. and determinerslikesome,most,etc.,theactualvaluesandperhapseventhepresenceortheactivationofthescalefor thepurposesofcalculatingimplicaturesisdependentondiscoursecontext.Itisthediscoursecontextthatsuggeststhe relevantalternatives,anditistherequirementofcomputingaparticulardiscourserelationthattriggerstheSinference. ThereareinfactmanyeffectsofdiscoursestructureonS-inferences.Alocalistcomputationofalternativespredicts thatoneshouldnotgetthestandardimplicatures(theexhaustivityimplicatureforor,forinstance)insidethescopeof downwardentailingoperators.13MostGriceanaccountswouldagree.Butthisiswrongfortheantecedentsofconditionals
insomecases,whicharedownwardentailing.Consider(20),anditsparaphrase(21):
(20) Ifyoutakecheeseordessert,youpay20euros;butifyoutakeboththereisasurcharge.
(21) Ifyoutakeonlyacheesedishoronlyadessert,themenuis20euros;butifyoutakeboth,thereisa surcharge.
or
(22) IfJohnownstwocars,thenthethirdoneoutsidehishousemustbehisgirlfriend’s. (23) Ifonepersonreadsmybook,I’llbehappy.
Heretheinterpretationoftheconsequentforcestheantecedenttohavetheexclusivereading.Thisisafurtherindication thatthecalculationofthealternativesetrelevanttoderivingS-implicaturescannotbepurelylocalistbutdependsratheron theglobaldiscoursecontextinwhichitisembedded.
Thedependenceofimplicaturesondiscoursecontextsalsoshowsusthatwemusttakecarehowtocalculatethem. BothGriceans andlocalistsconsiderimplicaturestobecalculatedaftersemantics.Animplicationofthisview(made explicitinChierchia,2004)isthatimplicaturesthataren’tinconsistentwithestablishedfactsinthecommongroundorthe narrowsemanticcontentcontinuetobeoperativeasthediscoursecontentiscomputed.Thisinsensitivityofimplicatures toamorenuancedviewofdiscoursecontentgivesusthewrongresults.Considertheexample(24a)withitsembedded implicaturein(24b)
(24) a. Johneitherdidsomeofthereadingorsomeofthehomework
b. Johndidn’tdoallofthereading;Johndidn’tdoallofthehomework;andhedidn’tdosomeofthe homeworkandsomeofthereading.
Andnowconsiderthe followingdialogue.
(25) a. A:Johneitherdidsomeofthereadingorsomeofthehomework.
b. B:Johndidallofthereading,butyou’reright,hedidn’tdoallofthehomework.
Whathappenstotheimplicature(24b)inthisdiscoursecontext?Tomyears,(25a--b)hastheimplicaturethatJohndidall ofthereadingandsomeofthehomework.Infactthisisanimplicatureof(25b).Butthisimplicaturecancelstheimplicature of(25a)thatJohndidn’tdosomeofthehomeworkandsomeofthereading.Thus,implicaturesinteractinimportantways withdiscoursemoveslikethecorrectivemovegivenbyB.WeneedtointegrateS-implicaturesintodiscoursecontentand
12Thisexchangeinvitesanextendedevaluationofhowviewsoncontrastivetopicimpingeonthisenterprise(Lee,2010a,b).Forlackofspace,I
cannotdojusticetotheintriguingparallelsbetweentheobservationshereandthatwork.
13Adownwardentailingoperator
structureandthencomputetheappropriateupdateofthatcontentaftertakingintoaccountB’scorrectivemove.This impliesthatwecannotcalculateimplicaturesmerelyatasententiallevel,asmostGriceansandlocalistshaveassumed. Weneedamuchmorefinegrainedviewofthediscoursecontexttocalculateimplicaturesproperly.14
Anotherproblem withthe current(localist andGricean)accountsofS-inferencesisthattheseinferencesare not alwayscancellable.Inparticular,whenS-inferencesarerequiredfordiscoursecoherence,theyarenotcancellable. (27) a. Johnhasanevennumberofchildren.Hehasfour.(implicatureisthathehasexactly4)
b. #Johnhasanevennumberofchildren(p1).Hehasthree(children)(p2).
c. Johnhasanevennumberofchildren(p0
1),andhehasatleastthree(children)(p02).
