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RunningHead:Gradientsymbolsincodemixing

Title:Coactivationinbilingualgrammars:Acomputationalaccountofcodemixing*

MatthewGoldrick1,MichaelPutnam2,&LaraSchwarz21NorthwesternUniversity2PennsylvaniaStateUniversity

*WegratefullyacknowledgeMattCarlson,MaríadelCarmenParfaitaCouto,BrianHok-

ShingChan,MargaretDeuchar,JaneGrimshaw,GéraldineLegendre,JohnLipski,Akira

Omaki,ShanaPoplack,LilianaSánchez,PaulSmolensky,ColinWilson,andMasayaYoshida

forhelpfulcommentsanddiscussion.ThisresearchwassupportedbyNSFgrant

BCS1344269.

Addressforcorrespondence:

MatthewGoldrick

DepartmentofLinguistics

NorthwesternUniversity

2016SheridanRd.

Evanston,IL60208USA

matt-goldrick@northwestern.edu

Keywords:Codemixing,GradientSymbolicComputation,doublingconstructions

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Abstract

Alargebodyofresearchintobilingualismhasrevealedthatlanguageprocessingis

fundamentallynon-selective;thereissimultaneous,gradedco-activationofmental

representationsfrombothofthespeakers’languages.Anequallydeeptraditionofresearch

intocodeswitching/mixinghasrevealedtheimportantrolethatgrammaticalprinciples

playindeterminingthenatureofbilingualspeech.Weproposetointegratethesetwo

traditionswithintheformalismofGradientSymbolicComputation.Thisallowsusto

formalizetheintegrationofgrammaticalprincipleswithgradientmentalrepresentations.

Weapplythisframeworktocodemixingconstructionswhereanelementofanintended

utteranceappearsinbothlanguageswithinasingleutteranceanddiscussthedirectionsit

suggestsforfutureresearch.

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CoactivationinBilingualGrammars:

AComputationalAccountofCodeMixing

Oneofthemoreamazingfeatsofbilinguallanguageproductionisthefluent

integrationoftwolanguageswithinasingleutterance.Werefertothisphenomenonas

codemixingtoemphasizetheintegrationoftwolinguisticsystems,usingthis

synonymouslywithtermssuchasintra-sententialcodeswitching.Anextensivebodyof

researchhasidentifiedimportantrolesforthegrammaticalprinciplesofthesource

languagesinconstrainingcodemixing(see,e.g.,Deuchar,2005;Muysken,1995;Myers-

Scotton&Jake,1995;Poplack,1980,forreviews).Paralleltothislineofresearch,several

decadesofresearchhasprovidedawealthofevidencesuggestingthatbilinguals

simultaneouslyco-activateelementsfromeachlanguageduringproduction.Forexample,

whenintendingtonameapictureofadog,aSpanish-Englishbilingualwillsimultaneously

activate,tovaryingdegrees,representationscorrespondingtoEnglish(DOG)andSpanish

(PERRO)forms(seee.g.,Kroll&Gollan,2014,forareview).Thissuggeststhatmental

representationsinbilingualspeakersincorporateblendsofstructuresfromeachlanguage

(i.e.,notDOGorPERRO,butarepresentationthatisbothDOGandPERRO).

Giventhestrengthoftheevidenceforgrammaticalprinciplesaswellasblend

representations,wearguebelowthatanadequatetheoryofbilinguallinguisticcognition

mustbeabletoincorporatebothoftheseelements.Discretegrammaticalprinciplesmust

beintegratedwithgradientblendrepresentations;currently,noexistingframeworkdoes

so.Inthiswork,weproposesuchanintegrationusingtheGradientSymbolicComputation

framework(GSC;Smolensky,Goldrick,&Mathis,2014).Thisgrammar-basedformalism

incorporatessymbolicrepresentations,whoseelementsareassociatedwithcontinuous

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activationvalues.WeshowhowaGradientSymbolicapproachtocodemixingcanallowus

toaccountforgrammaticalconstraintsonblendedrepresentationsthatemergeincode

mixing.

Webeginbyreviewingtheevidenceforblendrepresentationsinbilingualsacrossa

varietyofprocessingcontexts.Tohighlighttheinteractionofblendrepresentationsand

grammaticalprinciples,wethenexamineindetailcodemixingproductionswhereblended

elementsareovertlyproduced—anelementoftheutteranceisdoubled,appearinginboth

languageswithinasingleutterance.Withtheseempiricaldatainmind,wedevelopaGSC

accountofcodemixing.Wedemonstratehowitaccountsforempiricallyobserved

restrictionsondoubling,anddiscussthefutureresearchdirectionsitsuggests.

Whileourfocusisontheinteractionofgrammaticalprinciplesandthegradient

representationalstructure,itisimportanttonotethatmanyotherfactorscontributeto

codemixing.Inparticular,sociolinguisticfactorsplayanimportantroleinlanguagechoice

andbilingualidentity(foranoverview,seeGardner-Chloros,2009).Whiletheseare

outsidethescopeofthiscurrentwork,theydefineanimportantavenueforfuture

developmentofourapproach.

BlendRepresentationsinContextswithoutCodeMixing

Blendrepresentations

Manypsycholinguistictheoriesareframedwithinaspreading-activationor

connectionistperspective(Rumelhart,Hinton,&McClelland,1986;seeGoldrick,2012,fora

recentreview).Insuchtheories,mentalrepresentationsaregraded,distributedpatternsof

activation,anumericalquantityassociatedwithsimpleprocessingunits.Thisallowsfor

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blends:representationalstatesinwhichmultiplerepresentationalelementsoccupy(to

varyingdegrees)asinglepositionwithinalinguisticstructure.

Forexample,supposeanativeSpanishspeakerisproducingasentenceinEnglish:

“YesterdayIwenttotheparktowalkmydog.”Whileplanningthisutterance—in

particular,whileretrievingtheappropriatefinalnounfrommemory—many

psycholinguistictheoriesofbilingualismassumethatthespeaker’sproductionsystem

entersthestateshowninFigure1(see,e.g.,Kroll&Gollan,2014,forareviewofsuch

proposals).Inthisnetwork,therearethreetypesofrepresentationalunits.Theinputtothe

systemconsistsofsemanticfeaturesalongwitharepresentationoftheintendedlanguage

ofresponse.Activationspreadsfromtheseunitstoasetofunitscorrespondingtolexical

items(e.g.,‘lemmas’).Figure1Ashowstheflowofactivationthroughtheconnectionist

network;Figure1Bprovidesanalternativeviewofthedistributionofactivationoverthe

lexicalitems.

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Figure1.A.DepictionofpsycholinguisticprocessingmodelduringproductionofDOG.

Thicknessofcircledenotesrelativeactivationofunit.B.Alternativedepictionofthestate

ofthissystem,focusingongradientactivationatthelexicallevel.

Insucharepresentation,theintentiontoproduceasinglelexicalitem(asinglenoun

inthephrase‘my___’)resultsinthesimultaneousco-activationofmultiplemental

representations.Lexicalselectionprocessessimultaneouslyconsiderthetarget(DOG),

semanticallyrelatedwordswithinthesamelanguage(CAT),andnon-targetlanguage

words(PERRO).ThiscanbeseeninFigure1A+B,wheremultiplerepresentational

elementshavevaryingnon-zeroactivation.Thestateofprocessingasinglewordisthusa

blendofmultiplelinguisticrepresentations.Thisrepresentationalhypothesisisoften

referredtoasco-activationorparallelactivation.Weusethetermblendtoemphasizethat

themultipleelementsarenotsimplysimultaneouslyactivated;theyareco-presentwithin

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<furry> <pet> <canine> [ENG]

MESA GATO PERRO DOG CAT TABLE

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Det 0.90 MY 0.10 MI

N 0.90 DOG 0.50 CAT 0.30 PERRO 0.25 GATO 0.10 TABLE 0.05 MESA

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asinglepositioninthelinguisticrepresentation(e.g.,headofaparticularnounphrase;this

ishighlightedinthedepictioninFigure1B).

Empiricalevidenceforblendrepresentations

Activationbasedrepresentationsdonotrequireblends(onecouldassign0toall

non-targetrepresentationsinFigure1,activatingonlyDOG).Itisalsonotimmediately

clearwhatfunctionalmotivationwouldrequireblendstates.InapurelyEnglishutterance,

whyshouldoneconsiderSpanishwords?Thismakesitallthemorestrikingthata

substantialbodyofevidencesupportssuchblendrepresentations.KrollandGollan(2014)

provideanextensivereviewofevidencefrommultilingualspeakers(seeMelinger,

Branigan,&Pickering,2014,forareviewofevidencefrommonolinguals).Here,we

emphasizeafewkeyrecentstudiesthatprovideevidenceofsuchrepresentationsduring

productionofphrasesandsentences.

Akeypredictionofblendrepresentationsisthatthespreadofactivationwillleadto

thepartialactivationofnon-targetrepresentationsatotherlevelsofprocessing.Following

theexampleabove,whenproducingtargetDOG,thepartialactivationofthelexical

representationPERROispredictedtoleadtopartialactivationofrepresentationsofthe

/p/sound.Incontrast,whenproducingCAT,thePERROrepresentationshouldbeless

active,resultinginlessactivationofthe/p/sound.Consistentwiththisprediction,many

studieshavedemonstratedthatproductionisfacilitatedwhenthereisaphonological

relationshipbetweenthetargetutteranceandnon-targettranslationequivalents.

Spalek,Hoshino,Wu,Damian,andThierry(2014)examinedGerman-English

bilingualsproducingadjective-nounphrases.Forbothbehavioralandelectrophysiological

measures,theyfoundthatsecond-languageEnglishproductionwasfacilitatedwhenthe

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Englishadjectivesharedphonologicalstructurewiththenoun’sGermantranslation

equivalent(e.g.,“blueflower:”bluesharestheinitialsoundsoftheGermantranslation

equivalentBlume;contrastwith“greenskirt:”greensharesnosoundswiththeGerman

translationequivalentRock).Whilesignificant,effectsofnon-dominantL2Englishon

productionofdominantL1Germanphrasesweresmaller,limitedtoelectrophysiological

measures.Theseresultsareconsistentwiththepresenceofblendrepresentations,but

suggestthatthedegreetowhichnon-targetrepresentationsarepresentinblendsis

modulatedbytherelativestrengthofeachlanguage(suchthatBlumeismoreactiveduring

processingofflowerthanviceversa).

