Explaining Sonority Projection Effects

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1 ExplainingSonorityProjectionEffects RobertDaland a,brucehayes a,marcgarellek a, JamesWhite a,andreadavis b,ingridnorrmann c a DepartmentofLinguistics,UCLA; b DepartmentofLinguistics,Universityof Arizona; c DepartmentofSpanish&Portugese,UCLA Abstract Sonorityprojectionreferstobehavioraldistinctionsspeakersmakebetween unattestedphonologicalsequencesonthebasisofsonority.forexample,among onsetclusters,thewell formednessrelation[bn]>[lb]isobservedinspeech perception,speechproduction,andnonwordacceptability(albright,inpreparation; Berent,Steriade,Lenertz,&Vaknin,2007;Davidson2006,2007).Webeginby replicatingthesonorityprojectioneffectsinanonwordacceptabilitystudy.thenwe evaluatetheextenttowhichsonorityprojectionispredictedbyexisting computationalmodelsofphonotactics(coleman&pierrehumbert1997;hayes& Wilson2008;etalia).Weshowthatamodelbasedonlyonlexicalstatisticscan explainsonorityprojectioninenglishwithoutapre existingsonoritysequencing principle.todothis,amodelmustpossess(i)afeaturalsystemsupporting sonority basedgeneralizationsand(ii)acontextrepresentationincluding syllabificationorequivalentinformation.

2 1 Introduction TheSonoritySequencingPrinciple(SSP)isthecross linguisticgeneralization thatthemostwell formedsyllablesarecharacterizedbyasonorityrisethroughout theonsettothenucleus,andafallfromthenucleusthroughoutthecoda(sievers 1881;Jesperson1904;Hooper1976;Steriade1982;Selkirk1984).Forexample,the onset[bn]ismorewell formedthantheonset[lb]becausetheformercontainsa smallsonorityrise(obstruenttonasal)andthelattercontainsalargesonorityfall (liquidtoobstruent).afundamentalgoalofphonologicaltheoryistounderstand broadgeneralizationslikethessp. Acompleteunderstandinginvolvesanswerstothefollowingquestions.Isthe SSPsynchronicallyactiveinspeakers grammars,oradiachronicbyproductof physicalfactorsgoverningspeechperceptionandproduction,orsomecombination ofboth?ifthesspisapartofspeaker sgrammars,isitinnate,orlearned,orsome combinationofboth?andiflearned,fromwhat?howisknowledgeofthessptobe formallycharacterized?andhowisitdeployedduringspeechproductionand speechperception? WhatisknownatpresentisthattheSSPissynchronicallyactiveinspeakers grammars(althoughthisdoesnotruleoutdiachronicfactorsinaddition).themost recentformofevidencetosupportthisconclusionistheexistenceofsonority projectioneffects responsestonovelstimulithatvarydependingontheextentof thesonorityviolation.inparticular,stronglyssp violatingclustersaremorelikely tobeproducedandperceivedwithvowelepenthesis,e.g.[lb] [ləb]ismorelikely than[bn] [bən](davidson2006,2007;berentetal.2007). 1 Thesearetermed projectioneffects(inthesenseofbaker,1979)becausetheoffendingclustersare systematicallyandequallyabsentfromspeaker sinput,andyetspeakersappearto differentiatesomeclustersaslesswell formedthanothers. WhatisnotknownishowtheSSPcomestobeapartofspeakers grammars; infact,thisiscontroversialintheliterature,andaprincipalgoalofthispaperisto contributetothedebate.thispaperfocusesonthefollowingquestions: 1. Whatpropertiesmustanyphonotacticmodelhaveinordertopredict sonorityprojectioneffects? 2. HowdospeakerscometopossessknowledgeoftheSSP?Ifitisnotinnate, uponwhatkindofexperienceisitbased? 1 LisaDavidson(p.c.)andDoncaSteriade(p.c.)suggestthat sonority maynotbeatruephonological primitive,butratherconsistsofahostofphoneticfactors.forexample,davidson(2010)proposesan accountofher(2006)productioneffectsintermsofarticulatory(mis)coordination.weimaginethat perceptualepenthesis(dupouxetal.,1999;berentetal.,2007)canbeaccountedforsimilarlytothe productionaccountoutlinedinwilson&davidson(inpress):thephonotacticprobabilityofthe epentheticparseissomuchhigherthantheintendedparsethatthelistenersimplymisconstruesthe tokenascontainingthephonotacticallyacceptablesequence.theseareallimportantquestionsthat deservefurtherresearch,butforthepurposesofthepresentpaper,whatiscrucialisthatbehavioral variationcanbepredictedforclustersspeakershavenoexperiencewith,andthisvariationgenerally linesupwithtraditionaldefinitionsofsonority.webelievetheexperimentalandmodelingresults presentedherearejustascompellingwhethersonorityisinterpretedasatruephonological primitiveorasacovertermforavarietyofphoneticproperties. 2

3 3 Wedeferthequestionofmodelpropertiesforthemoment.Asforhowsomething likethesspcomestobeknown,wedistinguishlexicalisttheories inwhichthessp isprojectedfromthelexicon fromuniversalisttheories.thelexicalisthypothesisis consistentwithabodyofworkdemonstratingotherphonotacticgeneralizations thatareprojectedfromthelexicon(e.g.frisch&zawaydeh2001;hay, Pierrehumbert,&Beckman2003).Theuniversalisthypothesiscomesintwoforms. ThemostdirectformistopositthattheSSPisinnate.Theinnatistapproachis commoncurrencyinlinguistictheory,althoughformanyspecificaspectsof grammaritisdifficulttofindatheoristwhoadvocatesaninnateexplanation.the otheruniversalapproachthathasbeenproposedisthatthesspisphonetically grounded learnedfromexperienceinproducingandcomprehendingspeech,and universalbecause certainbasicconditionsgoverningspeechperceptionand productionarenecessarilysharedbyalllanguages,experiencedbyallspeakersand implicitlyknownbyall (Hayes&Steriade2004).Thesepossibilitiesare schematizedintable1. Hypothesis Projectedfrom lexicalist lexicon innatist UniversalGrammar phoneticallygrounded speechperception/productionexperience Table1.ExplanationsfortheSonoritySequencingPrinciple. Atpresent,thelexicalisthypothesisisthedominantexplanationfor phonotacticknowledge:evidencefromavarietyofmethodologiesconvergesonthe conclusionthatthelexiconisanimportantseatofphonotacticgeneralizations.for example,thestrengthofgradientocp Placeeffectsinnonwordacceptability judgementsispredictablefromlexicaltypestatistics(frisch&zawaydeh2001;see alsocoleman&pierrehumbert1997).asanotherexample,nonwordrepetition accuracyisbelievedtoindexphonotacticproficiency(coady&evans2008)andis stronglypredictedinchildrenbytheirvocabularysize,asconsistentwiththeview thatthephonotacticgrammarisprojectedfromthelexicon(edwards,beckman,& Munson2004;seealsoHayetal.2003).Thequestionisnotwhetherthelexiconisa sourceforphonotacticgeneralizations,butwhetheritisthesolesource. Toshowthatthereissomeothersource,itwouldbenecessarytofinda particularphonotacticgeneralizationanddemonstratethatitcannotbeprojected fromthelexicon.justsuchanargumenthasbeenmadeforthessp,instrongeror weakerforms,byseveralauthors.theargumentgoesasfollows:lexicalistmodels assignwell formednessonthebasisoflexicalfrequency.unattestedclustershavea frequencyof0.therefore,lexicalistmodelsshouldclassifyallunattestedclustersas ungrammatical,andcrucially,equallyungrammatical.inotherwords,theyshould failtopickoutsome(stronglyssp violating)clustersasmoreungrammaticalthan other(weaklyssp violating)ones.sonorityprojectioneffectsoccur,andsolexicalist modelsareunabletoaccountforthem.thisargumentismadeexplicitlybyren, Gao,&Morgan(2010,abstract):