AGriceanoralocalistshouldpredictthat(27b)isOK,sincetheimplicaturetothestronger,‘‘exactly’’meaningofthree
shouldbeblocked.However,itisnot,and(27b)isinfelicitous.Ihypothesize thisstemsagainfrom aninteractionof discoursestructureandimplicatures:thereisaparticularsortofelaborativemovegoingoninthesecondclausesof (27a--b),whichaccountsforthe‘‘freezingoftheimplicature’’.
AfinalindicationthatsomethingisamisswithcurrentaccountsofS-inferencesistheirwell-knownfragility---i.e.,their dependenceoncontextualeffectsandontheirlogicalform.AsChemla(2008)notes,localisttheoriespredictthat(28b) shouldnothavetheimplicaturebelow,makingastarkcontrastbetween(28a)and(28b).
(28) a. Johndidn’treadallofthebooks. Johnreadsomeofthebooks.
b. Nostudentreadallofthebooks.? Allofthestudentsreadsomeofthebooks.
Forlocalists,thepredictedimplicatureof(28b)is:Nostudentreadsomebook---orsomestudentsreadsomeofthe books,whichisweakerthantheimplicaturetestedbyChemla.However,(28b)isequivalentto:
(28c) Allthestudentsdidn’treadallofthebooks.
andthisintuitively (andona localisttheory)implicates thatall the students readsomeofthe books. Soequivalent meaningsseemtoyielddistinctimplicatures!
Interestingly, D-inferences are not closed under arbitrary first order equivalences either. Consider the logical equivalencein (29a).If D-inferences werecomputed ondeepsemantic contentand hence closedunderfirst order equivalences,wewouldpredictnodifferencebetween(29b)and(29c)since(29b),wherethe relationofExplanation linkingthetwoclausesisinferred,isperfectlycoherentincontrastto(29c),wherenodiscourserelationisinferred: (29) a. Someonepushedhim$CLNoteveryonedidn’tpushhim.
b. Johnfell.Someonepushedhim(Explanationinferred) c. #Johnfell.Noteveryonedidn’tpushhim
FewpeoplethinkthatD-inferencesarecompositionallydeterminedatthesyntaxsemanticsinterfacesothisfailureof substitutivity,whichisequivalenttoafailureofcompositionality,isnotmuchofasurprise.InGLthisfailurecomesabout becauseD-inferencesaredependentoninformationaboutlogicalformandabouttheglobaldiscoursecontext,rather thanjustsemanticcontent.
6.1. CombiningD-inferencesandS-implicatures
IhavegivenargumentsthatcallintoquestiontheempiricaladequacybothofGriceanandlocalistaccountsofimplicature. Suchaccountsdon’texplainthefragilityofS-inferences,theiroccasionaluncancelability,andtheirsensitivitytodiscourse context.Mysimple,alternativehypothesisisthatS-inferencesnotonlyusethegenerallogicunderlyingGL’scomputationof D-inferences,but,likeD-inferences,arealsodependentthestructureofthediscoursecontext.15MakingS-implicatures
14Wecancontinuethispatternwithmorecomplexembeddedexamples.
(26) a. A:Someofthestudentsdidsomeofthereadingorsomeofthehomework. b. B:Atleastonestudentdidallofthereading,butotherwiseyou’reright.
ItwouldseemthatB’scorrectionstillleavesmanyoftheimplicaturesofhisoriginalstatementintact;he’sstillcommittedtotheimplicaturethat someofthestudentsdidn’tdoallofthehomeworkandthatsomeofthestudentsdidn’tdoallofthereadingandsomeofthehomework.Weneeda morefinegrainednotionofimplicaturerevisioninthefaceofcorrections.
dependentondiscoursecontextshouldnotcomeasasurprise.Thebehaviorofothersortsofnon-assertoriccontent,like presupposedcontent,alsohascomplexinteractionswithdiscoursestructure(AsherandLascarides,1998).Asover30 yearsofworkonpresuppositionhasshown,itisunwisetotrytocomputepresuppositionswithoutexamininghowthe surroundingdiscoursecontextmightaffectthesepresuppositions.Butunlikepresuppositions,atheoryofS-implicatures needs,notatheoryofaccommodationorofbinding,butatheoryoftriggering.Morespecifically,wemustanswerthe question:whendoesadiscoursecontextlicenseorinduceanappropriatealternativesetoverwhichtocompute(scalar) inferences?