Anothersetofstudiesarguingforco-activationofmultiplerepresentationshas

comparedtheproductionoftargetsthatsharephonologicalstructurewiththeirtranslation

equivalent(e.g.,EnglishANCHOR—DutchANKER)tothosewithnooverlap(e.g.,BOTTLE

—FLES).Theformerareoftenreferredtoas‘cognates’inthepsycholinguisticliterature;

however,nohistoricalconnectionbetweenthetranslationequivalentsisrequired.The

logicisthatsimultaneousactivationoflexicalrepresentationsinthetwolanguagesshould

facilitateprocessingofanysharedphonologicalstructure,producingacognatefacilitation

effect(Costa,Caramazza,&Sebastián-Gallés,2000).Forexample,simultaneouslyactivating

ANCHORandANKERwillservetofacilitateretrieval/planningofsharedsegments/ŋ/,/k/,

/ə˞/.Starreveld,DeGroot,Rossmark,andVanHell(2014)recentlydocumentedcognate

facilitationduringsentenceplanning.Dutch-Englishbilingualsreadaloudsentenceswith

anembeddedpicture(e.g.,apictureofaanchorappearedinthepositionoftheblankinthe

sentence“Inthemiddleofthesquarewasan____withathickchainattachedtoit.”).When

producingpicturenamesinL2English,participantsshowedcognatefacilitation.Following

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thestudyreviewedabove(Spaleketal.,2014)aswellasmanyotherresults,theseeffects

weremuchstrongerinL2thanL1production.Furthermore,cognateeffectswere

modulatedbythesentencecontext.Whenthesentenceplacedgreaterconstraintsonthe

wordthatcouldfitinthespaceoccupiedbythepicture(e.g.,“Popeyethesailormanhasa

tattooofan____onhisarm.”),cognateeffectswerediminished.Aswiththepreceding

study,theseresultssuggestthatwhileblendsarepartoflanguageproduction,thedegree

towhichnon-targetrepresentationsarepresentismodulatednotonlybytherelative

strengthofeachlanguage,butalsobythedegreetowhichcontextsupportstheretrievalof

aspecifictargetword.

Finally,someofthestrongestevidenceforblendrepresentationshascomefrom

studiesthathavedocumentedtheliteralco-productionofmultiplerepresentations.The

simultaneousco-presenceofmultiplelinguisticrepresentationsduringplanningleadsto

thesimultaneousproductionofactionsassociatedwiththeserepresentations.Pyersand

Emmorey(2008)examinedtheoralandmanualproductionsofbimodalbilinguals:native

speakersofaspokenlanguage(English)andamanuallanguage(AmericanSignLanguage;

ASL).Duringconversationswithnon-signers—wherethebimodalbilingualsintendto

speakasingle(oral)language—theysimultaneouslyproducedASLandEnglish

grammaticalmarkers.Atratesmuchhigherthannon-signers(butlowerthanintheirASL

productions),thebimodalbilingualsfurrowedtheirbrowswhileproducingwh-questions

(e.g.,“Howmanysiblingsdoesshehave?”).Thisoccurredinspiteofthefactthatspoken

Englishexplicitlymarkswh-questions(makingdouble-markingunnecessarytoexpressthe

intendedmessage).NotethatthisgestureispragmaticallydispreferredinspokenEnglish,

whereitconveysnegativeaffect.PyersandEmmoreyarguedthatthismodulatedtherate

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ofco-productions,asco-productionsweremuchhigherforconditionals(e.g.,“Ifitrains,

classwillbecanceled;”associatedwithraisedbrows).Thisprovidesfurtherevidencefor

constraintsonthedegreeofactivationofnon-targetrepresentationsinblends.

Inthebimodalbilingualcase,thetwolanguagesarenotcompetingforexpression

onthesamecommunicationchannel.Moresubtleco-productionscanbefoundduring

productionoftwoorallanguages.Whileco-activationenhancesretrievalofshared

phonologicalstructure,theheightenedactivationofnon-targetlanguagerepresentations

shouldincreasecross-languagephoneticinterference—theintrusionofnon-target

languagephoneticpropertiesintobilingualproductions.Forexample,whileSpanishand

Englishshareacommonsetofvoicingcontrastsininitialstops(e.g.,/b/vs./p/),the

phoneticrealizationofthiscontrastisdistinctineachlanguage(pre-voicedvs.short-lag

voiceonsettimeinSpanish;shortvs.long-laginEnglish).Thisconflictleadsnon-native

speakerstoproducethesesoundswithphoneticpropertiesintermediatebetweenthetwo

languages(Flege,1991).Amengual(2012)showedthatthiscross-languagephonetic

interferenceisenhancedforcognates.Whenreadingsentencesaloud,Spanish-English

bilingualsproducedinitialstopsinSpanishwithmoreEnglish-likepropertiesincognates

vs.non-cognates.NosuchdifferencewasfoundintheproductionsofSpanish-Catalan

bilinguals(wherethetwolanguageshavesimilarphoneticrealizationsofthiscontrast).

Otherresultssuggestthatthesecognateeffectsarenotsimplyword-specificphonetic

patternsinbilingualspeech,butratherreflectdynamicpropertiesofbilingualproduction.

Olson(2013)andGoldrick,Runnqvist,andCosta(2014)foundthatphoneticinterference

wasincreasedwhenparticipantswererequiredtounexpectedlycode-switchduring

picturenaming(vs.trialswhereparticipantsdidnotswitchlanguages).Forvoicelessstops,

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Goldricketal.foundthatthiscontext-specificphoneticinterferenceeffectisenhanced

duringproductionofsinglecognatevs.non-cognatewords—suggestingthatthecognate

effectreflectsthecontext-specificactivationoftargetandnon-targetlanguage

representations.

Summary:Blendrepresentationsinbilingualproduction

Evenwhenintendingtoproduceasingleforminasinglelanguage,bilinguals

simultaneouslyactivateformsinbothlanguages.Thedegreeofco-presenceinsuchblend

representations,andourabilitytoobservetheeffectsofthisco-presence,isclearly

constrained.Tosomedegreethislikelyreflectsphysicalconstraints.Itisimpossibleto

placeasinglesetoforalarticulatorsintwocontradictorypositions.Inthesecases,the

productionsystemislimitedtoblendedarticulations,reflectingapartialcompromise

betweencontradictoryactions.However,manyoftheotherconstraintsonblendsclearly

reflectabstract,cognitiveprinciples.Evenwhenfreedfromphysicalconstraintsonco-

production,thepropertiesofbimodalbilinguals’blendsaremodulatedby

affective/pragmaticconstraints.Thepropertiesofunimodalbilinguals’blendsreflectthe

relativestrengthofthetwolanguagesandthecontextinwhichatargetwordisbeing

produced.

BlendRepresentationsinCodeMixing

Integrationofgrammaticalprinciplesincodemixing

Giventheevidenceforco-activationofthetwolanguagesincontextswhere

speakersintendtoproduceonlyonelanguage,itisunsurprisingthatco-activationisa

fundamentalpropertyofcodemixing.Critically,speakersarenotonlyutteringlexicalitems

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frombothlanguagesbutarealsointegratinggrammaticalprinciplesfromeachlinguistic

system.

Theintegrationcanbeseenincross-linguisticsyntacticpriming,whereexposureto

astructureinonelanguageincreasestheprobabilitythatspeakerswilluseasimilar

structureinanotherlanguage(seePickering&Ferreira,2008,forareview).Forexample,

Hartsuiker,Pickering,andVeltkamp(2004)foundthatwhenSpanish-Englishbilinguals

heardapassiveconstructioninSpanish,itincreasedthelikelihoodthattheywould

produceapassivevs.activeconstructioninEnglishonasubsequenttrial.Suchpriming

doesnotonlyaltertheprobabilityofattestedstructures.Incertaincontexts,itcanallow

forthetransferofgrammaticalpatternsfromonelanguagetoanother,reflectingthe

integrationofknowledgeofeachlanguage.Forexample,inmanycontextsSpanishdoesnot

allowforthewordorderadjective-noun,thetypicalwordorderpatternobservedin

English.Hsin,Legendre,andOmaki(2013)foundthatinSpanish-Englishbilingualchildren

primingcouldallowfortransferofthiswordorderfromEnglishtoSpanish.

Suchintegrationalsooccursinthecontextofintra-sententialcodemixing.For

example,Kootstra,vanHell,andDijkstra(2010)elicitedcodemixedutterancesfrom

Dutch-Englishbilinguals.ParticipantsdescribedpicturesbycompletingaDutchsentence

fragmentthatbiasedspeakerstoproduceoneofseveralwordorderspossibleinDutch

(Subject-Verb-Object[SVO],SOV,orVSO).Whencuedtoproduceamixedstructure(i.e.,

usingatleastoneEnglishwordtocompletetheDutchfragment),participantspreferredto

usethewordordercommontobothgrammars(SVO).Asimilarpreferenceforcongruent

grammaticalpatternshasbeenfoundinspontaneousmixingcorpora(forreviewsand

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discussion,seeDeuchar,2005;Muysken,1995;Myers-Scotton&Jake,1995;Poplack,

1980).

Blendsandco-productionincodemixing

Whenspeakersintendtomixlexicalitemsandgrammaticalprinciplesfromtwo

languages,wealsoobserveblends.Someofthemostdramaticexamplescomefrom

bimodalbilingualcodemixing.ForASL-Englishbilingualsthepredominanttypeofcode

mixingiscodeblending:co-productionoforalandmanualelements(Bishop,2010;

Emmorey,Borinstein,Thompson,&Gollan,2008).Thesecross-modalproductionsare

typicallysemanticallyequivalentandsynchronizedintime.Inexamples(1)and(2),the

Englishglossofthesignproductionisshowninitalicsbeneaththepointinthesentence

wherethesignroughlyoccurred;underliningindicatesthespeechthatco-occurredwith

thatsign.

(1) Andthere’sthebird.(Emmoreyetal.,2008:48)bird

(2) NowIrecentlywentback.(Emmoreyetal.,2008:48)nowIrecentlygo-to

Inunimodalbilingualsthereissubtleevidenceofco-activationinarticulation.