4 ThesensitivitytotheSSPcanhardlybeaccountedforbylexicalstatisticfactors becausemandarinsyllableshavenoonsetclustersandnocodaconsonantswiththe exceptionof[n]and[ŋ],soallthestimuliinourexperimentswerealientothem. Thesensitivitycannotbeexplainedbyphoneticconfusionseither,becausesimilar sensitivityhasalsobeenfoundinreadingtasks(berent2009).thetwofindings shedlighton basicquestionsofgenerativegrammarbyindicatingthatthessp,as auniversalprinciple,mayconstituteapartofhumanlinguisticknowledge. Berentetal.(2007)arguesimilarly.Theyshowthataparticularlexicalmodel,the Vitevitch&Luce(2004)PhonotacticProbabilityCalculator,hasnostatistically significantcorrelationwiththeresultsoftheirsonorityprojectionstudy.they conclude(pp ): OurfindingsdemonstratethatEnglishspeakersmanifestsonority related preferencesdespitethelackoflexicalevidence,eitherdirect(i.e.,theexistenceof therelevantonsetsintheenglishlexicon)orindirect(thestatisticalco occurrence ofsegmentsinenglishwords). Experimentalresultsalongtheselines(seealsoBerent,Lennertz,Jun,Moreno,& Smolensky2008;Albright2009)constituteintriguingevidenceforthehypothesis thatthesspisnotprojectedfromthelexicon.inthetheoreticaltaxonomyoftable 1,theymaybetakenassupportingeithertheinnateorthephonetically grounded hypotheses.however,asberentetal.(2007,p.624)pointout,theargumentrelies onthefailureofparticularstatisticalmodelstopredicttheresult,andthereisno guaranteethatothermodelswillsimilarlyfail.itisthispointthatwepursuehere. Lexicalistmodelsassignwell formednessonthebasisoflexicalfrequency. Thekeyquestion,however,isfrequencyofwhat?Segmentsareanaturalstarting pointforphonologicalanalysis,andthereisabundantevidencethattheyrepresent apsychologicallyimportantlevelofrepresentation.however,segmentsarenotthe onlyrepresentationavailableforanalysis,andfromaphonologicalstandpoint,they arenotnecessarilyeventhebestone.analternative,notedbyberentetal.,isto considermodelsthatemployfeatures,i.e.acousticand/orarticulatoryproperties thataresharedbynaturalclassesofsegments. Ifamodelislimitedtocountingsegments,thenitistruethat,forexample, theonsets[tl]and[lt]areequallyunattested.however,fromafeaturalperspective, theonset[tl]receivesmorelexicalsupportthantheonset[lt].therearemany attestedonsetclustersthatarefeaturallysimilarto[tl],e.g.,[pl],[kl],[tr],[tw],[sl]. Incontrast,therearenoattestedonsetclustersthatareequallysimilarto[lt].A lexicalistmodelthatgeneralizesacrossmultiplefeaturallevelsofabstractionmight distinguishdegreesofwell formednessbetweentheseclustersonthisbasis,even thoughthesegmentalfrequencyofeachclusteris0.indeed,atleasttwolexicalist modelshavebeenproposedthatdogeneralizeonthebasisoffeatures:thehayes& Wilson(2008)PhonotacticLearnerandAlbright s(2009)featuralbigrammodel. However,thereisasyetnopublishedworkassessingfeature basedcomputational modelsforsonorityprojection(thoughseealbright,inpreparation). 4

5 Thus,thegoalofthispaperistotestavarietyofpublishedcomputational modelsofphonotacticsonthiscaseofsonorityprojectioneffects.thevalueofa directcomparisononthesamestimuliisthatwemaygainclearinsightonwhat modelpropertiesareresponsibleforsuccessandfailureonthisparticular phonotacticdomain whichmayinformourunderstandingastowhatcollectionof propertiesthenextgenerationofmodelsshouldhave. Inordertoassessthepredictiveutilityofamodel,itisnecessarytohave humanbehavioraldataforthemodeltoexplain.inthiscase,thefocusissonority projectioneffects,andsowebeginthepaperbycollectingnonwordacceptability ratingswithnonwordswhoseonsetclustersvaryintheextentofssp violation.asa matterofgeneralinterest,wealsoincludednonwordswithfrequentlyattested onsets(like[bl])andmarginallyattestedonsets(like[bw]). Withnonwordacceptabilitydatainhand,thepaperwillproceedtothe modelingstage.weimplementanumberofcomputationalmodelsofphonotactics describedintheliterature,specifically: classicalbigrammodel(jurafsky&martin2009) featuralbigrammodel(albright2009) syllabicparser(coleman&pierrehumbert1997) PhonotacticLearner(Hayes&Wilson2008) PhonotacticProbabilityCalculator(Vitevitch&Luce2004) GeneralizedNeighborhoodModel(Bailey&Hahn2001) Theadequacyofthemodelsisassessedbylinearregressionagainstthenonword acceptabilitydata. Toanticipatebriefly,wefindthatsomepublishedmodelsexhibit considerablesuccessinpredictingsonorityprojectioneffects.thekeyfindingsare discussedindepthlater;fornowtheymaybesummarizedasfollows:alexicalist modelcananddoespredictsonorityprojectioneffectsifithas(a)thecapacityto representsonority,and(b)arepresentationofphonologicalcontextthatisrich enoughtorepresenttheexpectedsonoritylevel.inotherwords,lexicalistmodels exhibitsonorityprojectionwhentheyareequippedwiththerepresentationsand architecturenecessarytodoso.thisworksupportsalexicalistaccountofthessp. Thepaperisstructuredasfollows.InSection2,wedescribetwoexperiments collectingnonwordacceptabilityjudgementsfromthemechanicalturk,anonline laborforum.insection3,wegivebriefdescriptionsofthecomputationalmodels testedhere,nonecontainingthesspasabias.insection4,wedescribetheresults ofcomputationalmodeling;eachmodelwastrainedonthesameenglishlexiconand thenassessedonitsabilitytopredicthumanjudgementsforunattestedclusters varyingintheirdegreeofssp violation.insection5,wediscusstheempirical findingsofthisworkandtheirtheoreticalimplications. 2 SonorityProjectioninAcceptabilityRatings Inthissectionwedescribeanonwordacceptabilityjudgementexperiment withnonwordsthatweredesignedtovaryinthelevelofsspviolation.webegin withasummaryofsonorityscales,followedbyabriefdescriptionofthemechanical 5