Hereinanutshellistheapproach:discourserelationslikeContrast,Correction,Parallel,QAP,andvariousspeciesof Elaborationinducestructuralconstraintsonthediscourseintheformofstructurepreservingmapsbetweenconstituents. Togetherwithprosodicstress,whichtypicallysignalsalexicalchoice,thesestructuralmapsprovideasetofalternatives relevant tocalculatinganSinference.Whenthe requisiteelementsforconstructingalternativesarenotpresent,the alternativesaren’tgeneratedandneitheristheinference.Butthereisalsoaco-dependencebetweenS-inferencesand discoursestructure.Sometimes,inferredS-inferencesarerequiredtoestablishdiscourserelations.Whenthelatteristhe case,thenIpredictthattheS-inferencesarenotcancellablewithoutaffectingthecoherenceofthediscourse.Iwillthusbe abletoaccountforthediscoursesensitivityofS-inferences,theirfragilityandtheiroccasionaluncancelability.
Tobuildacaseformyclaim,IwilllookatexamplesthatlocalistslikeChierchiaetal.(2008)haveputforwardtoargue fortherobustnessoflocalistimplicaturecomputations.Iwillshowthatinallofthoseexamples,itisthediscoursestructure thattriggerstheembeddedS-inference,andinsomecasestheS-inferenceisrequiredtomaintainthediscourserelation established.Inthelattercases,the S-inferencesarenotcancellableexceptonpainofdiscourseincoherence.
Let’sfirsttakealookatthelargecollectionofexamplesinChierchiaetal.(2008)allofwhichinvolvethediscourse relationofCorrection.
(30) a. Joedidn’tseeMaryorSue;hesawBOTH.(onlyaclearexhaustiveinterpretationoftheembedded disjunctionispossible).
b. ItisnotjustthatyouCANwriteareply.YouMUST.
c. Idon’texpectthatsomestudentswilldowell,IexpectthatALLstudentswill.
(30a--c) all are only felicitous as corrections of assertions that are echoed under the scope of the negation. The observationisthattheechoicuseofcorrectionin(30)makestheembeddedimplicatureshappen.Infact,they’renot subsequentlycancelableeither.From anSDRTperspective,all oftheseexamples involveCorrection tosomeprior constituentp0,oftheformJoesawMaryorSue.Thecorrectionmoveinthefirstclauseof(30a)mustcorrectsomethingin
p0,andthesecondclauseelaboratesandineffectsayswhatthecorrectedelementshouldbe.Inthiscasetheonlything
thatcanbecorrectedistheimplicaturethatJoedidn’tseeMaryandSue.
Asher(2002)(writtenalmostadecadeearlier)providesananalysisofdiscourserelationsintermsofamapfromthe source(theconstituenttobelinkedtothediscoursestructure)toatarget(adiscourseconstituentthatservesastheother termoftheCorrectionrelation).Thismapexploitsprosodiccuesandthelogicalstructureoftheconstituents.Itcanalsobe madetoserveourpurposeshere.16MyaccountofCorrectioninvolvesthefollowingconstraint:
!Correction(a,b)holdsonlyifKbentails:Kaandthereisamapm:Kb!Kasuchthatthereisatleastsomeelementxof
KbKb(m(x)/x)>Ka.Theelementxissaidtobethecorrectingelementandshouldbeprosodicallymarked.
