Inferen&alorganiza&oningrammarsystems:Wordstructure,paradigmorganiza&onandlearningFarrellAckermanUniversityofCaliforniaatSanDiego

(RobMaloufSanDiegoStateUniversity)

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Minélkülönösebbvalami,annálkevésberejtélyes- SherlockHolmeskalandjai

Thebigques+on:Howdowedemonstratethatthemorecuriousaphenomenonseems,thelessmysteriousitactuallyis?

Q1:Whatensuresthelearnabilityofcomplexinflec+onalsystems? H1:(Partly)theinferen+alorganiza+onthatemergesandinheresincomplexinflec+onalsystems:I(ntegra+ve)complexityasconstrainedbytheLowEntropyConjecture.

Contributoryques+ons:

Q2:Whatisthenatureofwordinternalstructure?Q3:Whatisthenatureofparadigmorganiza+on? Q4:Whatisthenatureoflearningasitrelatestoparadigmorganiza+on?

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Outlineofthepresenta&on

AndtheendofallourexploringWillbetoarrivewherewestarted Andknowtheplaceforthefirst&me.T.EliotLiOleGiddingV

1.Theempiricalchallengeandtheproblemsitraises:Finnish

2.WordsandParadigmsasPart/Wholerela+ons:Uralicand WesternNilo+c

3.Quan+fyingrela+onsbetweenwords:PiteSaami

4.BacktoFinnish

5.Conclusions

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1.Theempiricalchallengeandtheproblemsitraises

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Afundamentallearnabilityproblem

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Afundamentallearnabilityproblem

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Afundamentallearnabilityproblem

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Thebasicchallenge

Q1:HowcanaFinnishchildreliablypredicte.g.,thesingulartransla+ve1sgpersonpossessorkoirakseni`turnintomydog’givenknowledgeofe.g.,thenomina+vesingularkoirafortheLEXEMEcat,aswellasallcorrectlyproduceallotherformsofthislexeme?

Q2:Howdoessheextrapolatetothefullset(s)offormsforallotherLEXEMEs?

Alterna+vely,howdospeakersreducetheuncertaintyofpredic+ngonewordformfromknowledgeofanother(pa\ernof)wordforms?

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Expressionsofdespair(seeBaermanToAppearonSeriforanotherbigchallenge)

AndersenonDinka(WesternNilo+c):(but,seeBaermanonNuer2012onrelatedlanguageNuer) Fromtheverybeginningoflinguis&cresearchonDinka,ithasbeennotedthatnumberinflec&onofnounsinthislanguageisirregular.Mi\erutzner(1866:15)andBeltrame(1880:22–24)statedthatthereisnogeneralruleforformingthepluralfromthesingular,andbothauthorsmadeobserva+onsaboutthetypesofphone+cdifferencesexis+ngbetweenthesingularformandthepluralformofanoun…Thatnumberinflec+onofsimplena+venouns,suchasthose…above,isindeedirregularandunpredictable,hasrecentlybeenestablishedbyLaddetal.(2009).Thepluralformcannotbepredictedfromthesingularform,norcanthesingularformbepredictedfromthepluralform,andthenumberinflec&onmayappeartobetotallyirregular.2014:226

Carstairs-McCarthyonPolish:

IfthePluralweretakenintoaccount,too,theamountofblurringcouldnotdecreaseandmightevenincrease,asissuggestedbydeBray'sgloomycomment(1980,p.273):"thestudenthastolearnforeach[noun],apartfromtheNom.sing.,atleasttheGen.sing.andNom.andGen.p1.aswell,andpreferablyalsotheDat.andLoc.sing.2000:818

VajdaonKet(EurasianIsolate)

ThelexicalentryofeachKetfiniteverbthereforecontains,inaddi&ontoitspurelyderiva&onalmorphemeshapes,aformulathatpredeterminestheconfigura&onofitsactantagreementmarkers.Thisformulacannotbepredictedinthegrammarbasedonanyoverallsetofsyntac&cfunc&ons,seman&croles,orotherformalstemfeatures....Thisstrategynecessitatestheunprecedentedclaimthatmostinflec+on-bearingposi+onsintheKetverbarespecifiedidiosyncra+callybythelexicalentryofeachindividualstem.Thoughfiniteverbmorphemesareagglu&na&veonaphonologicallevel,withseparatorelementso^enappearingbetweenthem,seman&callytheyexhibitanetworkofextendedandmul&pleexponencesthatrivalsthemostfusionaloflanguages.

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Asimple(minded)answer

A:IfeachverbLEXEMEhasasinglestemandeachdis+nctmorphosyntac+ccategorye.g.,casehasauniquemarkerorexponentforeachofitsvalues,i.e.,NOM,TRANS...,thesolu+oniseasy:

Morphotac+cschema:[lexicalstemN-CASE-POSS]

1.koira-kse-nidog-TRANS-1SG.POSS `intomydog’

ReflectsCorbe\’sopera+veno+onofcanonicalinflec+onalencoding,i.e.,thelogicalextremeinthreedimensionsofwordencoding(Brownet.al.2013,Corbe\2015)

a)uniquemorphotac+cs, b)uniquestem,andc)uniquemorphologicalmarkerthatmodelse.g.agglu+na+vesystemslikeTurkish