6 Turk.Thenonwordsarethendescribed,followedbytheacceptabilityexperiment. Theexperimenthadtwoconditions:inthefirstcondition,participantsratedforms onalikertscale;inthesecondcondition,participantscomparedtwoformsand selectedthebetterchoice.thesectionconcludeswithatheoreticaldiscussionof sonorityprojection,andamethodologicalcomparisonofthesensitivitiesoflikert ratingversuscomparison. 2.1 Sonorityscale Todeterminewhetherparticipantsexhibitsonorityprojection(andwhether phonotacticmodelscanexplainit),itisnecessarytohaveanindependentmeasure ofsonority.anumberofsonorityscaleshavebeenproposedintheliterature(e.g. Steriade1982;Selkirk1984;Clements1988;Parker2002),generally 2 havingthe followingproperties: eachsegmenthasasonorityvaluerepresentedbyaninteger segmentsaregroupedintosonorityclassessharingthesamesonorityvalue theminimallysonorousclasshasasonorityvalueof0 sonorityincrementsby1betweenclasses TheriseofasequenceXYisdefinedassonority(Y) sonority(x).thenthesspcanbe formalizedbydefiningathresholdforacceptablerises,e.g. onsetsmusthavearise ofatleast2 impliesthat[bl]isacceptablesolongassonority(l) sonority(b) 2.This typeofformulationhasprovenremarkablysuccessfulindelimitingonset inventoriescross linguistically(seereferencesabove),andiswhatjustifiesthe assignmentofparticularintegervaluestoparticularsegmentclasses. Scalesproposedintheliteraturedifferchieflyingranularity.Elaborated scalessuchasselkirk(1982)distinguishobstruentvoicingandmanner,vowel height,andrhoticity.weselectedthecoarse grainedscaleinclements(1988): obstruents(0)<<nasals(1)<<liquids(2)<<glides(3)<<vowels(4).thisscale makesonlyuncontroversialdistinctionsrepresentingtheconsensusofthe phonologicalcommunity TheMechanicalTurk TheMechanicalTurk( providedbyamazon.com.itwasusedbecauseitoffersaquickandeasywayto conductwordacceptabilityandsimilarstudies thetotaltimetocompletedata collectionwasabout1hourforeachratingmethod,withacostof$3/participant+ 10%commissionforAmazon.com,whichcomparesfavorablywith2 3weeksand $5 $10/participantfortheequivalentlaboratorystudy.Qualityismaintainedinthe MechanicalTurkbytheapprove/rejectoption,andtheapprovalthreshold. Researchersmayrejecttheworkofanyindividualworker(andrefusetopay);they mayalsopre screenbyselectingworkerswhoseapprovalrateisaboveathreshold; therecommendedapprovalthresholdis95%.asaresult,workersandthewebsite arebothdirectlyincentivizedtoensureanoverallhighqualityofwork. 2 Selkirk sscalestartsat0.5forvoicelessstops.theremainderofthescalehastheseproperties. 3 Theanalysesreportedin 2.5werealsocomputedwiththerichlyelaboratedsonorityscaleof Selkirk(1982).Thegeneraleffectswerethesame:attestedness,andsonorityintheunattesteds. 6

7 7 AllparticipantswererecruitedfromtheMechanicalTurkusingthe recommended95%approvalthreshold.participantsgaveonlineconsentand completedabrieflanguagebackgroundsurveysurveyingenglishproficiency, dialect,andotherlanguagesspoken.resultswereretainedfromparticipants reporting high Englishproficiency(Likertrating:n=2;comparisonrating:n=12)or native proficiency(likertrating:n=17;comparisonrating:n=36).theresearch teaminspectednon nativeresultsandfoundthattheyexhibitedthesame qualitativepatternsasnatives,i.e.attesteds>>marginals>>unattesteds(seenext sectionfordetails).participantsreporting intermediate proficiencywerepaid,but theirresultswerediscardedandreplaced.one(native)participantwasexcluded fromthelikertconditionforratingover80%oftheitemsas Stimuli Thestimuliconsistedof96stress initialccvcvcnonwords,generatedby concatenatingacconsetwithavcvctail(e.g.,pr + eebid=preebid).therewere 48onsetsand6tails.Thus,eachonsetwaspairedwith2tails,andeachtailwas pairedwith16onsets(48*2=96=16*6).eighteenclustersthatneveroccuras Englishonsets(unattesteds)werechosentovaryacrossthewholerangeofsonority (e.g.[tl]involvesalargesonorityrisewhereas[rg]involvesalargesonorityfall). Alsoincludedwere18clustersthatoccurfrequentlyasEnglishonsets(attesteds) and12clustersthatoccuronlyrarelyorinloanwords(marginals,e.g.[gw]in Gwendolyn,[ʃl]inschlep).Attestedandmarginalclusterswereincludedtovalidate thetask(participantsshouldexhibitthepreferenceattesteds>>marginals>> unattesteds)andtoincreaseecologicalvaliditybyprovidingatleastsometestitems thatareplausibleenglishwords.sixvcvctailswereselectedtoyieldalmostno lexicalneighborsandtoavoidviolatinganymajorphonotacticconstraintsof English. ThelistofonsetsandtailsisshowninTable2,withsonorityvaluesin parenthesesfortheunattesteds: Attested Onsets Marginal Onsets UnattestedOnsets (sonority) Tails tw,tr,sw, shr,pr,pl, kw,kr,kl, gr,gl,fr, fl,dr,br, bl,sn,sm gw,shl, vw,shw, shn,shm, vl,bw, dw,fw, vr,thw pw(3),zr(3),mr(2), tl(2),dn(1),km(1), fn(1),ml(1),nl(1), dg(0),pk(0),lm( 1), ln( 1),rl( 1),lt( 2), rn( 2),rd( 3),rg( 3) ottiff[ ɑtɪf] eebid[ ibɪd] ossip[ ɑsɪp] eppid[ ɛpɪd] eegiff[ iɡɪf] ezzig[ ɛzɪg] Table2.Listofonsetsandtails. Thestimuliwerecounterbalancedinanumberofways.Eachtailappeared approximatelythesamenumberoftimesforeachsonorityrange,sothat,e.g. ottiff wouldnotappearmoreoftenwithrelativelywell formedunattestedonsets.thecooccurrenceoftailswithonsetphonemeswascounterbalanced;forexample, ottiff