Analyzingaspontaneouscodemixingcorpus,BalukasandKoops(inpress)foundthat

phoneticinterferenceeffectsinSpanish-Englishbilingualsincreaseatpointsclosertocode

switches.Thissuggeststhatco-productionsarenotuniquetobimodalbilinguals.

Blendswithoutco-production:Doublingconstructions

Blendingrepresentationsfromtwodifferentlanguagescanalsoyieldnon-

simultaneousarticulations.Languagesdifferinwordorder,mappingelementstodifferent

positionsinthesurfacestring.Thisraisesthepossibilitythatthegrammaticalprinciples

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fromeachlanguage—bothactiveduringcodemixing—couldbothbesatisfiedwithout

yieldingsimultaneousarticulation.Forexample,abilingual’sL1hasthewordorderverb-

objectandL2object-verb.Thestringverb(L1)-object-verb(L2)satisfiesthewordorder

constraintsofbothlanguages;theL1verbprecedestheobject,whiletheL2verbfollows

theobject.Althoughsuchstringsmightviolatestructuralconstraintsonlinguistic

representations,theywouldnotsufferfromarticulatoryincompatibility1.

Patternsofattesteddoublingconstructions:Areview

Althoughsuchconstructionsarecommonlydiscussed,onlyafewdetailed

referencesaredevotedexclusivelytothem(Chan,2009;Hicks,2010,2012;Muysken,

2000:104-6).Theymanifestinavarietyofconstituents,althoughpreferenceseemstobe

giventothedoublingoffunctionalelements(syntacticelementsexpressinggrammatical

relationships;e.g.,complementizers,determiners,prepositions,andauxiliaryverbs)over

lexicalitem(e.g.,nouns).Thefollowingexamples2provideanoverviewoftherangeof

doubledstructures.Thedoubledelementsareunderlinedineachexample.

(3) Complementizers:English-Japanese(Azuma1993:199)ifitgoesthreeroundsdattaraneifitgoesthreeroundswasifTAG‘Ifitgoesthreerounds.’

Notethatin(3),ifislocatedinitscanonicalplaceinEnglish(appearingatthestart

ofthedependentclause),andtheJapaneserainitsexpectedlocation(weretheutterance

fullyJapanese,rawouldappearattheendofthedependentclause).Examples(4)-(7)

illustratesimilardoublingforvariousotherelements,respectingthecontrastingword

orders.

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(4) Adpositions:English-Finnish(Poplack,Wheeler,&Westwood,1989:405)muttaseolikidney-statoaorta-anbutitwaskidney-fromtoaorta-to‘Butitwasfromthekidneytotheaorta.’

(5) Adverbials:English-Tamil(Sankoff,Poplack,&Vannianiarajan,1990:92)

AccordingtotheschedulepaDioNNutaanirukkaNum. accordingtooneonlybemust‘Accordingtotheschedule,theremustbeonlyone.’

(6) Coordinating:conjunctionsSpanish-Aymara(Stolz,1996:146,citingPorterie-

Guierrez,1988:355)perosorro-stiwaliastuturi-tajna...butfox-COOverykeen-3.SG.PRT.EVI‘Butthefoxwasverykeen.’

(7) VerbsEnglish-Tamil(Sankoffetal.,1990:93)

theygavemearesearchgrantkoɖutaatheygavemearesearchgrantgave.3.PL.PAST‘Theygavemearesearchgrant.’

Multi-wordchunkscanbedoubled,asshownin(8)(verb+adverb)and(9)(verb+

complementizer).

(8) Verb+AdverbEnglish-Japanese(Nishimura,1986:139)WeboughtabouttwopoundsguraikattekitanoWeboughtabouttwopoundsaboutboughtTAG‘Weboughtabouttwopounds.’

(9) Verb+ComplementizerEnglish-Korean(Chan,2008:800)

everybodythinkthatnay-kayenge-lulcalhanta-kosayngkakhayyoeverybodythinkCI-NOMEnglish-ACCwelldo-Cthink‘EverybodythinksthatI’magoodEnglishspeaker.’

Whilethesetypesofcodemixingutteranceshavebeenconsistentlydocumentedin

corpora,theyareclearlymarked;ingeneral,thesestructuresarelargelyavoided.Poplack

etal.(1988:405)reportthattheseblendsare“exceedinglyrare,”citingthattheyonly

found2intheirentirecorpus;Furukawa(2008)found7examplesin5hoursof

sociolinguisticinterviewdata.However,Nishumura(1986)andBackus(1992)suggestthat

theseblendsoccurinroughly3-5%oftheircorpusmaterials.Therarityofsuch

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productionsisunsurprising.Asnotedabove,theintegrationofgrammaticalprinciples

frombothlanguagesyieldsapreferenceforcongruentgrammaticalpatternsincode

mixing.Theexamplesaboveviolatethisprinciple;theyinvolvedoublingofelementsthat

aresubjecttoconflictinggrammaticalpatterns(e.g.,verb-objectvs.object-verbword

order).Furthermore,researchonnon-codemixedproductionssuggeststherearestrong

limitationsonblends;thedegreeofco-presencewithinablendishighlylimited.Ifdoubling

constructionsreflectblendrepresentations,wealsoexpectthemtobestrongly

dispreferred.

Surveyingthereportedinstancesoftheseconstructions,Hicks(2010)identifies

severalcross-linguisticgeneralizations.First,asnotedabove,doubledelementslocally

respectthewordorderofthesourcegrammars.Second,thedoubledelementsaretypically

heads;syntacticelementsthatdefinethesyntacticpropertiesofthephrasetowhichthey

belong.Thedoubledheadsshareanon-doubledcomplement;theothersyntacticelements

thatbelongtothephrase.Forexample,averbphrasecanbecomposedofaverb(thehead)

andanobject(thecomplement).InthedoublingconstructionVL1OL1VL2,doubledverbs

shareanon-doubledobjectcomplement(seealsoFurukawa,2008).Thus,strictlylocal

doubling(e.g.,VL1OL1OL2VL2)istypicallynotobserved.Finally,whilesomelanguages

exhibitdoublinginmonolingualcontexts(discussedfurtherbelow),Hicksnotesthat

doublingofelementsfromthesamelanguage(e.g.,analogousto(7),*gavegrantgave,

*gavegavegrant)arenotobservedduringcodemixing.

Insum,whiledoublingisrare,itisconsistentlyobservedacrossvarioussources;a

varietyofelementsparticipateinintrasententialcodemixingblends.Doublingisnotmere

repetitionofelements;itsoccurrenceisconstrainedbygrammaticalprinciples;doubled

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headssharenon-doubledcomplements;andequivalenceforgrammaticalfeatures.This

suggeststhatdoublingconstructionsarenotan“adhocproductionstrategy”(Sankoffetal.,

1990:92),butarerathercoherent,syntacticobjectsthataregovernedbygrammatical

principles.

BlendsinGrammaticalTheories:ApplicationtoDoubling

Blendrepresentationsclearlyplayaroleinbilinguallanguageprocessing.In

doublingconstructions,weseethattheseblendrepresentationsinteractwithgrammatical

principles.Howcanthisbeformallyspecified?Inthissection,wedevelopagrammatical

approachtocodemixingthatincorporatesblendedrepresentations.Weapplythisto

doublingconstructions,showinghowitaccountsfortheoccurrenceofdoublingaswellas

theempiricallyattestedconstraintsonthisphenomenon.

Overviewoftheproposal

Ouraccountisbasedaround3generalprinciples.Wefirstprovideanoverviewof

theseandthenexamineinsomedetailofhowtheycanappliedtotheempiricalpatternsof

doublingconstructions.

Principle1:Probabilisticgrammarswithweightedconstraints

Languageuse—inmono-ormulti-linguals—isdefinedinpartbyregularstructural

patterns(e.g.,EnglishrequiresSVO,whileDutchallowsflexibilitybetweenSVO,SOV,and

VSO).Grammarsallowustopreciselyspecifythestructureofthemappingbetweenform

andmeaningthatyieldsthesepatterns.Theformalismweusespecifiesgrammarsthrough

interactionofconstraintsonlinguisticstructure.Forexample,aconstraintonwordorder

mightpreferthatcertainlexicalcategoriesappearattheleftedgeofasyntacticphrase.

Constraintsareassociatedwithnumericalweightsthatdeterminetheirrelative

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importance;cross-linguisticvariation(e.g.,ifalanguagecategoricallyprefersSVOvs.SOV)

isspecifiedbychangesintherelativeweightingofconstraints.Ourgrammaticalformalism

alsoallowsustospecifynotjustcategoricalpreferences,butalsorelativeprobabilitiesof

differentstructures;thisallowsustocapturevariationinthemappingbetweenmeaning

andformwithinaspeaker(e.g.,variablewordorderinginaDutchspeaker’sproductions,

orvariablestructuresobservedincodeswitching).

Principle2:Gradientblendsofgrammars

Bilingualsspeakershavevaryingdegreesofcompetenceinmultiplegrammars,

allowingthemtoproducedistinctstructuresineachlanguage.Inourformalism,thisis

reflectedbyassociatingeachlanguagewithadistinctweightingofconstraints.These

language-specificweightingscontributetothegrammar,independentlyinfluencingthe

probabilityofdifferentstructures.However,asdiscussedabove,thetwolinguisticsystems

ofbilingualsinteract.Wemodelthisbyalsoincorporatingintothegrammaraweightingof

constraintsthatblendsthelanguage-specificweightings.Thedegreetowhicheach

languagecontributestothisblendreflectstherelativeactivationofthatlinguisticsystem.

Principle3:Gradientblendsinlinguisticrepresentations

Buildingontheconnectionistformalismsthatserveasthefoundationofmany

psycholinguistictheories,weassumethatthereissimultaneouscoactivationof

representationalelementsinboththeinputandoutputofthegrammar.Thisallowsfor

representationsthatblendelementsfrommultiplelanguages.