Canonicalinflec+onalencodingfunc+onsasalocusfromthesimplestencodingpa\ernbetweenmorphosyntac+ccategoriesandformsfortrackingcross-linguis+cdevia+onsfromit:ithasnonorma&ve(oruniversal)theore&calstatus,simplyaheuris&ctaxonomiconeand,thereby,differsfrommanymorpheme-basedproposals(seeSiddiqi&Harleyeds.MorphologicalMetatheory(toappear)forcompe+ngviews)

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Problemswiththesimpleanswer

StraighqorwardalignmentsofmorphologicalfeatureCONTENTandFORMaremuchrarerthanorensupposedandtheore+callymodeled(Ma\hews1991,Brownet.al.2013,Stump2001,2013,2016,Blevins2016,Harris(ToAppear)onmul+pleexponence),Corbe\2015,AckermanandBonami(ToAppear),among

others)and,

requisitesegmenta&onsofinternalstructureintomorphemicunitsandstructuralcons&tuentsareorenmorear+factualandindeterminatethanrecognized.(seeHocke\1987,Morpurgo-Davies1978,Ma\hews1991,Bochner1993,Anderson1990,Corbe\2009,2015,Stump2016,Blevins2016,BonamiandBenjamin2016,mongothers).

BothreflectLounsbury’s(1953)fic+veagglu+na+veanalogueasamodelforstructuralistmorphemicmorphology.

Relatedlyandworse,languagescommonly

(1)havemul&pleinflec&onal/declensionalclasses,and

(2)displayZipfiandistribu&onsofwordformswithinandacrosssthoseclasses.

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Mul&pledeclensionclassesinFinnish(Paunonen1976,Thymé1993,Thyméet.al.1994,Ackermanet.al.2009)

Pa\ernsofformvaria+ondefinedifferentdeclensionalclasses:Compare(8),(32),and(10)withrespecttoNomSg,GenSg,andPartSg.

Q:Isn’tallthisvariabilityworsethanuseless,andarguablyanimpedimenttolearnability?

1.ThenumbersintheglosscolumnrefertodeclensionclassesaspresentedintheSoome-ees+sõnaraamat(Finnish-EstonianDic+onary)KaljuPihel&ArnoPikamäe(eds.)1999:758-771Tallin:Valgus.Anearlyexplora+onofPCFPasrelatestoFinnishisfoundinPauonen1976.

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Itgetsworse:Zipfiandistribu&onofforms(Zipf1935,1949,Kornai1992,Yang2004,Chan2008,EllisandO’Donnell2011,Kurumadaet.al.2013,BonamiandBeniamine2015,Blevinset.al.2015,Finlay2015,LignosandYang(toAppear),Yang(toappear)amongothers)

Oneofthemostpuzzlingfactsabouthumanlanguageisalsooneofthemostbasic:wordsoccuraccordingtoafamouslysystema+cfrequencydistribu+onsuchthattherearefewveryhighfrequencywordsthataccountformostofthetokensintext(e.g.“a",“the",“I",etc.),andmanylowfrequencywords(e.g.“accordion",“catamaran",`ravioli".Piantadosi2015:1

Nosurprisethatinflec+onalmorphologyfollowsthesamedistribu+on:

Afewlexemesoccurfrequently,withskeweddistribu+onsoftheirinflectedforms,andmostlexemesandinflectedformsoccurrarely,ifatall.

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Itgetsworse:Zipfiandistribu&onofforms(Yang2004,Chan2008,EllisandO’Donnell2011,LingnosandYang(toAppear),Kurumadaet.al.2013,BonamiandBeniamine2015,Blevinset.al.2015,Finlay2015,amongothers)

Ascorporaincreaseinsize,theydonotconvergeonuniformlypopulatedparadigms.Instead,theyreinforcepreviouslya\estedformsandclasseswhileintroducingprogressivelyfewernewitems.Thisdistribu+onreflectsthefactthatinflectedvariantsofopen-classitemsobeyZipf’slawatallobservedsamplesizes.Blevinset.al.ToAppear.

CzechNa+onalCorpusSYN2010(OlivierBonamip.c.)

100millionmorphologicallytaggedwords64,302dis+nctnounlexemes561,668dis+nctnounwordforms900,228possiblewordforms(7cases,2numbers)Only66lexemesoccurwithfullparadigmsNosingleformisobservedforeverylexemeOnly110lexemesoccurinthevoc.pl(butmorefrequentinspokenlanguage,sameformasnom.pl)

Largerstudiesrevealsimilardistribu+onsinFrenchandPortuguese.

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Oldrecogni&onandsolu&onformul&pleclassesandpredic&onfromskeweddistribu&ons(Paul 1891, Anttila 1989, Wurzel 1989, Fertig 2013, among others)

Principalparts=defTheprincipalpartsofalexemeLareasetofcellsinL’srealizedparadigmfromwhichonecancategoricallydeducetheremainingcellsinL’srealizedparadigm.

(StumpandFinkel2013:11-13)

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All4La+ndeclensionclassesarepar++onedinto4PrincipalParts

PrincipalPartsare(categorically)predic+veofallinflectedformsofagivenlexeme.

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Ahypothesis:PrincipalPartsinthelightofInforma&onTheory

Morphologicalsystemsconsistofwordsthatareinforma+veaboutotherwords(Wurzel1987onimplica+onalrela+onsand“paradigmstructureconstraints”)

Informa+venessisquan+fiableintermsofcondi+onalentropyinInforma+on-Theory:wordsareinforma+veaboutotherwordstoaspecifiabledegree.