8 wouldnotappearmoreoftenwithanonsetcontaining/p/.repeatedsegments(e.g. dgeegiff)wouldbeindependentlydispreferredbytheocp,sotheseitemswere avoidedasmuchaspossible.onsetsandtailswerecombinedsoastoensurethatno nonwordhadmorethanonelexicalneighbor(neighbor=anexistingword obtainablefromthenonwordbyinserting,deleting,orsubstitutingonephoneme). Tocontrolforembeddedwords,weavoidednonwordswhoseC 1 C 2 VC 3 partsformed arealwordwithattestedandmarginalonsets;forunattestedonsets,nonwords whoseembeddedc 2 VC 3 partsformedarealwordweredistributedacrossthe sonorityrange.allofthenon wordswerepresentedinenglishorthographyinall capitalletters.toensurethatthestimuliwerephonologicallyunambiguous,they werepresentedtofivenaïveenglishspeakers;allnon wordswerepronouncedas intended,suggestingthatthespellingsarelargelyunambiguous. 2.4 DesignandProcedure Aftergivingconsentandfillingoutthelanguagebackgroundsurvey, participantscompleted6practiceitems,andthenperformedthemaintask.all itemswerepresentedonasinglepage,withradiobuttonsfortheanswers. FortheLikertratingcondition,participantswereinstructedthattheywould beratingpotentialnewwordsofenglish,thattheywouldseemultiplepotential wordsandthattheyshouldratethembasedonhowlikelyitwasthatthewords couldbecomenewwordsofenglishinthe21 st century.thepracticeitemswere STALLOP,SKEPPICK,THRISHAL,SHMERNAL,LBOBBIB,SHTHOKKITH,andwere intendedtoexposeparticipantstoawiderangeofwell formedness.eachitem consistedofasinglenonword,andtheresponseswere 1 (unlikely)to 6 (likely). Eachparticipantratedall96items;fourdifferentrandomizationswereusedto controlorder of presentationeffects. Forthecomparisonratingcondition,participantswereinstructedtochoose thenonwordthatseemedmorelikeatypicalenglishword.thepracticeitemswere STALLOPvs.THMEFFLE,LBOBBIBvs.PRIFFIN,THRISHALvs.FTEMMICK,SKEPPICK vs.mzibbus,shmernalvs.dwiffert,andshthokkithvs.thpellop.each uniquenonwordpairwaspresentedtoexactly1participant,andeachparticipant wasassignedalistof95items,sotherewere48participants(96*95/2pairs=4560 pairs=48participants*95pairs/participant).nonwordposition(leftorright)was counterbalanced,andparticipantlistswereconstrainedtonotcontainanynonword morethantwice. 2.5 Results Allregressionsweredoneusingthelmerfunctionfromthelme4package (Bates&Sarkar2006)inR(RDevelopmentCoreTeam2006).Asacheckonthe task,theentiredatasetwasregressed,usingtheorderedfactorofattestedness (unattested<<marginal<<attested)asthefixedeffect.linearregressionswith ratingasthedependentvariablewereusedforthelikertconditionbecausethe responsevariableisscalar;onset,tail,andparticipantwereincludedasrandom effects.logisticregressionwasusedforthehead to headcondition,witheachtrial splitintotwoobservationscorrespondingtoeachofthenonwords;thedependent variableindicatedwhetherthenonwordwaschosen(notethatthissplittingwas 8

9 necessarybecauseunlikenormallogisticregression,thetwochoiceschangefrom trialtotrial 4 );onset,tail,andparticipantpreferenceforleft/rightresponsewere includedasrandomfactors.todeterminewhethersonorityinfluencedlistener judgements,thedatasetswererestrictedtotrialscontainingonlyunattested clusters.sonoritywasusedasthefixedeffect,butotherwisetheregressionswere thesameasabove(linearforlikert,logisticforhead to head,samerandomeffects). Attestednesswasasignificantpredictorofwell formednessinboth conditions.marginals(nonwordscontainingmarginalonsets)wererated significantlyhigherthanunattesteds(likert:t= 7.4,p<1e 4; 5 head to head:z= 6.4, p<1e 9)andattestedswereratedsignificantlyhigherthanmarginals(Likert:t=10.1, p<1e 4;head to head:z=6.2,p<1e 9).Tovisuallyinspectwhetherthereisasonority effectintheunattestedclusters,fig.1plotsthisregression sunattestedcluster randominterceptsagainstsonority.theplotshowsthatsonorityisanexcellent predictorofthevarianceremaininginunattestestedclusters. 4 Thisanalysisseparatesatrialintotwoobservations,oneforeachnonwordofthepair.The statisticalmodelassumestheseobservationsareindependent,whichisfalsebecauseifonewordis chosentheothermustnotbe.thiscodingchoicereducesthepowerofthemethod,andhencecanbe regardedasconservative.onealternativemethodwasspecificallydesignedforsuchcircumstances, andisknownas alternative specificconditionlogisticregression (McFadden,1974)becausethe choicebetweenthealternativesisconditionedonpropertiesthatarespecifictoeachalternative,e.g. sonorityoftheonsetcluster.however,theredoesnotyetappeartobeanimplementationthatallows forrandomeffects.anotheralternativewouldhavebeentomodelthechoicebetweenleftandright, andtoincludeboththeleftandrightnonwords propertiesasfixedorrandomeffects;however,this ignoresthereal worldstructureoftheproblemsinceitassignsnumericallydistinctcoefficientsfor itemsthatoccurontheleftversustheright.suchamodelisincorrectbecause,forexample,[bl]isthe sameonsetwhetheritoccursontheleftortheright.inshort,thecurrentlyavailablestatistical methodsallhaveminorflaws.theanalysismethodweselectedisimplemented,interpretablebecause thereisonlyonesetofcoefficients,andconservativebecauseignoringperfectanti correlations withinapairshouldreducepower. 5 Degrees of freedom(df)areunreportedbecausedfisill definedforlinearmixed effectsmodels (Bates&Sarkar,2006;seealsoBates commentsathttps://stat.ethz.ch/pipermail/r help/2006 May/ html).Accordingly,thosep valueswerecalculatedwithmontecarlosamplingusing pvals.fncinthelanguagerpackage(baayen.davidson,&bates2008). 9

10 cluster coefficient pw mr tl zr fn rl ml dn km rn nl lmln pk rd dg lt rg sonority Fig.1.Unattestedcluster(random)coefficientsplottedagainstsonority. Thesonorityregressionconfirmedthatsonoritywasasignificantpredictorofwell formednessforunattestedonsets(likert:t=6.2,p<1e 4;head to head:z=7.4,p<1e 12). Formodelingpurposes,itwillproveusefultohaveacanonical acceptability score assignedtoeachnonword.wedefinethisastheproportionofcomparisons trialsinwhichanonwordwasselectedasbetterthanitscompetitor;thisvalueis usedinpreferencetorandominterceptsfromaregressionmodelforconceptual transparencyandforgreatercomparabilitytopreviousstudies(coleman& Pierrehumbert,1997),thoughthetwoarehighlycorrelated. 2.6 Discussion Theresultsofthenonwordacceptabilityexperimentdemonstratedseveral importantpatterns.first,boththelikertratingandcomparisonconditions exhibitedtheexpectedeffectofattestedness,withthewell formednessscale attested>>marginal>>unattested;thisshowsthatparticipantsrecruitedfromthe MechanicalTurkexhibitthesamecoarsebehavioraslaboratoryparticipantsin previousstudies.second,sonoritywasasignificantpredictorofacceptabilityfor unattestedonsets;thisresultisconsistentwiththehypothesisthatspeakershave internalizedknowledgeofthessp,butishardtootherwiseexplain.finally,as 10