Inthesectionsbelow,weelaboratethedetailsofthisgrammaticalproposal.Itis

importanttonotethatgrammarsdefinecognitiveprocessesatahighlevelofabstraction—

intermsofmappingbetweeninputsandoutputs.Thisiskeytodevelopingaclearand

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rigorousspecificationofwhatpreciselyacognitiveprocessdoes;whatarethetypesof

structuresthatarepredictedto(probabilistically)emergebyourtheoryoflanguage

structure?Weaimtodevelopsuchaframeworkforunderstandingthestructureofcode

mixing.However,itisimportanttonotethatunderstandingthecognitiveandultimately

neuralprocessesthatcomputetheseinput-outputmappingsiskeytodevelopinga

completetheoryoflanguageprocessing(fordiscussion,seeGoldrick,2011;Smolensky,

2006b).Grammaristhefoundationalcomponentatthebeginningofdevelopingacomplete

theory,butisbynomeansthefinalstep.

Relationshiptootherformalapproachestocodemixing

Generativetheoriesofcodemixing—suchastheonewefurtherdevelophere—can

bedividedintotwotypes.Onesetspecifiesgrammarsspecifictocodemixing.Rulesor

constraintsreferspecificallytocodemixedstructures,explicitlystatingpreferencesfor

distincttypesofcodemixing(Belazi,Rubin,&Toribio,1994;Bhatt,1997;DiSciullo,

Muysken,&Singh,1986;Joshi,1985;Legendre&Schindler,2010;Muysken,2013;Myers-

Scotton,1993;Poplack,1980;a.o.).AclassicexampleisPoplack’s(1980:586)Equivalence

Constraint:“Code-switcheswilltendtooccuratpointsindiscoursewherejuxtapositionof

LlandL2elementsdoesnotviolateasyntacticruleofeitherlanguage.”Here,the

grammaticalprinciplerefersdirectlytocodemixing,distinctfrom(butrelatedto)syntactic

patternsinnon-codemixedcontexts.Similarly,fromanOptimality-Theoreticperspective,

Muysken(2013:715)makesuseofconstraintssuchas“*CSL=Don’tswitchbetween

separatelanguages,eitherintheirlexiconorintheirgrammar.”

Analternativeapproachassumesthegrammaticalprinciplesoftwolanguagesare

integratedduringcodemixing,andthatthisintegrationyieldsthepatterns(Chan,2003,

20

2008,2009;Lohndal,2013;MacSwan,1999,2000;Mahootian,1993;Woolford,1983;a.o.).

SinceMahootian(1993),thispositioniscommonlyreferredtoasthe“nulltheory”ofcode

mixing,accordingtowhichmonolingualandbilingualgrammarsshouldbesubjectto

identicalrepresentational/grammaticalconstraintsandpsychologicalprinciples.

Ourapproachincorporateselementsofbothperspectives.Followingthenulltheory

perspective,weassumethatthefeaturesofcodemixingreflectgeneralprinciplesof

syntacticknowledgeandsentenceprocessing.Blendrepresentationsareageneralfeature

ofgrammaticalknowledgeandprocessing;theemergenceofdoublingconstructionsin

bilingualsisaconsequenceoftheprinciplesunderlyingthesegrammars.However,in

contrasttothestrongestversionofthenulltheory(e.g.,MacSwan,1999),weassumethat

grammaticalprinciplescanrefertolanguagemembership(e.g.,distinguishingthewell-

formednessoflexicalitemsinEnglishvs.Tamilbasednotonsyntacticfeaturesbutonthe

languagefromwhichtheitemoriginates).Thisiscriticaltounderstandingattested

doublingpatterns.Insuchconstructions,thedoubledelementshave(nearly)equivalent

grammaticalfeatures(e.g.,theymatchinagreementfeatures(tense,aspect,case)andshare

argumentstructurerequirements),yetsurfaceinpositionsappropriatetotheelement’s

sourcelanguage.Ifthegrammardoesnotmakereferencetothesourcelanguage,thereis

nomeansofcapturingthisrestriction.

Weightedconstraintinteractioninstochasticgenerativegrammars

OurtheoryutilizestheGradientSymbolicComputationformalism(GSC;Smolensky

etal.,2014).GSCisaconstraint-basedapproachedtogenerativegrammar,buildingon

workinOptimalityTheory(Legendre,2001;Legendre,Putnam,deSwart,&Zaroukian,in

press-a;Prince&Smolensky,1993/2004)andHarmonicGrammar(Legendre,Miyata,&

21

Smolensky,1990,2006;Pater,2009).Likeothergenerativegrammars,GSCdefinesa

functionthatmapsinputstructures(e.g.,logicalforms)tooutputstructures(e.g.,syntactic

structures).InGSC(andHarmonicGrammar),thegrammarisdefinedviaasetofweighted

violableconstraintsthatassignanumericalwell-formednessvalue(harmony)toeachof

thecandidateoutputsforagiveninput.GSCgrammarsarestochastic,generatinga

probabilitydistributionoveroutputforms(reflectingtherelativeharmonyofthe

candidates).

Tobuildupourtheory,webeginbymodelingmonolingualgrammars.Considera

simpleinputconsistingofasubjectandverb;asshowninFigure2,thiscanbelinearized

usingatleasttwosurfacesyntacticstructures.

Figure2.Twoalternativesurfacesyntacticstructurescorrespondingtotheinputgoes

(John).Thetextbeloweachprovidesabracketnotationcorrespondingtothetree,withthe

subscriptoneachopenbracketdenotingthecategoryoftheconstituent.

ThesesurfacesyntacticstructuresreflecttheassumptionsofX-bartheory(see

Carnie2010:Chapter7,forahistoricaloverview).Briefly,X-bartheoryplacesrestrictions

ontraditionalphrasestructuregrammars.Abstractingawayfrommorecomplex

phenomena,basicX-bartheoryassumesthatthebasicstructureofanextendedprojection

consistsoftwosyntacticphrases:XP,consistingofaspecifierandanX'phrase;andX',

!

! VP! ! ! ! !!!!!!!!VP! 3 3 John! !!!!!!!!!V'!! ! ! V'! !!!!!!John!! 3 3 !!!!!!!!!!goes!! !!!!Ø! !!!!!! goes!!!!!!!!!!!!!Ø!! ![VP!John![V'!goes]]! !! [VP![V'!goes]!John]!

!! !

22

consistingoftheheadelementX0andacomplementizer.Asillustratedhere,theextended

projectionoftheverbconsistsofaverbphrase(VP)withspecifierJohn,andaV'phrase

consistingoftheheadgoes(andanullcomplement).Thissimplifiednotationissufficient

forcapturingthebasicfactsaboutsyntacticconstituencyandallowsustospecifythe

patternsinwordordervariationunderlyingthedoublingexamplesweconsider.We

believethattheinsightsofthisanalysiswouldgeneralizetomorerecentrepresentational

frameworks(e.g.,BarePhraseStructure),whichretainedmanyoftheinsightsofthisbasic

system(seee.g.,Chametzky2000).

Tocharacterizethedifferencebetweenlanguagesthatpreferthelinearorder

subject-verbvs.verb-subject,webuildonGrimshaw’s(1997,2001)analysis.Grimshaw

proposedconstraintsonthealignmentofspecifiers,heads,andcomplementstoedgesof

extendedprojectionsinX-bartheory3.Therelativeweightingoftheseconstraintsderives

differentwordorderingpreferences;i.e.determiningwhetheraparticulargrammar

prefersanSVO-vs.anSOV-orderingofarguments.WeadaptthesetodevelopaGSC

analysis,usingconstraintsonstructuralwell-formedness(markednessconstraints).A

subsetoftheseisshownbelow:

(10) HEADLEFT:“EveryX0isleftmostinX-max.”ForeachX0incandidateC,decreaseC’sharmonyby1foreachterminalnodeinterveningbetweentheX0andtheleftedgeofitsXP.

(11) SPECLEFT:“EveryspecifierisleftmostinX-max.”

ForeachspecifierincandidateC,decreaseC’sharmonyby1foreachterminalnodeinterveningbetweenthespecifierandtheleftedgeofitsXP.

Apseudo-Englishweightingofthesetwoconstraintsisshownbelow.Thecolumns

showtheconstraints.Cellsineachcolumnshowtheconstraint’scontributiontothe

harmonyofeachcandidate(scaledbytheweightoftheconstraint).Here,sinceSPECLEFT

23

hasastrongerweightingthanHEADLEFT,thesubject-verbcandidatehasahigherharmony

value.Thefinalcolumngivestheprobabilityofeachcandidate.AsinMaximumEntropy

grammars(Goldwater&Johnson,2003;Hayes&Wilson,2008),theprobabilityisan

exponentialfunctionofitsharmonyrelativetotheothercandidates4.Inthisexample,the

harmonyofthesubject-verborderissomuchhigherthanverb-subjectthatitsprobability

isextremelycloseto1.0.Whilethesecondcandidatetechnicallyhasnon-zeroprobability,

itisextremelysmall;lessthan1x10–8.Thus,thegrammarisessentiallycategorical.

Table1.GrammarfragmentforEnglishwordorderInput:goes(John) SPECLEFT HEADLEFT

–20 –1 Harmony Probability[VPJohn[V'goes]] –1 –1 ≈1.0[VP[V'goes]John] –20 –20 ≈0

Iftherankingoftheconstraintsshifts,theprobabilityofdifferentcandidateswill

alsoshift.Thiscanspecifycross-linguisticvariation;considerthegrammarfragmentin

Table2.Here,HEADLEFThasamuchstrongerweightingthanSPECLEFT.Thisyieldsa

languagewithpost-verbalsubjects.

Table2.Grammarfragmentforverb-subjectwordorder

Input:goes(John) SPECLEFT HEADLEFT

–1 –20 Harmony Probability[VPJohn[V'goes]] –20 –20 ≈0[VP[V'goes]John] –1 –1 ≈1.0

Intheabovecases,thedifferencesinharmonyarequitelarge.However,as

differencesinharmonyofcandidatesgrowsmaller,variationcanresult:

24

Table3.Grammarfragmentforvariablewordorder

Input:goes(John) SPECLEFT HEADLEFT –12 –10 Harmony Probability

[VPJohn[V'goes]] –10 –10 ≈0.88[VP[V'goes]John] –12 –12 ≈0.12

Intheseexamplefragments,theweightingofconstraintshasbeenarbitrarily

decided.Ourassumptionisthatsuchweightingsareacquiredbylearnersbasedonthe

probabilitydistributionofformsintheirlinguisticexperience(Goldwater&Johnson,2003;

Hayes&Wilson,2008).Forexample,anEnglishlearnerwouldacquiremanyexamples

withthewordordersubject-verb;allelsebeingequal,thiswouldleadhertofavor

constraintweightingssimilartoTable1overthoseinTable2orTable3.Asthisdiscussion

isfocusedonexploringthebasicprinciplesofthetheory,wedonotundertakeadetailed

studyofthisacquisitionprocess.Theconclusionswedrawbelowwillnotbedependenton

theparticularweightvaluesusedtoillustrateouranalysis.