Thecategoricalityofpredic+venessdefini+onalofPrincipalPartsissimplyareflexofthepossibilitythatinsomesystemssomewordsareassociatedwithnounpredictability,i.e.arefullypredic+ve,withrespecttotheirrela+onstoother(formsof)words.(seeAckermanandMalouf2013,2015,BonamiandBenjamin(toappear)andBlevin(toappearfordiscussion)

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Generalformula&onoftheimplica&onproblem:TheParadigmCellFillingProblem(PCFP)

Speakersoflanguageswithcomplexmorphologyandmul+pleinflec+onclassesconfrontalargelearningtaskwhosesolu+onraisesfundamentalques+onsaboutthestructureofwords,andtheorganiza+onofmorphologicalsystems.Thistaskreceivesageneralformula+onastheParadigmCellFillingProblem(PCFP)inAckermanetal.(2009):

PARADIGMCELLFILLINGPROBLEM:Givenexposuretoaninflectedwordformofanovellexeme,whatlicensesreliableinferencesabouttheotherwordformsinitsinflec+onalandderiva+onal)family?

NotmuchaproblemforlanguageslikeEnglish,withsimplemorphology,orTurkishwithagglu+na+vemorphologyandstraighqorwardmappingbetweenmorphosyntac+cproper+esandforms.

Acentralproblemofmorphologyandlearnability,thoughmuchoftheliteratureinmorphologyandlearnabilityfocusesonword(andwordinternalmorpheme)segmenta+on,leavingsomewhatmysteriouswhattodowithrespecttoproduc+vityoncemanyinflectedwordshavebeenlearned.(Saffranet,al.1996,Fedzechkinaet.al.2011,FinleyandWiemers2013,2015,Gerken2005,GerkenandKnight2015,Gerkenet.al.2015,GagliardiandLidz2014,LidzandGagliardi2015,andmanyothers.)

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Uncertaintyreduc&on

Howdospeakersreliablyresolve/diminishuncertain+esintheselec+onoftheappropriateformforapreviouslyunencounteredword?

Theproblemseemsincreasinglydifficult:(i)thelargerthenumberofmorphosyntac+cproper+esalanguagecontains, (ii)thegreaterthenumberofallomorphicvariantsitusestoencodethem,and(iii)themoreextensivetheconjuga+onclassesandsubclasses,i.e.,dis+nc+vepa\erns,overwhichwordscanbedistributed.

Morphologicalcomplexityiscommonlycalculatedbyconsideringthesefactors

Ackerman&Malouf(2013)refertothisperspec+veonmorphologicaltypologyasEnumera&veComplexityorE-complexity:thisistheclassifica+onandquan+fica+onofmorphologicalphenomenabyreferencetofactors(i)–(iii)above,whichallfigureintheformalshapesofwords.(seeCarstairs-Mcarthy’sParadigmEconomyPrincipleandtheNoBlurPrinciplefora

highlyar+culatedformofthisview.)

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Gesngtoasolu&onforPCFP(forsolu&onswithinadifferenttheore&calperspec&veseeAllenet.al.,Allen

Hypothesis1:Thecross-linguis+callyprofuseshapevaria+onintheinternalstructureofwordformsandtheexternalpa\ernsofrelatednessbetweenwordformsareconstrained(inpart)byimplica+veorganiza+on(=I(ntegra&ve)Complexity)amongwordsasquan+fiedinlowcondi+onalentropyvalues(=LowCondi&onalEntropyConjecture(LCEC).(AckermanandMalouf2013,2015)

Hypothesis2:TheLCECisonestrategyofaddressingthelearnabilityof(complex)morphologicalsystemsgiventhesparsenessofthedatareflectedinZipfiandistribu+onsofinflec+onalwordforms.

Hypothesis3:GiventhedemonstrableSparsenessofS+muliandtheRichnessoftheS+muli(=thecurseofdimensionality(AslinandNewport2009:17))morphologicalsystemsmustbeorganizedinwaysthatfacilitatelearnability.

Hypothesis4:Tounderstandmorphologicallearning,onemustunderstandinflec+onalorganiza+onandtheLCECisanemergentconstraintshaping(many)morphologicalsystems.(forsimilardirec+onsseeRaczet.al.2015,PaterandMoreton2012,AllenandHanson2016,Allen2016,AllenandBeckerms,PulleyblankandArchangeli(ToAppear),Wedel2007,2009).

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Ageneralsolu&onharkingbacktotradi&onalWP

Q:Whatshouldmorphologistsmodel?

Hypothesis:Wordsandtheirpa\ernsoforganizedrela+ons(paradigmstructure)aretheprimaryobjectsofmorphologicalanalysis. Hocke\(1967)asks:IsacompactlyelegantIAanalysisofcomplexmorphologicalcomposi+onsinYawalmaniusefullyandinstruc+velyreplacedbythelesscompactWP?