In(30a)theCorrectionmoveissignalledbytheformof(30a)andnaturalprosody.ThereisanechoicuseofJohnsaw MaryorSue,thatthefirstclause(30a)denies.Sowenaturallyreadthisexampleasoccurringinadiscoursecontextin whichthereisaconstituentKp0,JohnsawMaryorSue,thatisthetargetoftheCorrectionmove.Inanaturaldialogue,you couldjustdrop(30a.1),the firstclauseof (30a).(30a.2),the secondclauseof (30a),elaborates onorspecifiesthe meaningthatthespeakermeanstosuggestasareplacementforthecorrectedcontent.Thefulldiscoursestructureof (30a)anditstargetisthen:
(30a0) Correction(a,p);p:Elaboration(30a.1,30a.2)
Given(30a),especiallytheelaboration(30a.2),weneedtoinvestigatehowtheconstraintonCorrectionissatisfied. Themapm:Kp!Ka(actuallythesubmapm:K30a:2!Kp0)maps^to_.ThismapsuppliesanS-alternativeforKp0:
John sawM& S.But Ka,encodingthe litteral meaningofJohn sawMaryorSue, doesn’tsatisfythe constrainton
Correction.Moreover,keepingKaasthe targetoftheCorrection wouldnotallowus tospecifyanysensiblerelation
between(30a.1)and(30a.2).Inthiscase,however,thepresenceofS-inferenceallowsarepairofthediscoursecontext, inwhichweaddtheimplicaturegeneratedusing(7),(8)andtheprocedureoutlinedinSection4,toKp0---i.e.,Kp0isreset
to:JohnsawMaryorSue, andJ. didn’tseeMaryandSue. Inotherwords, wehavea localaccommodationof the implicature within Kp0. The constraint on Correction is now satisfied. As Correction requires the presence of the
implicature,theimplicatureisnotcancellable,exceptonpainofdiscourseincoherence,aswitnessedin(30a″): (30a″) #Joedidn’tseeMaryorSue(orboth);hesawBOTH.
(30a″)isnonsensebecausethesentencehasstrongcluesindicatingCorrectionthusprecludinganyotherdiscourse relation,buttheCorrectionconstraintcan’tbesatisfied.Sonodiscourserelationcanbeinferred.
Theintroduction ofthe S-inference in the example above isa sort ofdiscourse based coercion. Noticethat the implicaturecalculatedisrelativetothemapm,onlyafterGLhasinferredadiscourserelation.Sothereisnoconflict betweentheGLcomputationofdiscoursestructure,whichisprimary,andthecomputationofS-implicatureswhichis secondary.mprovidestherelevantelementinthealternativesettoor;wethenproceedtocalculatetheimplicatureasin
Section4onthelocalpartoftheSDRS.TheinferenceoftheSimplicatureitself,however,istriggeredbytheneedto satisfytheconstraintsimposedbythediscoursemoveofCorrection.Thus,DandSinferencesarecodependent;theneed tocalculate a Dinferencetriggers the calculation of the Simplicature, and itisthe Simplicature that satisfies the constraintsoftheDinferences.
AnothersetofexamplesofembeddedS-inferencesconcernsthediscourserelationsofParallelandContrast.17 (31) a. [If[youtakesaladordessert<p1,[youpay20euros<p2]p3;[butif[youtakeboth<p4 [thereisasurcharge.]p5]p6
b. Ifmostofthestudentsdowell,Iamhappy;ifallofthemdowell,Iamevenhappier. c. IfyoucanfireJoe,itisyourcall;butifyoumust,thenthereisnochoice.
d. Everyprofessorwhofailsmostofthestudentswillreceivenoraise;everyprofessorwhofailsallof thestudentswillbefired.
Contrastalsoinvolvesastructurepreservingmapmfromsourcebtotargetaandrequiresthatatleastoneelementxoftb
besuchthatxandm(x)bedefeasiblycontradictory,inthe sensethattheydefeasiblyimply,incontext,contradictory propositions(Asher,1993).Contrastalsohasaparticularrestrictionwhenitinvolvestwoconditionals;themapmmust specifymaptheantecedentoftheconditionalinthesourcetotheantecedentoftheconditionalinthetargetandthetwo antecedentsmustbedefasiblycontradictory.Inthecaseof(31a),forexample,wehavetheContrastsignalledbythe presenceofthediscourseconnectorbut.Then:
!Contrastrequiresamapm:p6!p3suchthat
!m(p5)=p2andm(p4)=p1wherep1andp4aredefeasiblycontradictory.
!Giventhatthecontentofp1andp4arenotastheystanddefeasiblycontradictory,weneedtorepairthesituationwithan
S-inferenceifpossible.
!ThemapmprovidesamapfromA_BtoA^B.
!ThepresenceofthisalternativeallowsGLtocomputetheS-inference:(A^B)asinSection4relativetothelogical formofp2.Theimplicatureisnowaddedtop2,allowingustosatisfytheconstraintonContrast.