11 11 discussedbelow,whilebothconditionsexhibitedthesamepatternofsignificant differences,thecomparisonconditionwasmoresensitivefortheunattesteditems ofinterest.thesepointsarediscussedinturn Inclusionofnon nativespeakers Theresultsofthepresentstudyshowthatatacoarselevel,participants recruitedviatheinternetexhibitthesamebehaviorasparticipantsrecruited throughsubjectpoolsorcampusflyer.internetrecruitmentarguablyrepresentsa moreecologicallyvalidsampleofenglishspeakersthanastudywithmonolinguals, becauseanon trivialpercentageofspeakerssorecruitedareearlyorlatebilinguals. Thisisapotentialcauseforconcern,asevenhighlyproficientlatebilingualsmay exhibitsubtledifferencesinjudgementfromnativespeakers(coppieters,1987). Notehoweverthatinthisexperimenttheresearchgoalisnottoisolatecompetence oftheidealizedmonolingualenglishspeaker hearer,butrathertodetermine whethersonorityprojectionoccursinenglishnonwordacceptabilityjudgements. TheotherlanguagesourparticipantsreportspeakingincludeDutch,French,Hindi, Mandarin,Marathi,Punjabi,andafewothers;theselanguagesaregenerallyequally ormorerestrictivethanenglishwithrespecttoonsetsonorityprofiles.thus,the sonority violatingclustersinthepresentstudyareequallynoveltoallparticipants Sonorityprojection Thestatisticalmodelingresultsshowedthatsonorityisasignificant predictorofparticipants well formednessratingsforunattestedclusters.themost naturalexplanationforthisfindingisthatparticipantshaveinternalizedknowledge ofthessp.howeveritisworthconsideringthealternativehypothesisthatthese resultsreflectsomesortoforthotacticknowledge. Theorthotacticaccountcanexplainthecoarsedifferenceinratingbetween attested,marginal,andunattestedonsets,butitfailstoexplaintheeffectofinterest: sonorityprojectioninunattesteds.thefrequencyofallunattestedonsetclustersis (bydefinition)0,sotheyarecruciallynotdifferentiatedbyfrequency.moreover,the visualstructureoftheenglishalphabetdoesnotreflectitsphonology,e.g.rismore visuallysimilartopthantol,butmorephonologicallysimilartol.theprincipled relationshipbetweensonorityandwell formednesscannotbeexplainedbyenglish orthotactics Sensitivityatthebottomofthescale ThepatternofsignificantdifferenceswasthesameacrosstheLikertrating conditionandthehead to headcomparisoncondition.however,thecomparison taskwasevidentlymoresensitivefortheitemsofinterest,theunattestedonsets. Onebitofevidenceforthisclaimisthatthezstatisticforthehead to headsonority comparisonisgreaterthanthetstatisticforthelikertcomparison,witha correspondingdifferenceinsignificance(likert:t=6.2,p<1e 4;head to head:z=7.4, p<1e 12).ThepointcanbeappreciatedmoreclearlyinFig.2,whichplotsrawonset averagesfromthecomparisonconditionagainstthelikertcondition.(theonset average forthecomparisonconditionisdefinedastheproportionofcompetitions wonbynonwordscontainingthecluster.)

12 raw comparison average attested marginal unattested raw Likert average Figure2.ScatterplotofcomparisonscoresagainstLikertratings Thecomparisonaveragedifferentiatestheunattestedonsetclustersmuchbetter thantherawlikertaveragedoes.presumablythisoccursbecausethetarget, unattesteditemsareconcentratedatthebottomendofthewell formedness spectrum,yieldingnear floorratingsforallofthem.thisfactsuggeststhefollowing methodologicalpoint:innonwordacceptabilitystudies,head to headcomparisonis preferabletolikertratingwheneverthestimuliofinterestareconcentratedatone endofthewell formednessscale,owingtoceiling/flooreffectsinlikertratings. SimilarconclusionswerereachedinCoetzee s(2004)unpublisheddissertation,and bykager&pater(underrevision);anddifferentbutrelatedpointsareaddressedin Kawahara(ms);wementionthismethodologicalpointhereinthehopeofaverting unnecessaryreplication of effortinthefuture. 3 ComputationalModelsofPhonotactics Havingestablishedthehumanbehavioraldataofinterestonsonority projection,weturnnowtothequestionofexplainingthejudgementsthathumans make.inthissection,wegiveabriefoverviewofsixcomputationalmodelsthathave beenproposedtoexplainnonwordwell formednessjudgements.the trainingdata thatwillbeusedhereisthelexicondescribedin 4.1,thoughinprinciplethese modelscantrainonanylexicon. 3.1 Bigram 12

13 Classicalbigrammodelsassignprobabilitiescompositionally:theprobability ofthewholeistheproductoftheprobabilityofthesub partsandthewaytheyare combined.inclassicalbigrammodels,thesub partsarebigrams,andthewhole wordprobabilityistheproductofthetransitionalprobabilities.forexample, cat canbeexpressedas#kæt#(where#areboundarysymbols);itsbigramsare#k,kæ, æt,andt#(fordetailedexpositionseejurafsky&martin2009;forarecentlinguistic studyseegoldsmith&riggle,toappear).fromthese,theprobabilityof[kæt]is calculatedasin(1): (1)Calculatingprobabilityof[kæt]inaclassicalbigrammodel # k æ t # p(# k) * p(k æ) * p(æ t) * p(t #) Thetransitionalprobabilitiesareestimatedfromtrainingdatausingrelative frequency;forexamplep(k æ)isestimatedbydividingthefrequencyof[kæ]by thefrequencyof[k].thismodelistermedalexicalmodelbecausebigram frequenciesarecalculatedbytheirtypefrequencyinthetrainingdata inthe presentstudy,anenglishlexicon. Inthenaturallanguageprocessingliterature,wherebigramandrelated modelsareheavilyemployed,itisconsideredbestpracticetosmooththe transitionalprobabilities(manning&schutze1999;jurafsky&martin2009). Smoothingassignsamodestamountofprobabilitytounseenitems,soastoavoid assigningzeroprobabilitytoitemsthathappentobeabsentfromthetrainingset. 6 Inourimplementationoftheclassicalbigrammodel,weusedGood Turing smoothing(gale&sampson1995). 3.2 Coleman&Pierrehumbert(1997) Coleman&Pierrehumbert s(1997)modelissimilartoabigrammodelin thatitassignswordprobabilitiescompositionallybymultiplyingtheprobabilitiesof sub parts.however,itdiffersinthesub parts:wordsareparsednotintobigrams butintoaphonologically motivatedhierarchyconsistingofsyllables,onsets,and rhymes.separatecountsaremaintainedforstressedvs.unstressed,initialvs.noninitial,andfinalvs.non finalsyllables,foratotalofeightonsetandeightrhyme distributions.justasinthebigrammodel,thecountsareestimatedfromthelexicon. Ourimplementationdiffersslightlyfromwhatisdescribedintheoriginalpaper, becauseourtraininglexiconincludesmorethanjustthebinaryfeetonwhichthe originalimplementationisbased.therefore,ratherthanparsingintobinaryfeet, ourimplementationusesthedistributionoverallattestedstresspatterns. 6 SmoothingisappropriateforZipfiandistributions,inwhichnoveleventscontinuetobeobserved forarbitrarilylargesamples.segmentalbigramsinenglishfollowsuchadistribution(daland& Pierrehumbert,2011). 13