Tocoverthecomplexalterna&onsofYawelmanibyprincipal-parts-and-paradigmswouldtakemuchmorespacethanisoccupiedinthefirstsec&onsofthispaperbythemorphophoneme-and-rewrite-rulepresenta&on.Buttherewouldbeanetgaininrealism,forthestudentofthelanguagewouldnowberequiredtoproducenewformsinexactlythewaythena&veuserofthelanguageproducesorrecognizesthem-byanalogy.Therewouldremainthisdifference:thesitua+onforthestudentisar+ficiallysimplified.Heisenabledtooperate,inhisanalogizing,intermsofaneatminimalsetofreferenceparadigmsandafixedpoint-of-departuresetofprincipalparts.Thena&veuserofthelanguage,ofcourse,doesnotdothis.Heoperatesintermsofallsortsofinternallystoredparadigms,manyofthemdoubtlessonlypar&al;andhemayfirstencounteranewbasicverbinanyofitsinflectedforms.Forthena&veuser,theformsthatwehaveforconvenienceselectedtobeour'principalparts'havenosuchfavoredposi&on.Theyareaslikelytobecreatedanalogically,asneeded,asareanyoftheotherforms.HockeO1967:221

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Ageneralperspec&veharkingbacktotradi&onalWP

ThisconcurswithChomsky’sfavorableviewofWPoverIAandhisargueddispreferenceforthe“ill-advised”constructsrequiredinmorpheme-basedproposals:

“I know of no compensa+ng advantage for the modern descrip+ve reanalysis of tradi+onal paradigma+cformula+ons in termofmorphemesequences. This [=morphemicanalysis - FA] seems, therefore tobean ill-advised theore&cal innova&on... It seems that in inflec+onal systems, the paradigma+c analysis has manyadvantages and is to bepreferred… It is difficult to say anythingmoredefinite, since therehavebeen so fewaOemptstogivepreciseandprincipleddescrip&onofinflec&onalsystemsinawaythatwouldhavesomebearingonthetheore&calissuesinvolvedhere.”(Chomsky1965:174)

But,

a)51yearshavepassed.

b)Manyparadigma+capproacheshavebeendevelopedandappliedwithrigorandprecisionoverwidevarie+esofphenomenaandbroadarraysoflanguages,so

c)itisnolonger“difficulttosayanythingmoredefinite.”

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…wordsarenotmerelywholesmadeupof parts,butarethemselvesconstruableas partswithrespecttosystemsofformsin whichtheypar&cipate. MaOhews(1991:204)

2.WordsandParadigmsasPart/Wholerela&ons:UralicandWesternNilo&c

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Part/wholerela&ons:Theinternalstructureofwords

Internalcomposi&onofwords:wordsarecommonlythesmallestunitsofmeanings(seeRobins1959,Ma\hews1991,Blevins2016).

Cross-linguis+cimportanceofinternalstructureformorphologyisnotintheiden+fica+onofexponentsformeaningfulbits,i.e.,morphemesandorennotincons+tuentstructure,butinwaysthattheorganiza+onofexponentsfacilitatepa\ernsofdiscriminabilitythathelptodis+nguishandrelate(classesof)words.

Some+mes,thisinvolves(semi-)classicmorphemiccomposi+on,butmorecommonlyitrequiresconsideringwordsasrecombinantgestalts,i.e.,wholesconsis+ngofconfigura+onsofredeployedelements(segmental,suprasegmental)thateachalonedonotcontributeinvariantmeaningsindependentofthewordcontextsinwhichtheyoccur.

ExternalpaOernsofworddistribu&on:rela+onsbetweenwordsasinstruc+veasinstruc+veaboutmorphologicalorganiza+on.

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Part/wholerela&ons1:Internalcomposi&onofwords

Hungarian(Uralic)nominalmorphology:

Stemadj-NOMLZ-POSS-CASEMorphotac+cs

1.bátor-ság-om-ról‘aboutmybravery‘

Hungarian:(classic)agglu+na+onofmorphemicsuffixestolexicalstems

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Part/wholerela&ons1:Internalcomposi&onofwords

Mari(Uralic)verbalmorphology:singular2ndpastparadigmsforkol‘die’.

1stpastaffirma+ve1stpastnega+ve

1kolə̂-s-̆ə̂m`Idieds-̆ə̂mkolə̂`Ididn’tdie’

2kolə̂-s-̆ə̂c`youdied‘s-̆ə̂ckolə̂`youdidn’tdie’

3kolə̂-s̆`s/hedied‘ə̂s̆kolə̂`s/hedidn’tdie’

Synthe&cexpressionPeriphras&cexpression

Thesamepiecesdeployedindifferentmorphologicalconfigura+onsconveydifferentpolarityvaluesforverbs:theytakeondifferentfunc+onsinthewordcontextinwhichtheyoccur.

Theorganiza+on(gestalt)oftheelementsisasimportantastheelementsthemselves.

MariismorphologicallymoreE-complexthanEnglish,sinceithasmorphologicalmarkersforseveralpasttensesandperson/number,aswellasdifferentparadigmsforaffirma+veandnega+vepolarity.

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Part/wholerela&ons1:Internalcomposi&onofwords

AgardialectofDinka(EasternNilo+c)nominalmorphology:Andersen(2014)(seealsoRemijsen2005,Laddet.al.2009,Storch2005,amongothers)

Caseandnumberdis+nguishedbywordinternalinterac+onsamongfourparameters:(i)vowellength,(ii)tone,(iii)voicequalityofthevowel,and(iv)vowelqualityalterna&ongrade.

Contrastsbetween(pairsof)wordsdisclosethepa\ernednatureofmorphologicalorganiza+on.

DinkaismorphologicallymoreE-complexthanEnglish,sinceithasmanymorestrategiesforexpressingnumbercontrasts. 26

Mirrorimagepa\erning:

Singularfor‘elbow’hastriplelengthforitsvowelsandlowtonewhilethisisthewordinternalpa\ernforthepluralof‘thigh’.Thedoublelengthvowelsandlowtoneforthesingularof‘thigh’parallelsthesamepa\ernforthepluralof‘elbow’.