Onceagain,itisthediscoursestructureandtheneedtosupporttheD-implicatureofContrastintroducedbythediscourse particlebutthatprovidestherelevantalternativesandtriggerstheSimplicature.TheSimplicatureverifiesthestructural constraintonthediscoursecontextimposedbyContrast.Onceagain,thisisanimplicaturethatisnon-cancelableinthis discoursecontext;it’sasstrongasanyunembeddedimplicatures,strongereven.Theseexamplesleadtothefollowing generalization:
!IfthediscoursestructurerequirestheSimplicatureforcoherence,itisn’tcancellableexceptonpainofincoherence. (31b)providesanotherexampleofS-implicaturedrivenbytherelationofContrast.Thejuxtapositionandconnectionof thetwocomplexconstituentsformsthebasisoftheimplicatureinthefirstconstituent.Thestructuresareveryclose;itis justthedifference betweenthe twoquantifiers inthe conditionalthatvalidatethe twodifferentconsequentsand the contrastbetweenthetwoconditionals.Thenaturalmaptakestheantecedentandconsequentofthesourceandmaps themontoantecedentand consequentofthe target.Inotethatthemapspecifiesinfactthescale:mostvs.all.The
implicaturethatmostyieldsmostbutnotallisneededtovalidatethestructuralrequirementofContrast.Onceagain,itis discoursestructurethatlicensestheSimplicature.
Toverifythatitisthejuxtapositionofthetwoclausesthatdrivestheimplicatureconsider: (32) JohnlovesSusan.ButSamloveshertoo.
JohnlovesSusandoesn’timplicateonitsownthatotherpeople,andinparticularSam,don’tloveSusan.Buttosupport theContrastin(32),wegettheimplicaturethatSamisn’texpectedtoloveSusanorthatperhapslotsofotherpeople besideJohnaren’texpectedtoloveSusan.
BesidesContrast,therearemanyotherdiscourserelationsthattriggerS-implicatures.In(33b),wehaveplausiblya Continuationofthediscoursetopic(anandiseasilyinsertablebetweenthetwosentenceswhiletheinsertionofbutis slightlylessfelicitous),whatdidthestudentsdo?,.Asmanyhavenoted,(33b)containswhatsomehavelabelledapairof
contrastivetopics;thatis,inthetwoclausesthepredicationexploitsapartitionoverthestudentsandpredicatesproperties thatareincompatible.Toverifythisstructuralconstraint,onceagainweneedtotriggeranexclusivityS-implicaturein (33b),
(33) a. Twostudentswroteapaperorrananexperiment.(weak,orno,implicature)
b. Twostudentswroteapaperorrananexperiment.Theotherseitherdidbothormadeaclasspresentation. (exclusivityofthedisjunction)
c. Threestudentsdidmostoftheexercises;therestdidthemall.
ParticularkindsofelaborationsalsogenerateS-inferencesthatareuncancellable.Consideragain: (27) a. Johnhasanevennumberofchildren.Hehasfour.
b. Johnhasanevennumberofchildren,four.
c. #Johnhasanevennumberofchildren(p1).Hehasthree(p2).
d. #Johnhasanevennumberofchildren(p1),three(p2).
e. Johnhasanevennumberofchildren(p1),andhehasatleastthree(p2).
Thestructureof(27a--c)impliesthatp2modifiestheDPjusttoitsleft.Notealsothatyoucan’tintroduceand)betweenthe
twoclauses(27a,b)or(27c,d),thoughyoucanwith(27e).Thesecluestellusthat(27a--d)exemplifythediscourserelation ofentity-elaborationorE-elab,andthesecondtermoftherelationmustidentifysomeobjectmentionedinthefirstterm. HeretheobjectinquestionistheevennumberofJohn’schildren.TomeettheidentificationconstraintonE-elab,fourmust meanexactlyfour.Thus,asisbynowfamiliar,theconstraintsondiscoursestructuremaketheSinferencein(27a,b) uncancellable.Ontheotherhand,whileE-elabissignalledin(27c,d),theconstraintonidentificationoftheevennumber can’tbemet.So theseexamplesarepredictedtobeinfelicitous.WhileitispossibletohaveE-elabin (27e),it’snot necessaryorevenpreferred;insertinganandbetweenthetwoclausesisastrongsignalthatanon-elaboratingdiscourse relationisinplay.