14 Hereisanillustrationofhowthemodelcomputestheprobabilityoftheword agenda: (2)Calculatingprobabilityof[әˈd ʒɛndә]inthecoleman/pierrehumbertmodel ω σ [ s,+i, f] σ [+s i f] σ [ s i+f] O [s,+i, f] R [ s,+i, f] O [+s i f] R [+s i f] O [ s i+f] R [ s i+f] ә d ʒ ɛ n d ә P(agenda)=theproductof P(ω=σ [ s] σ [+s] σ [ s] ) probabilityofamedial stressedtrisyllable P(O [ s,+i, f] = ) probabilitythatonsetofinitialstresslesssyllableisnull P(R [ s,+i, f] =[ә]) probabilitythatrhymeofinitialstresslesssyllableis[ә] P(O [+s, i, f] =[d ʒ]) probabilitythatonsetofmedialstressedsyllableis[d ʒ] P(R [+s, i, f] =[ɛn]) probabilitythatrhymeofmedialsyllableis[ɛn] P(O [ s, i,+f] =[d]) probabilitythatonsetoffinalstresslesssyllableis[d] P(R [ s, i,+f] =ә]) probabilitythatrhymeoffinalstresslesssyllableis[ә] Aswiththebigrammodel,Good Turingsmoothingwasused;aseparatesmooth wasdoneforeachonsetandrhymedistribution. 3.3 Albright(2009) Thefeaturalbigrammodelisbroadlysimilartotheclassicalbigrammodel describedabove.itdiffersinhowthetransitionprobabilitiesarecalculated.rather thantreatingeachsegmentasadistinct,uniquetype,itdeploysphonological features,sothateachsegmentmaybecharacterizedbyanyofthenaturalclassesto whichitbelongs.forexample,thesegment[b]canbeconstruedas[+labial], [+consonantal],[+labial,+consonantal],[+labial, nasal],andsoon.thelikelihoodof abigramiscalculatedfromits best natural classfeaturaldescription,accordingto (3): (3) FormulaforselectingfeaturalbigramsintheAlbright(2009)model 7 l(xy)=max A,B p(ab)*p(x A)*p(y B) 7 Notethatthisformulaassignsalikelihooddistributionratherthanatrueprobability distribution,becausethevaluesdonotsumto1.thisiswhyl(xy)isusedinsteadofpr(xy). 14

15 where AandBrepresentnaturalclassestowhichxandyrespectivelybelong p(ab)isthetypefrequencyofnaturalclassbigramabinthetraininglexicon p(x A)=1/ A (1overthenumberofsegmentsinA) p(y B)=1/ B Theoverallrationaleofthemodelisthatawordcontainingpopulousnaturalclass bigramsarelikelytobeparticularlywell formed,especiallywhenthesegmentsthat instantiatethenaturalclassformalargeshareofthatclass spopulation.therestof thecomputationworksanalogouslytotheclassicalbigrammodel. Weranourownimplementationofthemodel,meanttofunctionidentically toalbright sbutfacilitatetheuseofourownfeaturesetandtrainingdata. 3.4 Hayes&Wilson(2008) TheHayes&Wilson(2008)PhonotacticLearnerisaconstraint based learningmodel.constraintsarestatedinthephonologicalvocabularymade standardbychomsky&halle(1968)andsubsequentwork.forexample,the constraint*#[+sonorant, syllabic][+consonantal]militatesagainstword initial[lb] clustersandsimilarssp violatingforms.justaswiththefeaturalbigrammodel,the featuresallowthehayes/wilsonmodeltomakegeneralizationsoversegments, includinggeneralizationsbasedonsonority. Toassesswell formedness,thehayes/wilsonmodelemploysthemaximum entropyvariant(dellapietra,dellapietra,&lafferty1997;goldwater&johnson 2003)ofHarmonicGrammar(Legendre,Miyata,&Smolensky1990;Smolensky& Legendre2006;Pater2009;Potts,Pater,Jesney,Bhatt,&Becker2010).Each constraintc i hasanonnegativeweightw i.awordxisevaluatedbyfindingits constraintviolationcountsc i (x),multiplyingeachviolationcountbythe correspondingweight,andtakingthesum.thenegativeofthissumisknownasthe harmonyofx,andthelikelihoodofxistheexponentialofitsharmony.toensure thisisatrueprobabilitydistribution,likelihoodisdividedbyanormalization constantthatguaranteesitsumsto1: (4)ProbabilityofwordxinHayes/Wilsonmodel Pr(x)=e harmony(x) /Z harmony(x)= i w i C i (x) Z= x Ω *harmony(x) (Ω * isthesetofallpossiblewords) Theconstraintsdeployedinthegrammararefoundbyasearchalgorithm thatattemptstoidentifyconstraintsthatbestexplainthetraininglexicon.the algorithmprivilegesconstraintsthatarebrief(fewfeaturematrices),accurate(low expected/observedviolations),andgeneral(coveringlargenumbersofpossible forms).thenumberofconstraintsthatthealgorithmincludesinagrammarcanbe setbytheuser.wecausedthemodeltoterminateat400constraints,andexplored theeffectofconstraintnumberbyconsideringsub grammarsincludingonlythe 15

16 first100,150,200,250,300,and350constraints.weranthealgorithmusingthe softwarepostedatwww.linguistics.ucla.edu/people/hayes/phonotactics/. 3.5 Vitevitch&Luce(2004) TheVitevitch&Luce(2004)PhonotacticProbabilityCalculatoriswidely usedinpsycholinguisticresearch.itresemblesseveralmodelsdescribedalreadyin thatitassignsascoretoawordbydividingitintopartsandcombiningtheir probabilities.themodelissimilartoabigrammodelinthatitusesbigramsaswell theirsimplercousinunigrams. Themodelemploysapositionalrepresentation,basedonleft to rightserial positionofsegments.separatecountsaremaintainedforeachposition.forexample, theprobabilityof[b]asthefirstsegmentofawordisbasedonwhatfractionofall word initialsegmentsare[b];theprobabilityof[b]asthefourthsegmentofaword isbasedonwhatfractionofallfourth positionsegments(inwordswithatleastfour segments)are[b],andsoon.inthebigramversion,analogouscomputationsare carriedoutonbigrams. Themodelusesaweightingsystemevidentlyintendedtoprovidea compromisebetweentypeandtokenfrequency.itweightsunigramsandbigrams bythelogoftheirtokenfrequencies,whicharerescaledbythetotallogfrequency weighttogetunigramandbigramprobabilities. Ourimplementationreflectsthestandardpracticethathasevolvedin experimentalworkmakinguseofthismodel:aunigramscoreiscalculatedasthe sumoftheunigramprobabilities,andabigramscoreiscalculatedanalogously(see thesub partprobabilitiesarenotmutuallyexclusive,summinginthiswayimplies thatnonwordscorescannotbeinterpretedasprobabilities. 3.6 Bailey&Hahn(2001) TheGeneralizedNeighborhoodModel(Bailey&Hahn2001,hereafter BH2001)isanexemplarmodelinwhichthewell formednessscoreofanitemis determineddirectlyfromthelexicon,bythesumofitssimilaritiestoexistingwords. Thisisincontrasttotheothermodelsdiscussedabove,inwhichagrammarisfirst projectedfromthelexicon,andthenwell formednessisevaluatedbythegrammar. Thesimilarityofanoncewordω i toanexistingwordω j iscalculatedfrom thestring editdistanced ij.string editdistanceiscalculatedfromthenumberof insertions,deletions,andsubstitutionsneedtochangeω i toω j.asintheoriginal paper,weusedaninsertionanddeletioncostof0.7,andtheproportionofshared naturalclasses(frisch,broe,&pierrehumbert1997)asthesubstitutioncost.the similarityofω i toω j isgivenbyexp( D d ij ),wheredisascalingfactor.similarlyto Vitevitch&Luce(2004),logtokenfrequencyweightingwasincluded,althoughthis modeladoptsamorecomplicatedquadraticweightingscheme.thetotalscorefora formiscalculatedbysummingsimilarities;wedifferslightlyfrombh2001by summingovertheentirelexicon,anoperationthatwasnotcomputationallyfeasible in2001.thefullformulaisgivenin(5): 16