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Shilluk(WesternNilo&c)(Remijsen&Ayoker2014)

Shillukpresentsarichsystemofmorphologicalmarkingwithasmallsegmentalfootprint.Morphologicalexponenceischaracterizednotbytheconcatena+onofdiscretemorphemes,butratherbyastackingofmorphologicalopera+onswithinaconfineddomain,consis+ngofthestemandalimitedwindowofaffixes.Insuchasystem,morphologicalmarkingisrestrictedbythefactthatthestemsyllablecanhaveonlyonespecifica+oneachfortone,length,vowelquality,ATR,andthestem-finalconsonant,andthesespecifica+onsneedtoconveybothlexicalandmorphologicalinforma+on.Onewayinwhichtheuseoftheseresourcesismaximizedisthroughdistributedexponence,wherebyamorphophonologicalpa\ernrealizestwomorphosyntac+cvalues.Remijenet.al.ToAppear:17

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SomeShillukverbclasses(Remijsen&Ayoker2014)

Remijsenet.al.ToAppear:17

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Part/wholerela&ons1:Internalcomposi&onofwords

Firstdeclensionpar++vesinEstonian(Blevins2016:83) Alloftheformsarediscriminablydis+nct,exhibi+ngthesamepa\ernsofdis+nc+veness,includingpa\ernsofsyncre+smforPartSgandIllSg.

Firstdeclensionstemsandthemevowels

Therearenopiecesofformthatareuniquelyassociatedwithmorphosyntac+ccaseandnumberproper+es,butthereisasetofphonologicalresourcesthatgetreusedtocreatedis+nc+vewordshapes.

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Dis+nc+veforms

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Part/wholerela&ons1:Summary

Internalstructure:discrimina+vefunc+on,nota(necessarily)composi+onalfunc+on:dis+nguishingwordsfromoneanotherorviasyncre+smsiden+fyingpa\ernsofiden+ty.

Thewordisfrequentlythesmallestmeaningfulunitandthepa\ernsthatcharacterizeanddis+nguish(typesof)wordsmakeswordsdiscriminablefromoneanother:

Wordsaremadeupofreusedpiecesreconfiguredtoservedifferentpurposesandtofacilitatediscriminabilityamongwords:Gurevich(2006:44)onGeorgian

Themeaningofthewholewordlicensestheexponentstobeused,butthereisnoprecondi+onthatthemeaningsoftheexponentshavetocombinetocomprisethemeaningofthewhole.Composi&onalitymay,indeed,emerge,butasasideproductratherthanacentralprinciple,orperhapsasaneffec&velearningstrategy.Thewholeitselfmaycontributemeaningtothemeaningsoftheparts,ormayoverridethemeaningsoftheparts.

Theadop+onofwordsasindependentandnecessaryunitsofanalysisalsopermitswords,inturn,tobepartsoflargersystems.

Consequenceofpermi�ngwordstobecontrastedwithwords:thepossibilityofdiscoveringmorphologicalorganiza+on(paradigma+csystemsorinforma+onniches)inthesystemsofrela+onsbetweenwords.

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Part/Wholerela&ons2:ExternalpaOernsofworddistribu&on

Blevins2006:549

Blevins2006:551

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Pervasivepa\ernsofimplica+veinterdependencies

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Cooldata,butsowhat?

Pesetsky(2009:464)expressesappropriateskep+cismaboutsimilar“cabinetsofcuriosi+es”iden+fiedinEvansandLevinson’s(2009)againstlanguageuniversals,sincetheimportanceofunusualvariantsoffamiliarconstruc+onsw/oanalysisishardtoevaluate.

So,whatsortofanalysiscanbedeveloped?

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3.Quan&fyingrela&onsbetweenwords:PiteSaami

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PiteSaami

AllnaturallanguagesshowacertaindegreeofwhatBaermanetal.(2010:2)call“gratuitous”morphologicalcomplexityandWurzel(1986:76)describesas“ballast”inthelinguis+csystem.

PiteSaami(Wilbur2014:109)

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PiteSaamihaseightnominaldeclensionsshowingdis+nctgradeandsuffixpa\erns.

Sincetheassignmentoflexicalitemstopar+culardeclensionsislargelyarbitrary(thoughinfluencedbyphonologicalfactors),theseclassesaddcomplexitytotheinflec+onalsysteminawaythatservesno(evident)communica+vepurpose.

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ExtractedpaOernofformvaria&ondistribu&on

PiteSaami(Wilbur2014:102)

Pa\ernofstemandaffixvaria+on(stemspar++ontheinflec+onalfeaturespace(BonamiandBoyé

2006,2007))

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Informa&on-Theore&cinsights

Q:Whatpoten+atesthelearnabilityofthesystem?

A:Systemicrela+onsamongwordsorganizedintermsoflowcondi+onalentropies,i.e.,thepredictabilityofanunknownform,givenknowledgeofanotherformofthatword.

H:Quan+fy“predic+on”orasareduc+oninuncertainty,orinforma+onentropy(Shannon1948)

Complexinflec+onalsystemsareorganizedinwaysthatfacilitatethereliableguessingfromknownformstounknownformsandthisorganiza+oncanbemadevisiblebyusingInforma+on-Theore+cmeasuresofEntropyandCondi&onalEntropy.