Toprovideconcreteweightvaluesforthepurposeofillustration,weutilized

GoldwaterandJohnson’s(2003)learningalgorithm(asimplementedintheMaxEnt

GrammarTool;Hayes,2009;weightswereroundedtoyieldintegervaluesforeaseof

exposition).Aweakuniformpriorwasusedforeachconstraint(µ=0; σ=107).Theprior

influenceshowconstraintweightsareupdatedduringlearning.Thispriorspecifiesatarget

valueforeachconstraintweight(here,zero,sothatconstraintweightsareassmallas

possible),alongwithapenaltyfordeviatingfromthattargetvalue(here,theveryhigh

varianceimpliesanextremelysmallpenalty).Thisreducesourexamplestoasinglefree

arbitraryparameter:thevarianceontheprior.Usingthistrainingalgorithm,this

25

parameter(combinedwiththetrainingdataexemplifyingagivenwordorder)completely

determinestheconstraintweightsbelow.

Head-complementwordordervariation

Forillustrationpurposes,thegrammarfragmentsabovearequitesimple,

consideringonly2possiblecandidateoutputsand2constraints.Inthissection,we

considerasomewhatmoreextendedexample,includingtwoadditionalconstraintsandan

explicitlydefinedspaceofpossibleoutputstructures.Thisallowsustospecifymonolingual

grammarsthatcontrastinwordorder—specifically,subject-verb-objectvs.subject-object-

verb(againbuildingonGrimshaw,1997,2001).

Modelingconstructionsincludingcomplementsrequiresanadditionalmarkedness

constraint,paralleltothoseproposedabove:

(12) COMPLEFT:“EverycomplementisleftmostinX-max.”ForeachcomplementincandidateC,decreaseC’sharmonyby1foreachterminalnodeinterveningbetweenthecomplementandtheleftedgeofitsXP.

Extendingthesetofcandidates,weconsidernotonlythosethatvaryinwordorder

butalsothosethatomitelementsoflexicalconceptualstructure.Theseavoidviolationsof

theconstraintsabovebysimplyleavingoutelements(acandidatewithnocomplements

cannotviolateCOMPLEFT).Toinsurethatsuchcandidatesaredispreferred,weusea

faithfulnessconstraintthatassignswell-formednessbasedontherelationshipbetween

syntacticandsemanticstructure(afterLegendre,Wilson,Smolensky,Homer,&Raymond,

1995):

(13) PARSE:“Lexicalconceptualstructureisparsed.”DecreasecandidateC’sharmonyby1foreachelementoflexicalconceptualstructurethatdoesnothaveacorrespondingelementinC’ssurfacesyntacticstructure.

26

Forthisdiscussion,weassumecandidateoutputsarelimitedtothoseincludingX-

bartreesthatparseallelementsoflexicalconceptualstructureoranypossiblesubsetof

elements.Wefurtherassumethatelementsoflexicalconceptualstructureareparsedinto

theappropriatesyntacticpositions(e.g.,subjectisparsedintoSpec).Foraninputwitha

verb,subject,andobject,thisyieldsthecandidatesetshowninTable4.Constraintweights

weredeterminedbytrainingondatareflectingthecontext-neutralEnglishwordorderfor

thisparticularinput:100%subject-verb-object(e.g.,“Theygaveagrant”;Berk,1999).Note

thatanEnglishlanguagelearnermighthavesomewhatdifferentweightingsforthese

constraints,asshewouldbeexposedtodifferentinputs(e.g.,inputswithnoobject

complement)andwouldhaveamuchlargersetofconstraints.

Table4.Grammarfragment:Englishsubject-verb-objectwordorder.Blankcellsindicatethecandidatedoesnotviolatetheconstraint.NotethatsinceCOMPLEFThasaweightingof0,violations of the constraint do not decrease harmony. Probabilities are rounded; those lessthan1x10-4arerepresentedas0.Input:gave(they,grant)

SPECLEFT HEADLEFT COMPLEFT PARSE

–13 –12 0 –25 H Pr[VPthey[V'gavegrant]] –12 0 –12 1[VPthey[V'grantgave]] –24 0 –24 0[VP[V'gavegrant]they] –26 0 –26 0[VP[V'grantgave]they] –26 –12 –38 0[VPthey[V'gave]] –12 –25 –37 0[VP[V'gave]they] –13 –25 –38 0[VPthey[V'grant]] 0 –25 –25 0[VP[V'grant]they] –13 –25 –38 0[V'grantgave] –12 –25 –37 0[V'gavegrant] 0 –25 –25 0[VPthey] –50 –50 0[V'gave] –50 –50 0[V’grant] –50 –50 0ø –75 –75 0

27

Thistrainingprocedureyieldsastrongweightingtoourfaithfulnessconstraint.

Althoughdeletingelementsoflexicalconceptualstructureallowsmanycandidateoutputs

inTable4toavoidviolationsofthemarkednessconstraints,theyincurone,two,orthree

penaltiesfromthefaithfulnessconstraint,substantiallyloweringtheirharmony.The

relativerankingofthemarkednessconstraintsdetermineswhichofthefirstfourfully

faithfulcandidatesareselected.Thesecondmost-highlyweightedconstraintprefers

specifiersoccurtotheleftoftheV'projection,rulingoutthethirdandfourthcandidates.

Thethirdconstraint,preferringthatheadsbeleftmost,thenrulesoutthesecond,yielding

thesubject-verb-objectwordorder.

LanguageslikeTamilexhibitacontrastingcontext-neutralwordorderpattern,

subject-object-verb(Sarma,1999;Schiffman,1999).Trainingonthesedataforthesame

inputyieldsacontrastingweighting:

28

Table5.Grammarfragment:Tamilsubject–object-verbwordorder.Blankcellsindicatethecandidatedoesnotviolatetheconstraint.NotethatsinceHEADLEFThasaweightingof0,violations of the constraint do not decrease harmony. Probabilities are rounded; those lessthan1x10-4arerepresentedas0.

Input:gave(they,grant)

SPECLEFT HEADLEFT COMPLEFT PARSE

–13 0 –12 –25 H Pr[VPthey[V'gavegrant]] 0 –24 –24 0[VPthey[V'grantgave]] 0 –12 –12 1[VP[V'gavegrant]they] –26 –12 –38 0[VP[V'grantgave]they] –26 –26 0[VPthey[V'gave]] 0 –25 –25 0[VP[V'gave]they] –13 –25 –38 0[VPthey[V'grant]] –12 –25 –37 0[VP[V'grant]they] –13 –25 –38 0[V'grantgave] 0 –25 –25 0[V'gavegrant] –12 –25 –37 0[VPthey] –50 –50 0[V'gave] –50 –50 0[V'grant] –50 –50 0ø –75 –75 0

ThesolechangetotheweightingistherelativestrengthofHEADLEFTandCOMPLEFT.

Nowthatthelatterhasahigherweighting,thereisareversaloftherelativeharmonyofthe

firsttwocandidates;objectcomplements,notverbalheads,areleftmostinV'.Thisyields

theappropriatesubject-object-verbwordorder.

Codemixinginconstraint-basedgrammars

Havingdemonstratedthatourformalismcanrepresentcross-linguisticdifferences

inwordorder,weconsiderthegrammarsutilizedbybilinguals(e.g.,anEnglish-Tamil

bilingual).Asreviewedabove,inintra-sententialcodemixingbilingualsintegrate

grammaticalprinciplesfromeachlinguisticsystem.InGSC,grammarsaredefinedbythe

weightingofconstraints.Wethereforeformalizethisintegrationbyhavingtheweightsof

constraintsinthegrammarunderlyingcodemixingreflectbothlinguisticsystems.

29

Weproposetoassociateeachlinguisticsystempresentinacodemixedutterance

(L1,L2)withanactivationvalue(αL1,αL2;thesumofthesevaluesmustbe1).Thisscales

theamounteachlinguisticsystemcontributestothemodulationofeachconstraint’s

violations.Specifically,violationsofeachconstraintCarescaledbythesumoftheC’s

rankingineachlinguisticsystem,weightedbytheactivationofthatsystem.Thisallowsfor

interactionsbetweenthetwolinguisticsystems(aseachcontributestoharmonyforevery

element).Thisscalingvalueisadditionallyincreasedbytheactivationofalinguisticsystem

iftheconstraintreferstoanelementinthatsystem.Thislatterfactorencodesa(violable)

preferenceforlinguisticelementstoobeythepropertiesofthesourcelanguage.

Forexample,supposeHEADLEFThasweighting–10inL1and–5inL2;theactivation

ofL1is0.75andL20.25.AnL1headthathas1positioninterveningbetweenitandthe

edgeofXPwillincuraharmonypenaltyof1*[–10*(0.75+0.75)+1*–5*(0.25)]=–16.25.

AnL2headthathas1positioninterveningbetweenitandtheedgeofXPwillincura

harmonypenaltyof1*[–10*(0.75)+1*–5*(0.25+.25)]=–10.0.TheL1headincursa

slightlygreaterpenaltybecauseofthestrongerweightingofthisconstraintwithinthe

sourcegrammar.

Blendsingrammaticalrepresentations

WeightedconstraintsarenotanovelclaimofGSC;theseoverlapwithexisting

formalismsincludingHarmonicGrammarandMaximumEntropymodels.Anovelfeature

ofGSCistheincorporationofblends.Specifically,GSCproposesthatelementsofsymbolic

grammaticalrepresentationsareassociatedwithactivationvalues.Thisincludesall

elementsofsyntacticrepresentations:thenodesofthetree(bothterminalandnon-

terminalelements)aswellasthelinksbetweennodes.Thisallowsforthespecificationof

30

blends;multiplerepresentationalelementsthatwouldoccupyasinglepositionorroleina

discretesymbolicrepresentationcanbeco-present,tovaryingdegrees.Inpreviouswork,

wehaveexaminedtherolethatblendsplayinmonolinguallanguageprocessing.For

example,inphonologicalspeecherrors(mispronouncingbataspat),thereisevidencethat

targetanderrorsoundrepresentationsareco-activated(theonsetoftheerrorsyllablepat

isablendsimultaneouslycontainingelementsofboth/b/and/p/;Goldrick&Chu,2014;

Smolenskyetal.,2014).Here,weextendthisverygeneralrepresentationalprincipletothe

domainofbilingualism,focusingonblendsinvolvingelementsfromtwodistinctsource

languages.