Question answerpairsalsotrigger S-implicatures.18Aquestion induces,dynamicallyspeaking, apartitiononthe
informationstate(Groenendijk,2008;Asher,2007).Acompleteanswerpicksoutonecellinthepartition;indirectanswers (whichstandintheIQAPrelationtothequestiontheyaddress)mayrequirereasoningoradditionalinformationtoinfera completeanswer.Sometimestheadditionalinformationcomesfromanimplicaturegivenbyastructurepreservingmap fromtheresponsetothequestion.IQAPcaninfactgiverisetoanoveranswerinwhichwegetmorethanjustacomplete answertothequestion;wegetamoreinformativesubsetoftheelementofthepartitionpickedout.
Aparticularlyinterestingcaseinvolvesprosodicallymarkedoveranswerstopolarquestionslikethefollowing. (34) a. DidJohneatallofthecookies?
b. JohnateSOMEofthecookies.
(34b)isanoveranswerto(34a).Byitself(34b)doesn’tprovideenoughinformationtocomputeananswertothequestion. Buttheprosodicmarkinggivesrisetoastructurepreservingmapfromtheresponsetothequestionthatmustmapthe focussedelementtoanelementofthesametypeinthequestionwhilepreservingasthenonfocussedstructureand content as far as possible.In thiscase the prosodically marked someis mapped toall, and provides the relevant alternativeset.ThelackofafullansweralsotriggerstheS-inference,andincludingtheinferencethatJohndidn’teatallof
thecookiestogetherwith(34b)providesacompleteanswerto(34a).Thus,(34b)alsogivesmoreinformationthanjusta simplenowouldhave.
Aresponsethatonitsownfailstogiveacompleteanswertoaquestioncanalsotriggerembeddedimplicaturesand onesthatwouldn’tbecalculatedfromstandardlexicalalternativesforsome.Consider,forinstance,theS-implicatureof (35b),whichisthatJohnbelievesthatnotmanyofthestudentspassedtheexam,ortheimplicatureof(36b)whichisthat everyonedidn’treadmostofthebooks.Theseimplicaturesfollowgiventhestructurepreservingmappingrequiredby question-answerpairsthatmapssometomanyin(35b)andsometomostin(36b).
(35) a. DoesJohnbelievethatmanyofthestudentspassedtheexam? b. JohnbelievesthatSOMEofthestudentspassedtheexam. (36) a. Dideveryonereadmostofthebooks?
b. EveryonereadSOMEofthebooks.
Noticethatonceagainitistheadditionoftheimplicaturesintheseresponsesthatgivesuscompleteanswerstothe questionstheyarepairedwith.19
Yetanothercaseofanimplicaturearisingfromthepresenceofadiscourserelationconcernsthecasewhereaspeaker respondstoaquestionwithanotherquestion:20
(38) a. A: WhereisJohn? b. B: WhereisJill?
SDRT’sGLlinks(38b)viatherelationofQuestionElaborationorQ-elab,whichhasaparticularsemantics.Q-elab(a,b) holdsiffananswertobhelpsdetermineananswertoa.Andthisisindeedthe‘‘implicature’’thatinterpretersdrawfrom (38b)---namelythatBbelievesthatgettingananswertohisquestionwillhelpfindananswertoA’squestion.
Ifwetakethelineofthoughtdevelopedheretoitsinclusion,itimpliesthatevenunembeddedSinferencesarenotthe productofGriceanstylereasoningdependentonsomesetofstipulatedalternativesbutratherlargelydependentonthe computing of discourse structure. Consider againunembedded disjunctions. The S-inferences conveyed by simple unembeddeddisjunctionsarepredictednottoarisewhennotneededtoverifyconstraintsimposedbydiscoursestructure ortoinferdiscourserelations.TxurrukaandAsher(2008)arguethatdisjunctionsaredefeasiblemarksoftherelation Alternation.Alternationpartitionsthesetofdiscoursepossibilitiesintonon-emptysetsrelativetosometopic,whichcanbe introducedviaaquestionorsimpleassertion.21Whenthetopic,however,alreadycontainsthedisjunction,theconstraint thatisaconsequenceofAlternationisnotmetandsoneitherAlternationnortheexhaustivityimplicatureholds,asin(40): (40) a. DidJohnmeettheVicePresidentorthePresident?
b. HemusthavemettheVicePresidentorthePresident,sincehegotthejob.
AsimilarmoralholdsforSinferencesgeneratedbyquestionanswerpairs.Ifthey’renotrequiredbytheconstraintson discoursestructure,theSinferencesdon’tarise,eveniftheimplicatureisconsistentwiththeinformationinthediscourse context.