Whatweneedtoknow:

1)TheParadigmCellEntropyforeachcelli.e.,howthechoicesofexponentsforeachcellcanbecalculatedintermsofthedegreetowhichachoicebetweenthemisuncertain.

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Informa&on-Theore&cinsights3

(2)theCondi&onalEntropybetweenpairsofcells,sothatwecandeterminehowmuchtheknowledgeoftheforminonecellreducestheuncertaintyassociatedwithselec+ngapairedcell,H(Y|X)

Howmuchinforma+ondoesthepresenceofXhaveforpredic+ngY,orhowsurprisedarewethatgivenXwegetY?

What’simportantissurprisal:measureoftheamountofinforma+onexpressedbyapar+cularoutcomemeasuredinbits,where1bitisachoicebetween2equiprobableoutcomes.3

Theintui+on:Outcomeswhicharelessprobable(hardertopredictandmoreuncertain)havehighersurprisal,

Surprisalis0bitsforoutcomeswhichalwaysoccur(p(x)=1)andapproaches∞forveryunlikelyevents(asp(x)approaches0.

3)TheAverageCondi&onalEntropyastheaveragedsumofallofthepairwisecondi+onalentropiesprovidesuswithageneral“interpredictablitybetweenforms”measure.

3.Forpresentpurposeswewillassumeallofthetasksbelowreflectequiprobabledistribu+ons.Thisactuallyprovidestheupperboundofentropyvalueswithfrequencyinforma+onand/orseman+candphonologicalcondi+onslikelyreducingentropy(seereferencesforexplora+onsalongtheselines)

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Calcula&ngParadigmCellEntropy

Compara+veDeclensionClassesinPiteSaami(Wilbur2014:109)

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Cellscanberealizedbydifferentnumbersofallomorphs:Illa+vesingularhas5allomorphs.

Givenequiprobabilityassump+ons,themorethenumberofchoices,thehighertheentropy.(formorerealis+cassump+onsseeAckermanet.al.2009,Bonami2015,Sims2016,amongothers)Eachmemberofarealiza+onsetisassociatedwithanentropyvaluereflec+ngthedegreeofsurpriseofitsselec+on.

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An(un)realis&ctaskanditsentropies:ParadigmCellEntropy

Aspeaker’stask:Guessthewordformforaspecificcell.

Thiswilldependonthenumberofpossiblerealiza+onsforeachcell:

Illa+vesingularonlyhasfivepossiblerealiza+onsandanentropyof2.250bits,whilethemostdiversecellshaveanentropyat3.00bits(=8choices)

Averageentropyacrossallcellsis2.66;thisaverageisameasureofhowdifficultitisforaspeakertoguesstherealiza+onofanyonewordformofanypar+cularlexemeintheabsenceofanyinforma+onaboutthatlexeme’sdeclension=ParadigmcellentropyAnentropyof2.66bitsisequivalenttoselec+ngamongonly22.26=6.31equallylikelyalterna+ves:

PiteSaamihaseightdeclensions,butselec+ngtherealiza+onforapar+cularwordformofalexemeisasdifficultasachoiceamongali\lemorethansixequallylikelyalterna+ves.

39

39

Arealis&cspeaker’stask:Condi&onalEntropy

Quan+fyingthepredictabilityofoneformgiventheother:measurethesizeofthesurpriseassociatedwiththeseformsusingcondi+onalentropyH(Y|X),theuncertaintyinthevalueofYgiventhatwealreadyknowthevalueofX:

Itmeasureshowmuchentropyremainsforagivenforminagivencellifaforminanothercellisalreadyknown.

Thepoint:ThesmallerH(Y|X)is,themorepredictableYisonthebasisofX,i.e.,thelesssurprisedoneisthatYisselectedgivenknowledgeofX.

WhereXcompletelydeterminesY,thecondi+onalentropyX(Y|X)is0bits:giventhevalueofX,thereisnoques+onremainingastowhatthevalueofYis.(ThinkofPrincipalParts)

But,ifXgivesusnoinforma+onaboutYatall,thecondi+onalentropyX(Y|X)isequaltoH(Y):giventhevalueofX,wearejustasuncertainaboutthevalueofYaswewouldbewithoutknowingXatall.

40

40

AverageCondi&onalEntropiesinPiteSaami

41

ForPiteSaamiexample,H(P)is0.116bits,equivalenttoachoiceamongonly20.116=1.08equallylikelydeclensions.

WhilePiteSaamihaseightnominaldeclensionsfromthepointofviewofalexicographertryingtodescribethelanguage,foraspeakertryingtousethesystemithasonaverageonlyslightlymorethanone:thisistheI(ntegra+ve)-complexityofthisparadigm.

Providesaquan+ta+vemeasureofthedescrip+onsandinsightsaboutparadigmstructure(Wurzel1989,Ma\hews1991)andawaytocalculateI-complexityofsystem.

41

Iden&fyingdegreesofinforma&vity

42

ColumnsaveragesE[col]areameasureofpredictedness,orhowdifficultitistoguesstherealiza+onofacell(onaverage)givenknowledgeofsomeothercell

Rowaveragesindicateacell’spredic&veness:theaverageuncertaintyinanotherparadigmcellgivenknowledgeofthatcell.

Thenomina+vesingularisverypredic+vebuthardertopredict:onitsbasisallotherformsarecompletelypredictable,makingitaprincipalpartintheclassicalsense.