Forourinitialdiscussion,wefocusoncaseswheremultipleelementsareco-present

tothesamedegree;thissufficestoillustratethegeneralanalysis.Weillustratethiswith

example(7),repeatedbelowforconvenience.

(14) Doubling:VerbsEnglish-Tamil(Sankoffetal.,1990:93)theygavemearesearchgrantkoɖutaatheygavemearesearchgrantgave.3.PL.PAST‘Theygavemearesearchgrant.’

Weanalyzetheinputtothegrammarincodemixingcontextsasconsistingofblends

ofsemanticelements.Fortheexampleabove,weanalyzetheinputastheco-presenceof

twoverbalelements—drawnfromtwodistinctlanguages—whichsharemultiple

arguments(shownin(15)below).Thisrepresentationinstantiatesacoreclaimofthe

blendanalysisofdoublingconstructions:thesimultaneouspresence,intheinputtothe

grammar,ofthesemanticrepresentationunderlyingthedoubledelements.

(15) (3rd plural, grant)!"ɖ!"##!"#$

31

Blendinginsyntacticrepresentationsisakeypartofouranalysisofdoubling

constructions.Ingeneral,weanalyzesuchconstructionsinvolvingtwoV'phrases,with

distinctheads,thatoccupythesamepositioninthetree.TheseV'-projectionssharetwo

complements:anindirect(me)andadirectobject(grant),withtheseelements

simultaneouslyassociatedtobothV'.Figure3illustratestherepresentationhypothesized

for(15).Notethatweadoptaternary-branchingstructureforthedoubleobject

construction.Ouranalysisdoesnothingeonthisassumption;abinarybranchingVP-shell

structure(Larson,1988)couldalsoincludeblends,andwouldyieldsimilarresultshere.

Figure3.HypothesizedblendstructureforEnglish-Tamildoublingconstructiontheygave

me(aresearch)grantkoɖutaa.Thetextbeloweachprovidesabracketnotation

correspondingtothetree.Dashedlineshighlightblendedcomponentsofthe

representation.

Inthisexample,therearetwoV'(headedbygavevs.koɖutaa),sharingthe

complementsmeandgrant.ThesetwoV'simultaneouslyserveastheheadofVP(ablend

ofnodesinthesamepositioninthetree).Thisisakeypartofouranalysis,asitplaceseach

ofthedoubledelementsinthesamerolewithinthesyntacticstructure.Thissetsupthe

!

! !! !!!!!!!!!VP! ! ! ! !!!!!!!!They! !!!!!V'V'!! !!!!! !! !!!!!gave!! !!!!!!!!!!!!koɖutaa!!! ! !!!!!me!a!grant!!! !! ![VP!They![V'!gave![V'!me!a!grant]!koɖutaa!]!]!

!! !

32

structuralrelationshipsthatensurethedoubledelementsexhibitparalleltense,aspect,

agreement,andcasefeatures.

Thusfar,ourdiscussionofblendinghasfocusedontheblendingofelementswithin

astructuralposition(e.g.,twoV'projectingfromtheheadposition;twoverbsoccupying

thesameroleinsemanticstructure).However,aseachelementofarepresentationcanbe

associatedwithanactivationvalue,blendingispredictedtoextendtotherolesthemselves.

ThisisdepictedinFigure3,wherethesameargumentsaresharedacrossthetwophrases.

Thisrepresentsablendingofpositionsorsyntacticrelationships;onenodeinthetree(e.g.,

theindirectobject)hasthesametypeoflinktotwodistinctnodes(e.g.,V'headedbyan

EnglishverbandtheV'headedbyaTamilverb).Inouranalysis,thissharingofthe

complementsiscritical,asitallowstheblendedstructuretobelinearized.Iftwolexical

itemssimultaneouslyoccupytheheadofVP,thereisnowaytodeterminewhichoneof

themshouldoccurfirstinthesurfacestring;simultaneitymeansthereisnoprecedence

relationshipbetweenthephrases.However,becausetheprecedencerelationshipswithin

eachphraseshareacommonelement(gaveprecedesmeandgrant,meandgrantprecedes

koɖutaa),acompleteorderingoftheterminalscanbedetermined(bytransitivity,gave

mustprecedekoɖutaa).

Asreviewedinprecedingsections,thereisampleempiricalevidencethatblendsare

subjecttobothphysicalconstraints(e.g.,unimodalbilingualscannotplacearticulatorsin

contradictorypositions)aswellascognitiveconstraints(e.g.,affective/pragmatic

constraints,relativestrengthofthetwolanguages,grammaticalcontext).GSCsuggestsa

cleartheoreticalmotivationforsomeofthesecognitiveconstraints(Smolenskyetal.,

2014).Inmanycases,purelygrammaticalconstraintswillpreferblendsthatdonotreflect

33

thestructuralprinciplesofthesourcegrammars.Forexample,ifconstraintspreferthatall

elementsbeattheleftedge(i.e.,specifier)ofXP,whynotplaceallelementsinthatposition

simultaneously?Thiscandidatewouldsatisfyalltheconstraintsabove;intheabsenceof

otherprinciples,itwouldhavethehighestharmony.Byallowingthegrammartoavoid

makingchoicesbetweenstructuresexhibitingdifferentwordorders,thisblend

representationwouldpreventGSCfromcapturingkeypropertiesofcross-linguistic

variation.GSC,unlikemanypreviousconnectionistproposals,thereforeincorporatesan

explicitdispreferenceforblendrepresentations(Smolenskyetal.,2014).Forthepurposes

ofthisdiscussion(focusedonsimultaneouspresenceofequallyactiveelements),we

representthisasaconstraintthatsimplyreferstothepresencevs.absenceofblended

elements5:

(16) QUANTIZATION:“Candidatesmustbediscretesymbolicstructures.”ForeachblendedstructuralelementincandidateC,decreaseC’sharmonyby1.

ItisimportanttoemphasizethatQUANTIZATIONplaysakeyroleinmonolingual

grammars.Althoughwehaveemphasizedtheirroleinbilinguallanguageprocessing,blend

representationsareaubiquitousfeatureofmonolingualprocessingaswell(Melingeretal.,

2014).Allgrammaticalcomputations—notonlythoseinvolvedincodemixing—must

thereforeevaluaterepresentationswheremultipleelementsoccupythesamestructural

role(Smolensky,etal.2014).

Withrespecttothecurrentdiscussion,itisimportanttonotethatQUANTIZATIONis

violable;otherconstraintscancompelthepresenceofblends.Thenextsectionexaminesa

situationinwhichthiscanoccur.

34

Analysisofdoublingconstructions

Combiningtheresultsoftheprevioussections,weexamineconditionsunderwhich

doublingconstructionscanbeproduced.Welimitourselvestocandidatesthatparseall

elementsoflexicalconceptualstructureoranypossiblesubsetofelements(inthiscode

mixingcase,thisincludeselementsfrommultiplelanguages).Parsedelementsare

associatedwithappropriatesyntacticpositions.Weextendthiscandidatesettoincludethe

blendstructuredepictedinFigure3,simplifyingtheexamplebyomittingtheindirect

object.Followingthesectiononcodemixing,theconstraintrankingsinTable4[English]

andTable5[Tamil]arecombinedtodeterminethegrammarusedtoevaluatecode-mixed

constructions.WeincludetheQUANTIZATIONconstraintasalanguage-independent

constraint,examininghowitsrelativeweightingaffectstheprobabilityofblend

constructions.

ThetableauinTable6illustratesonerankingthatqualitativelyapproximatesthe

empiricaldistributionofdoublingconstructions—non-zero,butrelativelysmall

probability.

Table 6. Grammar fragment: Doubling construction, Tamil-English code mixing (seeappendix for full set of candidates). Blank cells indicate the candidate does not violate theconstraint.Probabilitiesarerounded;thoselessthan1x10-4arerepresentedas0.Input:

(3rd plural, grant)!"ɖ!"##!"#$

SPECLEFT HEADLEFT COMPLEFT PARSE QUANT

English:0.5activation –6.5 –6 0 –12.5 Tamil:0.5activation –6.5 0 –6 –12.5 Combinedweighting –13 –6 –6 –25 –8 H Pr

a.[XPthey[X'gave[X'grant]koɖutaa]] –30 –12 –16 –58 0.039b.[XPthey[X'koɖutaa[X'grant]gave]] –42 –12 –16 –70 0c.[XPthey[X'grantkoɖutaa]] –12 –6 –37.5 –55.5 0.48

35

Theobserveddoublingconstruction(candidatea)violatesseveralmarkedness

constraints:

• WithrespecttoHEADLEFT,itreceivesatotalharmonypenaltyof30dueto:

o Languagegeneralconstraints:–24=–6*4violations(3forkoɖutaa

and1forgave)

o English-specificconstraints:–6=–6*1violation(forgave)

o Tamil-specificconstraints:0=0*3violations(forkoɖutaa)

• ForCOMPLEFTthepenaltyis–12:

o Languagegeneralconstraints:–12=–6*2violations(forgrant)

o English-specificconstraints:0=0*2violations(forgrant)

• TwoviolationsoftheQUANTIZATIONconstraintyieldapenaltyof–16(forthe

twoV'simultaneouslyprojectingfromtheheadofVP,aswellasgrant

occurringasacomplementinbothV').

However,unlikecandidatesthatdeleteEnglishorTamilverbs(e.g.,candidatec),

theobserveddoublingconstructionsavoidviolationsofthefaithfulnessconstraintPARSE.

Theprobabilityofthedoublingconstructionrelativetonon-doubledcandidateslike(c)is

thereforerelatedtotheweightingoffaithfulnessrelativetothemarkednessconstraints

above.