17 (5)NonwordacceptabilityscoreinBaileyandHahn(2001) score i = j (Alogf j2 +Blogf j +C) exp( D d ij ) where logf j =log(tokenfrequencyofω j +2) D=5.5; 8 d ij isthestring editdistance Owingtodifferencesbetweenthetraininglexiconandtestitemshereversusin BH2001,weconsideredseveralsetsoffreeparameters: Label A B C basis fig estimatedfromfigureinbh2001 oral oraltaskinbh2001(bailey,pc) writ writtentaskinbh2001(bailey,pc) lin nofrequencyweighting 3.7 Summary Eachofthemodelsdiscussedintheprecedingsectionisalearningmodel.It istrainedonalexiconofalanguageandassignsscalarwell formednessvalues basedonagrammarprojectedfromthelexicon(orbasedonthelexiconitself).a summaryofmodels propertiesisgiventable3. model output basedon from bigram probability segmentalbigrams lexicon grammar syllabicparser probability syllabicconstituents lexicon grammar featuralbigram likelihood featuralbigrams lexicon grammar PhonotacticLearner likelihood featuralconstraints lexicon grammar PhonotacticProbability scalar positionalbigrams lexicon grammar Calculator Generalized NeighborhoodModel scalar string editdistance lexicon Table3.Summaryofmodelproperties Forthemodelswhoseoutputshaveaprobabilisticinterpretation(thefirstfourin Table3),theoutputswerelog transformed.thiswaspartlydoneforcomparison withwell formednessratingssincecoleman&pierrehumbert(1997)foundthat nonwordlog likelihoodswerelinearlyrelatedtohumanacceptabilityjudgements;it wasalsosimpler,astheunderlyingcomputationsareactuallyperformedinthelog domain.nosuchlogtransformwasappliedtothescoresforvitevitch&luce(2004) andbailey&hahn(2001),bothforgreatercomparabilitytoexistingstudies,and sincethesevaluesarescalarsthatdonothaveaprobabilisticinterpretation. 8 TheapproximatevalueofDwaskindlysharedbyToddBailey,asweretheA/B/Cvaluesforthe oralandwritset.thelinsettingwasrecommendedbyareviewer. 17

18 4 Modelingnonwordacceptabilityjudgements 4.1 TrainingonanEnglishlexicon Themodelsdescribedinsection3arelexicalistlearningmodels,meaning thatthewell formednessscorestheyassignaredirectlyorindirectlyprojectedfrom thelexicon.forafaircomparison,itisnecessarytotrainallmodelsonthesame lexicon.thissubsectiondescribesthetraininglexicon. Ourgoalwastocreatearepresentativedictionaryofthewordslikelytobe knowntotheparticipants.weusedthecmupronouncingdictionary ( bin/cmudict)transcriptions,selectingonly thosewordsthathaveafrequencyofatleast1inthecelexwordformdatabase (Baayen,Piepenbrock,&Gulikers1995).Fromthisset,weremovedcompounds, residualinflectedforms,andformscreatedbyhighlytransparentprocessesof morphologicalderivation,yieldingasetof18,612wordsinphonemictranscription. Twoversionsofthetrainingsetwereused.Inone,syllabificationwas lexicallyspecifiedbyannotatingconsonantsasbelongingtothecodaornot. 9 Inthe other,codapositionwasnotdistinguishedinthelexicalform.thephonemesofthe trainingsetweresupplementedbyafeaturechart.(thelexiconandfeaturescharts areavailablefromthecorrespondingauthoruponrequest.)thefeaturechartwas usedbythefeaturalbigrammodel,thephonotacticlearner,andthegeneralized NeighborhoodModel.Forthesefeaturalmodels,annotatedcodaconsonantswere featurallyidenticaltotheironsetcousinsexcepttheyweremarked[+rhyme];for thenon featuralmodels,annotatedcodaconsonantswerecountedasdistinct atomicsymbols,i.e.onset[b]wasjustasdistinctfromcoda[b]asitwasfrom[l]. 4.2 Method Eachmodelwastrainedonthetraininglexiconandwasthentestedonthe setofnonwordsusedinexperiments1and2.trainingconsistedofestimating modelparametersasdescribedin Testingconsistedofassigningawellformednessvaluetoeachnonwordstimulus. 4.3 Results Togetabroadoverviewofmodelperformance,wecalculatedforeachmodel thecorrelationofitswell formednessscorewiththeempiricallyderivedwellformednessscorefromtheexperimentalhead to headdatain 2.5.These correlationsareshownintable4.thefocusofthispaperisonsonorityprojection, sowhatisofmostinterestisamodel sabilitytopredictvariationamongthesubset ofunattesteditems.however,forcompletenessandgeneralintellectualinterest,we alsocomputedcorrelationsfortheattestedandmarginalsubsets,aswellasthe entiredataset.thesearereportedintable4. syllabification no syllabification 9 Syllabificationwasassignedusingthemaximumonsetprinciple(Selkirk,1982):medialconsonant sequenceswereparsedwiththelongestonsetthatoccursword initially.giventhattheseare learningmodels,itisreasonabletowonderhowthehiddenstructureofsyllabificationislearned.we leavethisissueforfutureresearch. 18

19 model attested marginal unattested overall attested marginal unattested overall albright bigram coleman gnm.fig gnm.oral gnm.writ gnm.lin hw hw hw hw hw hw hw vl.uni vl.bi Table4.CorrelationsofmodelratingswithExperiment2scores.Key:albright=featural bigram;bigram=classicalbigram;coleman=coleman&pierrehumbert(1997);gnm.set= GeneralizedNeighborhoodModelwithparameterset;HW[n]=PhonotacticLearnerwithn constraints;vl.uni/bi=phonotacticprobabilitycalculator,unigramandbigrammodels, respectively. Good modelcorrelationsarebolded(seetextfordetails). Modelsarearrangedintherows,withmembersofthesame family adjacenttoone another.thecolumnsaredividedintotwogroups,withsyllabifiedtraining/testing ontheleft,andunsyllabifiedinputontheright.thecolumnsrepresentthesubsetof thedatabeingregressed,andtheentriesineachcellrepresentthecorrelation.for example,thetopleftmostnumericalcellindicatesthatthesyllabifiedfeatural bigrammodelratingshada27%correlationwithhumanjudgementsonthe nonwordswithattestedonsets.thesecorrelationsprovideaconvenientmacrolevelsummaryofthemodels predictions. Tosimplifyfurtheranalysis,fromeachfamilyweselecteda best model whichinourjudgementrepresentedthebestornear bestperformanceofthat family.forexample,hw100(syllabified)wasselectedfromthehayes/wilson familybecauseithadthe(near )highestattested,unattested,andoverall correlations.theintentionistofocusinonthemostinformativecomparisons thoseinwhichwecanbesurerelativelypoorperformanceisnotsimplytheresult ofanunfortunatechoiceofparametersforamodel.putanotherway,itiseasierto understand6dataseriesthan30,andsincemanyofthedataseriesareparametric 10The overall scoreincludesvariationwithinandacrosssubsets.forexample,thebigrammodel doesnotdowellatdistinguishingunattesteditemsfromoneanother(low unattested correlation) butitdoesdistinguishunattestedsasaclassfromattestedsasaclass(high overall correlation). 19