42

I-complexitygeneraliza&onsacrosslanguages?2

TheLowEntropyConjectureisthepredic+onthatlanguageswillshowlowaveragecondi+onalentropyalongthelinesdiscoveredfortheselanguages.

Ackerman&Malouf(2013)refertothismeasureascalcula+ngtheI(-ntegra+ve)-complexityofamorphologicalsystem:itismeasureoftransparencyoftherela+onsofpa\ernsofwordsinparadigm.

2.Addi+onalconfirmingempiricalresults:PiteSaami(AckermanandMaloufabove),Estonian(Blevins,Baerman),TundraNenets(Ackermanetal.),Tlingit(Cable),Murrinhpatha(MansfieldandNordlinger),Portuguese(BonamiandLuis),French(BonamiandBeniamine),Nuer(Baerman),Voro(Baerman),PalantlaChinantecandKadiweu(SimsandParker).

43

43

Observa&ons

TheLCECreflectsastrategyforhowcomplexmorphologicalsystemsareorganizedinawaytoinsurelearnability,despiteluxuriantE-complexity(manydifferentforms,manydifferentclasses)andskewedZipfiandistribu+onofsparses+muli.

Representsthediscoveryofarobustprinciple,asta+s+callanguageuniversal,ofcross-linguis+cmorphologicalorganiza+onthatonlybecomesclearwhentheinternalstructureofwordsandtheirexternaldistribu+onsarerecognizedasprimarytheore+calobjectsofanalysis-wordsarenotepiphenomena.

Morphologicalsystemsmustbesimpleinwaysthatallowthemtobelearnedandusedbyna+vespeakers,irrespec+veofhowcomplexwordsandparadigmsmayappearaccordingtoexternalmeasures.

Speakersmustgeneralizebeyondtheirdirectexperience:

Morphologicalsystemsmustpermitspeakerstomakeaccurateguessesaboutunknownformsoflexemesbasedononlyasmallsampleofknownforms.

ThisistheIntegra&veComplexityofasystem:therela+veinforma+vityassociatedwitheachformandhowthisdefineslanguagepar+cularpa\ernsofinterpredictabilitybetweenforms.

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Animportantobserva&onconcerningwordinternalstructure

Resultsdonotdependon(universal)assump+onsaboutpar+cularformalproper+esofwords,onlyonwhetheraspeakercandiscriminatebetweentwoforms:

specificformtype,eithersynthe+corperiphras+c,andthemannerofdiscrimina+on(whetherbyaffixes,tones,stress,ablaut,orensemblesofthese)isirrelevant,aslongasfortheformsarediscriminablefromoneanother.

45

Animportantobserva&onconcerningwordinternalstructure

A(hypothe+cal)straighqorwardlyagglu+na+velanguagehasanaveragecondi+onalentropyof0bits,asexpected:

asdoesahypothe+calfusionallanguage.

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Organizedoraccidentalmappings?MonteCarloSimula&ons

Language Declensions Cells Realiza&ons Paradigmentropy

BootstapAvg

Bootstrapp

Fur 19 12 80 0.517 1.316 0.001Pite-Saami 8 14 70 0.116 0.322 0.001Russian 4 12 26 0.538 0.541 0.383

Fur

Resultsbasedonuniformtypefrequencies(MaloufandAckerman2010,2013,2015)

Pite-Saami

Simula+onscomparetheentropiesassociatedwithactual

47

4.BacktoFinnish

48

Finnishimplica&veorganiza&on(Ackermanet.al.2009)

Givens+mulustuohta‘birchbark(part.sg)’,thereiscorrectassignmenttoclass32basedontheanalogicalpropor+onkuusta:tuohta::kuusi:TUOHI.

Ifthes+mulusisanon-diagnos+cwordform,correctclassassignmentisunderdetermined.S+mulusnuken‘puppet(gen.sg)’couldbeassignedeithertoclass9orclass8,basedonthecompe+nganalogicalpropor+onsnallen:nuken::nalle:NUKKEversusoven:nuken::ovi:NUKKI.

Ifthes+mulicomprisethepairnuken‘puppet(gen.sg)’andnukkeja‘puppet(part.pl)’,thentherecorrectassignmentofthiswordtoclass9.(=jointentropy(BonamiandBeniamine2015,

1.ThenumbersintheClasscolumnrefertodeclensionclassesaspresentedintheSoome-ees+sõnaraamat(Finnish-EstonianDic+onary)KaljuPihel&ArnoPikamäe(eds.)1999.Tallin:Valgus.

49

49

Finnishimplica&veorganiza&on(Ackermanet.al.2009)

50

Most Predicted

Most Predictive

Most Predicted

Most Predictive

50

5.Conclusions

51

Currentdirec&ons

(1)iden+fylargerdatasetssupplementedwithfrequencyinforma+ontoserveasobjectsofmeasurementtoreplacethemeasurementofformsderivedfromdescrip+vegrammars,aswellasdevelopingappropriatetoolsfortheirmeasurement(Bonami2014,Boye

ms.,Sims2015,Bonami&Beniamine2015,BaermanonSeri(toappear),amongothers)

(2)morecarefullyexplorethenatureofthephonological/phone+cs+mulicons+tu+veofwordinternalstructureand,moregenerally,inquireabouttheappropriateformsthatwordsasobjectsofanalysisshouldtake=morphophone+cs(Lehiste1972,Kempsetal.2005,Blazej&Cohen-Goldberg2015,Seyfarthetal.2015,Plaget.al.2015,amongothers)

(3)explorehowanalogicalinferencemayrelyuponimplica+veorganiza+oninthelearningofcomplexmorphologicalsystems(Baayen&Ramscar2015,Ramscaretal.2015),and

(4)iden+fycross-linguis+cgeneraliza+onsconcerningpossibleconstraintsontheorganiza+onofmorphologicalsystems(Stump&Finkel2013,Baermanetal.2015,Ackerman&Malouf2015,Sims&Parkertoappear).