Assumingfaithfulnesshasastrongenoughweighttocompelthepresenceof

doubling,theattestedcandidate(a)willbepreferredtounattestedcandidate(b)duetothe

influenceoflanguage-specificconstraints.Thetwocandidatesincurequalviolationsofthe

languagegeneralconstraints,but(b)incursextraviolationsoflanguage-specific

constraints(2additionalEnglish-specificviolationsforgave).Solongastheselanguage-

36

specificconstraintshaveanon-zeroweighting,thegrammarwillassignhigherprobability

totheattestedform.

Predictedlimitationsondoublingconstructions

Ouranalysisabovefocusedonanexamplethat,followingtheempiricalpatternsof

doubling,consistedoftwoheadswithasharedcomplement.Weassumethatdoubled

complements—specifically,argumentsofverbs—areunattestedbecausesuchstructures

wouldviolateChomsky’sThetaCriterion,whichstatesthat“eachargumentbearsoneand

onlyonetheta-role,andeachtheta-roleisassignedtooneandonlyoneargument”(1981:

35;seealsoChan,2003,2008,2009).Forexample,contrasttheattestedtheygaveEnglish

grantgaveTamilwiththeunattestedtheygrantTamilgavegrantEnglish.Inthelatter,theTheta

CriterionisviolatedasbothgrantTamilandgrantEnglishsharethesamerole(theme).In

contrast,intheattestedexamplethethemeisoccupiedbyasingleentity(grantEnglish,

sharedacrossthetwoverbs)sothereisnoviolation.Weassumethatviolationofthis

constrainteithercausesthegrammartocategoricallyruleoutsuchstructuresor,

alternatively,greatlyreducestheirprobability(iftheThetaCriterionisrealizedviaa

stronglyweightedconstraint).

Anovelpredictionofouraccountisthatdifferentdistributionsofdoublingshould

beobservedforexpletivevs.non-expletiveelements.Expletiveelementsarethosethat

appearsolelyforstructuralconsiderationsandaresemanticallyvacuous(e.g.,inIt’s

raining;thepronounit doesnotactuallyrefertoaspecificagent).Ouranalysisattributes

thepresenceofdoublingtotheco-presenceofmultipleelementsintheinputtothe

grammar.Thisisreflectedbythecrucialroleoffaithfulness;PARSEprovidesanadvantage

fordoublingconstructions,inspiteoftheirincreasedviolationsofalignmentconstraints

37

andQUANTIZATION.Thismakesanovelprediction:weshouldnotobservedoublingof

expletiveelements(e.g.,Englishdo)alone.FollowingGrimshaw(1997,2001,2013,a.o.),

theoccurrenceofsuchelementscanbeattributedtostructural(i.e.,markedness)

constraintsratherthantothepresenceofexpletivesintheinputtothegrammar.Asthey

onlyappeartosatisfythestructuralrequirementsofotherelements,ouraccountpredicts

thatexpletivesshouldnotbedoubledinisolation.

Tomakethisconcrete,consideracasewheredoublingcouldbepredicted.English

andKoreanbothutilizedo-supportinnegatives(Grimshaw,2013),butexhibitcontrasting

wordorder.Liketheverb,Koreannegatives(anddo)appearfollowingtheobject,the

oppositeofEnglish:

(17) Chelswu-kappang-ulmek-cianiha-ess-ta(Hagstrom,1996:169)Chelswu-NOMbook-ACCread-CINEGdo-PAST-DECL‘Chelswudidnotreadthebook.’

Anaccountthatattributedthepresenceofdoublingtocontrastingsurfaceword

orderswouldpredictthatdoublingofeithertheverb,negativemorpheme,ordoalone

couldoccurinKorean-Englishcodemixing.Incontrast,ouranalysispredictsthatthe

doublingofdoaloneshouldnotoccur.Thepresenceofdoherereflectsstructuralwell-

formednessconstraints,triggeredbythepresenceofnegation(Grimshaw,1997,2013).

Thereisnoindependentmotivationtoincludethisexpletiveasidefromthis.Thus,

doublingofdoalonewouldviolateconstraintssuchasQUANTIZATIONwhileprovidingno

benefitwithrespecttoconstraintssuchasPARSE.(Infact,insertionofexpletiveelements

notpresentintheinputmayviolatefaithfulnessconstraintssuchasGrimshaw’sFULLINT.)

Bilingualdoublingcannotbeanalyzedasmovement

38

Havingoutlinedourproposal,webrieflyconsiderwhetherexistinganalysesof

doublingcouldprovideanalternativetoouranalysis.Doublingofelementsinmonolingual

grammarshasbeenafocusofrecentgenerativeresearch(see,e.g.,thecontributionsin

Barbiers,Koeneman,Lekakou,&vanderHam,2008).Thisistypicallyanalyzedasresulting

fromphonologicalrealizationofmultiplelinksinarepresentationalstructurelinkinga

syntacticelementfromitslocationinthesurfacesyntacticstructuretootherdistal

locationsinthesyntactictree(e.g.,derivationalchains;Jónsson,2008;Nunes,2004).Such

ananalysisdoesnotappeartobetenablefortheattestedexamplesofbilingualdoubling.

ConsidertheTamil-Englishexampleanalyzedabove,wherethereisdoublingoftheverb

gave.ThereisnoclearmotivationforsuchmovementinthegrammarofeitherEnglishor

Tamil.Evenifweweretoentertainsuchananalysis,itwouldviolateabasicprincipleofthe

localityofheadmovement—theheadofaprojection(here,theverb)cannotundergo

movementwithinthatprojection(Abels,2003).

Gradientco-activationanddirectionsforfutureresearch

Gradientactivationinblends—thekeytoaccountingfortherangeof

psycholinguisticdatareviewedintheintroductiontothispaper—isclearlyoutsidethe

scopeofanytraditionalgrammaticaltheory.IntheGSCframework,suchrepresentations

arepossibleinputsandoutputstothegrammar,andareassignedHarmonyvaluesby

constraints.Specifically,theviolationofeachconstraintreflectstheactivationofthe

constituentsreferredtobytheconstraint.Forexample(c.f.(13),emphasisaddedtoshow

contrastindefinitions):

(18) PARSE:“Lexicalconceptualstructureisparsed.”DecreasecandidateC’sharmonybytheactivationofeachelementoflexicalconceptualstructurethatdoesnothaveacorrespondingelementinC’ssurfacesyntacticstructure.

39

Theincorporationofactivationstemsfromprinciplesofconnectionistcomputation

(Legendreetal.,1990;Smolensky&Legendre,2006).GSC-representationsarerealizedby

real-valuedactivationvectorsoversimpleprocessingunits.Overthecourseof

computation,activationspreadsamongtheseunitsviaweightsthatimplement

grammaticalconstraints(Smolenskyetal.,2014).Critically,theactivationvaluesare

continuouslyupdated;thenetworkdoesnotsimply‘jump’fromonegradientsymbolic

representationalstatetoanother.Inordertoinsurethatthiscontinuousupdaterespects

thewell-formednessconditionsspecifiedbythegrammar,constraintsmustassignwell-

formednessvaluestothefullrangeofintermediate,gradientrepresentationalstates.

Harmonythereforevarieswiththeactivationofeachrepresentationalconstituent.

Inthecontextofcodemixing,gradientactivationofelementsintheinputwillalter

therelativeprobabilityoftheseelementsappearingintheoutput.Thisisbecause

violationsoffaithfulnessconstraintslikePARSEwillbescaledbyactivation.Foragiven

weightingofPARSE,theharmonypenaltyincurredbydeletinganelementwillbelessifthe

elementhasalowervs.higheractivationvalue.Lessactiveelementswillthereforebemore

likelytobedeleted.ThetableauxinTable7andTable8illustratethisforasimplesubject-

verbsentence(here,weassumeQUANTIZATIONisstronglyweighted,blockingtheappearance

ofoutputblends).

40

Table7.Effectsofvariationininputactivation:StrongbiastowardsEnglishvs.Tamil.Notethatcompetitorsinvolvingadditionaldeletionofinputelementshavebeenomitted(duetoviolationsofPARSE,theyhaveverylowHarmonyandthusoutputprobabilitynear0).

Input:

(3rd plural)!"ɖ!"## .!!"#$ .!

SPECLEFT HEADLEFT PARSE

English:0.5activation –6.5 –6 –12.5 Tamil:0.5activation –6.5 0 –12.5 Combinedweighting –13 –6 –25 H Pr[XPthey[X'gave]] –12 –15 –27 0.82[XPthey[X'koɖutaa]] –6 –22.5 –28.5 0.18Table8.Effectsofvariationininputactivation:WeakerbiastowardsEnglishvs.Tamil.Notethatcompetitorsinvolvingadditionaldeletionofinputelementshavebeenomitted(duetoviolationsofPARSE,theyhaveverylowHarmonyandthusoutputprobabilitynear0).Input:

(3rd plural)!"ɖ!"## .!!!"#$ .!"

SPECLEFT HEADLEFT PARSE

English:0.5activation –6.5 –6 –12.5 Tamil:0.5activation –6.5 0 –12.5 Combinedweighting –13 –6 –25 H Pr[XPthey[X'gave]] –12 –16.5 –28.5 0.18[XPthey[X'koɖutaa]] –6 –21 –27 0.82

Inthesetableaux,violationsofPARSEarescaledbytheactivationoftheinput

element.Forexample,inTable7,thefirstcandidatedeleteskoɖutaa.Languagegeneral

constraintsassignaviolationof–10=0.4*–25andTamilspecificconstraintsassigna

violationof–5=0.4*–12.5.ComparethistothefirstcandidateinTable8.Here,the

violationoflanguagegeneralconstraintsincreasesto–11=0.44*–25andTamil-specific

constraintsto–5.5=0.44*–12.5.Astheactivationofaninputelementincreases,thecost

ofdeletingitalsoincreases—itbecomesmorecriticaltopreservetheelement(reflectedin

theshiftinoutputprobabilitiesacrossthetwotableaux).

41

Gradientactivationofelementsintheoutputprovidesamechanismformodeling

thedatareviewedinthefirstsectionsofthispaper;gradientblendsobservedin

phonologicalandarticulatoryprocessinginspokenandsignedlanguages(e.g.,theco-

activationof<DOG>and<PERRO>duringSpanish-Englishbilingualproduction,depictedin

Figure1).Clearly,gradientsymbolstructureshavetheexpressivecapabilitytorepresent

suchstructures;throughoutthisdiscussion,wehaveassumedgradedactivationof

elementsoftheinputtothegrammar.Ourclaimisthatthedegreeofblendingpresentin

theoutputreflectsgrammaticalcomputations.