20 variants,itisbettertojustfocusonthe6 best ones.fig.3a fplotsmodelnonword predictionsagainstthecomparisonjudgementsfromtheexperiment. albright bigram attested marginal unattested coleman gnm.lin hw vl.bi Figure3Modelnonwordpredictionsversushumanjudgements.x axis:well formednessscore asdeterminedbyhead to headcomparisondata(z transformed);y axis:modelscore(ztransformed).eachpointrepresentsanonword.each best modelisplottedinadifferent pane:albright=featuralbigrammodel;bigram=classicalbigrammodel;coleman=coleman &Pierrehumbert(1997);gnm.lin=GeneralizedNeighborhoodModelwithnofrequency weighting;hw100=phonotacticlearner;vl.bi=phonotacticprobabilitycalculator 4.4 Discussion Severalpointsemergedfromtheresultsofthemodelingstudy.Themost significantfindingforlinguistictheoryasawholewasthatthereexistlexicalmodels thatexplainsonorityprojection,i.e.predictsonority relatedvariationinhuman behaviorforunattestedphonologicalsequences.amongthemodelstestedhere,the modelswhichweremosteffectiveatmodelingsonorityprojectioneffectswerethe PhonotacticLearner(Hayes&Wilson,2008)andAlbright s(2009)featuralbigram 20

21 model;wewillarguethatsonorityprojectionowestoafeaturalrepresentationof sonorityandarichenoughrepresentationofcontexttotracktheexpectedsonority profile.anotherfindingofinterestwasthatnocurrentmodelexcelledacrossthe well formednessspectrum,i.e.themodelsthatwerebestonunattestedonsetswere notbestonattestedonsets.thesepointsarediscussedindetailbelow Sonorityprojectionispossiblefromthelexiconalone Themosttheoreticallysignificantfindingofthepresentstudyisthatsonority projectionisachievedbyanumberofpublishedlexicalistphonotacticmodels.this findingdirectlycontravenespreviousclaimsintheliterature,suchasthefollowing passagefromberentetal.(2007,pp ): Our findings demonstrate that English speakers manifest sonority related preferences despite the lack of lexical evidence, either direct(i.e., the existence of therelevantonsetsintheenglishlexicon)orindirect(thestatisticalco occurrence ofsegmentsinenglishwords). Berentandcolleaguesfoundsonorityprojectioneffectsinperception,whichisa substantialcontributiontothefield,becauseitunequivocallydemonstratesthatthe SSPisapartofspeakers synchronicknowledge.whatwedisagreewithistheclaim thatthereisnolexicalevidenceforthesonority basedpreferences.itistruethat, forexample,lbandtlareequallyunattestedasenglishonsets,buttherearemany onsetclustersthatarefeaturallysimilartotlwhereastherearenonethatareso featurallysimilartolb.alexicalistmodelthatisequippedtomakegeneralizations onthebasisoffeaturesshouldinprinciplebeabletoexplainsonorityprojection, andwehaveshownherethatthisisexactlywhathappens. Fromthebeliefthatthereisnolexicalsupportforsonorityprojection,Berent andcolleaguesdrawtheinferencethatlistenersmustpossesssomeformof universalknowledge,whetheritarisesfrom inherentpreferencesofthelanguage system (p.593)orknowledgethatis inducedfromphoneticexperience (p.625). Ourresultsshowthattheinferenceofuniversal,non lexicalphonotacticknowledge doesnotfollowasalogicalnecessity althoughitmaystillbecorrect.inshort,the abilityofalexicalmodeltoexplainsonorityprojectioneffectbearsonfoundational issuesofourfield,becauseitrefutesapowerfulargumentfortheexistenceof universalphonotacticknowledge Modelpropertiesneededforsonorityprojection Beyondthesheerfactthatsonorityprojectionoccurs,itisofinteresttoknow whysomemodelsexhibititandothersdonot.wewillarguethatwhatisneededis theabilitytocapitalizeontworepresentationalproperties:asufficientlyrich representationofphonologicalcontext(e.g.syllabification),andasufficientlyrich representationofsonorityitself(e.g.features).thesyllabifiedfeaturalbigram modelexhibitssonorityprojection.howevertheunsyllabifiedfeaturalbigram modelsdoesnot,soremovingsyllabificationinhibitssonorityprojection.similarly, thesyllabifiedclassicalbigrammodeldoesnot,soremovingfeaturalgeneralization alsoinhibitssonorityprojection.thus,sonorityprojectionrequiresbothproperties. 21

22 Phonologicalcontext.Toexpresssonorityrestrictions,amodelneedstobe abletodistinguishcontextsthatconstrainthesonorityprofile,e.g.itshouldbe risingword initially.modelstrainedonsyllabifieddatacandothis,sincetheyare toldwhetheraconsonantsequenceisparsedasanonset,arhyme,orasa heterosyllabiccluster.withthisinformation,suchmodelsareinapositionto inductivelytrackthesonorityprofilescharacteristicofthesethreecontexts,and characterizewell formednessoftheseconfigurationswhentheyarefilledby particularsegments. Weillustrateusingthespecificexampleofthefeaturalbigrammodel.A clusterlike[lt]isperfectlyacceptableinenglishwhenitisnotanonsetcluster,e.g. halt,elton.whensyllabificationismadeavailabletothemodel,itshouldbeableto distinguishtheunacceptableonsetclusterfromtheacceptablecodaand heterosyllabicclusters.indeed,whenitistrainedwithsyllabifieddata,thealbright modelachievesacorrelationofr=.55withhumanjudgementsforunattestedonsets. Thecorrelationdropstor=.18whenthesamemodelistrainedonunsyllabifieddata (wewillshowlaterthatthislevelofcorrelationarisesmerelyfrommodelingtails). Sincetheonlydifferencebetweenthesetwocasesisthepresenceofsyllabification, itfollowsthatthecontextualinformationrepresentedbysyllabificationcausedthe difference.inotherwords,syllabificationprovidesasufficientlyrichrepresentation ofthecontextastoallowalbright smodeltorepresenttheexpectedsonority contour. Itispossibleforamodeltosucceedwithoutanexplicitrepresentationof syllabification.inparticular,withasufficientlylargenumberofconstraintsthe PhonotacticLearnerachievesroughlyequivalentperformancesonsyllabifiedor unsyllabifieddata.webelievethisowestothefactthatthephonotacticlearner allowstrigramconstraints.englishtrigramsprovidealevelofphonologicalcontext thatismorespecificthansyllabification;forexampleatrigrammodelcanuse structuraldescriptionsoftheform[xyc]and[xy#]inplaceofx coda y coda,aswas doneinchomskyandhalle(1968).atthesametime,scalingupamodeltotrigrams hasitsowncostsintermsofsparsenessofdataandcomputationalcomplexity (Jurafsky&Martin2009). Insummary,whatamodelneedsissomerepresentationofphonological contextthatissufficientlyrichastotracktheexpectedsonoritycontour(seekager &Pater,underrevision,foranotherstudyconcludingthatphonotacticmodelsmust representsyllabification).explicitsyllabificationisanespeciallysimpleand effectivemeansofdoingthis,asevidentfromthefactthatnearlyeverymodeldoes betteronnearlyeverysubsetofthedatawhenithasaccesstosyllabification. Phonologicalfeatures.Inadditiontophonologicalcontext,amodelneedsa systemofphonologicalfeatures.therationaleforthisclaimisverysimple:inorder tomakegeneralizationsonthebasisofsonority,amodelmustbeabletomake generalizations,anditmusthaveanexplicitrepresentationofsegments sonority. Phonologicalfeaturesperformbothofthesefunctions.Featuresrepresentinherent generalizations,becausethepresenceorabsenceofafeaturerepresentsan underlyingacousticorarticulatorypropertysharedbyanaturalclassofsegments. 22