(41) Didsomestudentsgototheparty? (42) Yes,somestudentswenttotheparty.
19TheapproachextendsnaturallytoWh-questions:
(37) a. Whoreadallofthebooksonthereadinglist? b. JOHNreadSOMEofthebooks.
Thisexamplefollowsthetreatmentofpolarquestions,excepttherearetwoprosodicallyprominentelementsintheresponse.Itisthesecondthat underthestructure-preservingmappinggeneratestheimplicature.
20ThankstoBartGeurtsforbringingupthisexampleattheNijmegenImplicaturesWorkshop,Nijmegen,January2012. 21
Here’sanexampleofAlternation,whichalsoinvolvesanauto-Correction. (39) SamorSusancame,orbothdid.
Themeaningofthefirstdisjunctof(39)hastobestrengthenedtoSamorSusanbutnotbothcame,ifthedisjunctsarebothtobeinformativeand Alternationistohold.
Here there is noprosodically marked element and no pairing of two distinct elements on a scale. Ipredict the implicaturenottoarise.
Let’snowreturntotheproblematic
(43) Noneofthestudentsansweredallofthequestions.
(43)doesnotseemtohave,inanoutofthebluecontext,theimplicature: (44) Allofthestudentsansweredsomeofthequestions
eventhough(43)isequivalentto
(45) Allthestudentsdidn’tanswerallofthequestions.
whichdoeshavethepredictedimplicature,becauseitsmorecomplexformsuggestssomesortofaCorrection.Anatural contextfor(45)is:
(46) a. A:Allofthestudentsanswerallofthequestions.
b. B:No,allofthestudentsDIDN’TanswerALLofthequestions.
Thereisanaturalprosodicprominencetothesecondoccurrenceallin(45)signallingalexicalchoicethatisthesourceof thedisagreement,whichgivesrisetoastructurepreservingmapandtherelevantimplicature.(43)inthiscontextless clearlyhastheimplicaturebecausetheCorrectionisalsosupportedbythechoiceofnone.
TheinteractionbetweendiscoursestructureandSinferenceshasimplicationsonhowevidenceforSimplicatureshas oftenbeengathered,asarguedbyGeurts(2009).Infactevenoutofthebluecontextsmayinvolvetacitquestionsunder discussioninthewaysuggestedbyRoberts(1996),whichmayberesponsibleforgeneratingmostifnotallSinferences, inthewaythatihaveoutlinedforthediscourserelationIQAP.IdiscussthisissuefurtherinAsher(inpress),whichis crucialtothesuccessofthisgenerallineofthought.
7. Conclusions
I’vearguedthatthereisaunifiedtheoryofimplicatures.Implicatures,understoodasdefeasibleimplications,arisefrom severalsources:semantics,discoursestructureorprosodytogetherwiththelogicalformofwhatissaid.Theyemployaxioms inanon-monotoniclogic,theGlueLogicofSDRT,whichworksonlogicalformsratherthansemanticcontentsinorderto preservetractabilityandexploitstructureatthelevelofthesentenceandthediscourse.ButtherearedistinctionsbetweenD implicaturesandSimplicatures;thelatteraretoalargeextentparasiticonthefirst.OnmyapproachSimplicaturesare triggeredbytherequirementsofthediscoursecontext;theyarecalculatedrelativetoasetofalternativeseitherprovided lexicallyorbythediscoursecontext,inlargeparttorenderconsistentortostrengthendiscourserelationsthatGLhasalready computed.Thetheorymakesseveralnewpredictions:Sinferencescanbe‘‘cancelled’’evenifthey’reconsistentwiththe purelysemanticcontentgiveninformationinthediscoursecontext;Sinferencesmayalsobeuncancellableevenintheface ofinconsistency,whentheyaremandatedbydiscoursestructure;embeddedS-inferences(bothnegativeandpositive) requireamoreelaboratediscoursesettingtobetriggeredandsoshouldbehardertogetwithouttheappropriatediscourse context.Thislineofthinkingalsosuggestsalineofempiricalresearch:giventherightdiscoursecontexts,embedded implicaturesshouldfollowaseasilyastheunembeddedones,tosomeextentconfirmedbyZondervan(2008).
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