Outsideofnumericalsimulations,thefinalblendstatesofourfirstimplementation

oftheQUANTIZATIONconstraint(Smolenskyetal.,2014)cannotbedetermined.Inmore

recentwork(TupperandSmolensky,inprogress)wehavethereforedevelopednew

realizationsofthisconstraintthataremoreamenabletoanalysis.Usingthesemethods,we

cancalculatetheoptimalblendstatepredictedbythegrammar.

Toillustratethisapproach,weconsideredthescenarioshowninFigure1—the

coactivationoftwonounsintheheadofanNPconsistingofadeterminerandnoun.For

thiscomputation,wesimplifiedourgrammar,focusingonlyonQUANTIZATIONand

FAITHFULNESS(asSpanishandEnglishagreeonwordorderfornounsinthesephrases).

FollowingthescenariodepictedinFigure1,weassumedthatEnglishhasgreateractivation

thanSpanish.AsshowninFigure4,thissetofconstraintweightings6assignedhighest

Harmonytoablendstatethatisclosestto<DOG>(reflectingthehigheractivationof

Englishvs.Spanish),yetcontainssomepartialactivationofthetranslationequivalent

<PERRO>(reflectingtherelativeweightingofQUANTIZATION).Critically,thisdegreeof

blendingisnotassumed,butisratherderivedfromtheconstraintsofthegrammar.

42

Figure4.RelativeHarmony(!!)ofvariousblendsof<DOG>(activationshownonXaxis)

and<PERRO>(activationshownonYaxis);lightercolorindicateshigherHarmony.The

optimalblend(0.81<DOG>,0.15<PERRO>)ismarkedwithanx.

Giveninputactivationsandrelativeconstraintweightings,aGSCtheorywillmake

predictionsaboutmultiplefacetsofcodemixedproductions:discrete(e.g.,output

probabilitiesofvariousstructures)aswellasgradient(e.g.,coactivationoftranslation

equivalents).Todevelopthisaccount,itisimportantthatwegainamoreprecise

understandingofthefactorsthatfacilitate(andinhibit)theactivationofrepresentations

withineachofabilingual’slanguagesduringsentenceprocessingaswellashowbilinguals

learntherelativeweightingsofgrammaticalconstraints.Critically,GSCprovidesuswitha

frameworkthatcanintegratethesevariousinfluencesoncodemixing—allowingusto

developaunifiedaccountofdiscreteandgradientpropertiesofbilinguallinguistic

knowledgeandprocessing.

43

Conclusions

Wehavesoughttobringtogethertwotraditionsinbilingualresearch.Studiesofon-

linebehaviorhaveestablishedthatblendrepresentations—wheremultipleelementsare

co-presentwithinasinglestructuralposition—playakeyroleinbilinguallanguage

processingatalllevelsoflinguisticstructure.Studiesofcodemixinghaveemphasizedthe

rolethatgrammaticalknowledgeplaysinconstrainingbilingualsentenceproduction.We

usedthephenomenonofdoublingtohighlighttheconnectionbetweenthesetwolinesof

research:theintegrationofblendrepresentationsandgrammar.Toformallylinkthesetwo

aspectsofbilingualcognition,weintroducedanaccountofcodemixingbasedinthe

GradientSymbolicComputation(GSC)formalism.Usingviolable,rankedconstraints,we

characterizedtheprobabilisticgrammarsunderlyingcodemixing.Therankingofsuch

constraintsreflectstheweightedsumofrankingsineachlanguageinvolvedinacode

mixedutterancealongwithacontributionfromthesourcelanguageofeachelement.

Crucially,blendrepresentationsarepartoftheinputandoutputofthegrammar.This

providesapredictiveaccountofdoublingconstructions;specifically,wepredict

restrictionsontheinsertionofexpletiveelementsinblendedstructures.Finally,our

approachcanbeextendedtoaccountforgradedblendrepresentationsinbilingual

languageprocessing.

Theprinciplesofouraccountofcodemixing—blendrepresentations;probabilistic

grammarswithweightedconstraints—comefromgeneralprinciplesofGSC.Theyarenot

postulatedtoaccountforbilinguallanguageprocessingspecifically,butratherreflect

principlesofthecognitivesystemthatholdforallspeakers.Similarly,thegrammatical

44

principlesweusetoaccountforcodemixingarethesameprinciplesthatunderlienon-

codemixedutterances.Ouraccountthereforedoesnotassumethatbilingualismingeneral

orcodemixingspecificallyrepresentsatypical,exceptionalcircumstances.Thatsaid,these

twoaspectsoflinguisticcognitionprovideakeytestcasefordiscoveringtheprinciples

thatunderliethecognitivearchitectureoflanguageprocessing.Codemixingisan

“experiment”inthenatural“laboratory”ofbilingualism,revealingtheinteractionofblend

representationsandgrammarthatisattheheartofGradientSymbolicComputation.

45

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Footnotes

1Consistentwithananalysiswheredoublingcanariseduetotheco-presenceofmultiple

elementsintheinputtothegrammar,elementsfrommultiplealternativeformulationsof

anintendedmessagearesometimesco-presentinmonolingualspeecherrors(Coppock,

2Doublingofinflectionalelementshasalsobeenreported,bothwheninflectionalelements

occurindistinctpositions(e.g.,prefixationvs.suffixation;Bokamba,1988;Myers-Scotton,

1993)andwhentheyoccurinthesameposition(Backus,1992).Thislattertypehasnot

beenreportedwithnon-inflectionalelements,whichisthefocusoftheanalysishere.

3Thisgeneralapproachisconsistentwithderivational/Minimalistapproachestogrammar

(seee.g.,Broekhuis&Vogel2013;Legendre,Grimshaw,&Vikner.2001;Legendre,Putnam,

deSwart,&Zaroukian,inpress-b)aswellasconstraint-basedmodelssuchasLexical

FunctionalGrammar(seee.g.,Bresnan2000;Kuhn2003;Sells2001a,b).

4GSCassumesastochasticoptimizationalgorithmthatconvergestoadistributioninwhich

theprobabilityofcandidatecis: !!(!)!!!(!)!!.Here,H(c)istheharmonyofcandidatec,xranges

overthesetofallpossibleoutputcandidates,andTisaparameteroftheoptimization

algorithm.HereweassumethatThasalowerlimitof1.

5SeeSmolenskyetal.,2014,fordetailsonthestochasticoptimizationprocessesthat

generalizethisideatovaryinglevelsofactivationofelements(whichresultsinnon-linear

changestorelativeharmonyofdifferentrepresentationalstates).

6QUANTIZATION’scontributiontoharmonyisbasedontheactivationofeach

representationalelementeinagivenstructuralposition: !!! 1− !! ! + !!!! − 1 !! ;

57

thisisweightedby–10.ThePARSEconstraint,weightedat+1,isdefinedas !!! !!! ,where

!!! istheactivationofeachelementintheinput(<DOG>=+2,<PERRO>=+1).Finally,

followingotherHarmonynetworks(Smolensky,2006a),thereisacontributionfromunit

Harmony(atermensuringtheharmonymaximumisafinitevalue): !! !! − !

!!

! ,

weightedat–11.

58

Appendix

Table A1. Grammar fragment: Doubling construction, Tamil-English codemixing, showingfull set of candidates. Blank cells indicate the candidate does not violate the constraint.Probabilitiesarerounded;thoselessthan1x10-4arerepresentedas0.

Input:(3rd plural, grant)!"ɖ!"##

!"#$ SPECLEFT HEADLEFT COMPLEFT PARSE QUANT

English:0.5activation –6.5 –6 0 –12.5 Tamil:0.5activation –6.5 0 –6 –12.5 Combinedweighting –13 –6 –6 –25 –8 H Pr

[VPthey[V'gave[V'grant]koɖutaa]]

–30 –12 –16 –58 0.039

[VPthey[V'koɖutaa[V'grant]gave]]

–42 –12 –16 –70 0

[VPthey[V'gavegrant]] –12 –12 –37.5 –61.5 0.001[VPthey[V'koɖutaagrant]] –6 –12 –37.5 –55.5 0.48[VPthey[V'grantgave]] –24 –6 –37.5 –67.5 0[VPthey[V'grantkoɖutaa]] –12 –6 –37.5 –55.5 0.48[VP[V'grantgave]they] –39 –12 –37.5 –88.5 0[VP[V'grantkoɖutaa]they] –39 –6 –37.5 –82.5 0[VP[V'gavegrant]they] –39 –6 –37.5 –82.5 0[VP[V'koɖutaagrant]they] –39 –6 –37.5 –82.5 0[VPthey[V'gave]] –12 –75 –87 0[VPthey[V'koɖutaa]] –6 –75 –81 0[VP[V'gave]they] –19.5 –75 –94.5 0[VP[V'koɖutaa]they] –19.5 –75 –94.5 0[V'gavegrant] –6 –75 –81 0[V'koɖutaagrant] –6 –75 –81 0[V'grantgave] –12 –75 –87 0[V'koɖutaagrant] –6 –75 –81 0[VPthey[V'grant]] –6 –75 –81 0[VP[V'grant]they] –19.5 –75 –94.5 0[VPthey] –112.5 –112.5 0[V'gave] –112.5 –112.5 0[V'koɖutaa] –112.5 –112.5 0[V'grant] 0 0 –112.5 –112.5 0Ø 0 0 –150 –150 0

59

Notethatthisgrammarfragmentpredictsthatintheabsenceofdoublingthemost

probablecodemixedproductionsareonesthatinserttheTamilverb,eitherintheTamilor

Englishwordorder.Notethatbothtypesofconstructionsareempiricallyattestedincode

mixing(Bhatt,1997).Whydoesthisoccurinthisspecificanalysis?TheHEADLEFT

constrainthasaweightingof0intheTamillinguisticsystemvs.–6intheEnglishsystem.If

onlyoneverbisretained(resultinginaviolationoffaithfulness),itisthereforemore

harmonictoretaintheTamilverb—itincursfewerviolationsofalignmentconstraints.In

thisfragmentwehavealsoincludedharmonicallyboundedcandidatestoillustrateall

possiblerepresentationaloutputforms.