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52

AndtheendofallourexploringWillbetoarrivewherewestarted Andknowtheplaceforthefirst&me.T.EliotLiOleGiddingV

Thebigques+on:

Q1:Whatensuresthelearnabilityofcomplexinflec+onalsystems? A1:(Partly)theinferen+alorganiza+onthatemergesandinheresincomplexinflec+onalsystems:I-complexityasconstrainedbytheLowEntropyConjecture.

Contributoryques+ons:

Q2:Whatisthenatureofwordinternalstructure?A1:Discrimina+veQ3:Whatisthenatureofparadigmorganiza+on? A3:Implica+ve Q4:Whatisthenatureoflearningasitrelatestoparadigmorganiza+on? A4:Analogical(implicitintoday’spresenta+on,butseepa\erngeneraliza+onliteratureonsta+s+cal

learning)

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Asurprisinglysimplecase

InChiquihuitlánMazatec,verbsaremarkedforpersonandaspectbyacombina+onoftones,finalvowel,andstemforma+ve(Jamieson1982,Capen1996,Baerman&Corbe\2010)

Posi+veparadigmforba3se2‘remember’

NEUTRAL INCOMPLETIVE

SG PL SG PL

1INCL ča2sẽ2 ča2sẽ42

1 ba3sæ1 ča2sĩ24 kua3sæ1 ča4sĩ24

2 ča2se2 ča2sũ2 ča4se2 ča4sũ2

3 ba3se2 kua4se2

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NEUTRAL INCOMPLETIVE

SG PL SG PL

1INCL 2-2 4-421 3-1 2-24 3-1 4-242 2-2 2-2 4-2 4-2

3 3-2 4-2

NEUTRAL INCOMPLETIVE

SG PL SG PL

1INCL -ẽ -ẽ

1 -æ -ĩ -æ -ĩ2 -e -ũ -e -ũ3 -e -e

NEUTRAL INCOMPLETIVE

SG PL SG PL

1INCL ča- ča-1 ba- ča- kua- ča-2 ča- ča- ča- ča-3 ba- kua-

-s-‘remember’

ToneclassB31

Finalvowel-e

Stem-forma+ve11

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Implica&onalrela&ons

Eachoftheseseparateinflec+onalsystemsshowconsiderablecomplexity

Eachlexicalitemisamemberofsomeconjunc+onineachofthesethreesystems

Therearepoten+ally6×10×18=1,080meta-conjuga+ons

Baerman&Corbe\reportthat109area\estedinCapen(1996)

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Implica&onalrela&onsTheseappeartobeindependentsystemsofinflec+onclasses

ByBaerman&Corbe\’scount,mostjointconjuga+onshaveonlyoneortwomembers;themostfrequenthas22

Knowingwhichclassalexemebelongstoinonedimensionprovidesrela+velyli\leinforma+onaboutanotherdimension:

Expectedentropyforchoosingaclassinadimensionis2.469bits

Expectedcondi+onalentropyforchoosingaclassinadimensionknowingtheclassinanotherdimensionis2.154bits

Jamiesonoffersdiachronicexplana+onsforthedevelopmentofthiscomplexity,buthowisitmaintained?

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Implica&onalrela&onsConsideralessabstractproblem:giventhestemforma+ve,finalvowel,andtonepa\ernofawordform,guessthestemforma+ve,finalvowel,andtonepa\ernforsomeotherwordform

Thisturnsouttobemucheasier:fortheposi+veneutralforms,theexpectedentropyis4.920bitsbuttheparadigmentropyisonly0.709bits

Everywordformprovidesinforma+onaboutallthreedimensions

Jamieson’sinflec+onclassesshowahighdegreeofinter-paradigmsyncre+sm,solis+nglexemesbyclassgreatlyoverstatesthevaria+on

ComparedtoModernGreek,wri+ngadic+onaryofChiquihuitlánMazatecissignificantlyharder(E-complexity),butspeakingitisn’t(I-simplicity)

58

Somecaveats

Entropycalcula+onsdependonmany,manyassump+ons

Iden+fica+onandenumera+onofforms

Frequenciesoflexemesandwordforms

Choiceof(sub-)paradigms

Generalizingfromasingle,randomlyselectedform

Thenumbersshouldbeinterpretedwiththisinmind

Whatisclear,however,isthatparadigmentropiesaremuchlowerthantheycouldbe

59

Tes&ngentropyclaims

Theimplica+onalstructureoftheparadigmsiscrucialtoreducingparadigmentropy

Howcanwetestthis?

Nullhypothesis:ParadigmentropyoflanguageLisindependentofparadigmorganiza+on

Ifthisistrue,thenL0,aversionLwiththesameformsandthesameclassesbutadifferentorganiza+on,shouldhavemoreorlessthesameparadigmentropy

Bootstraptest:samplewithreplacementfromthespaceofpossibleL0’s,andcomparetotheobservedL

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Chiquihuitlán Mazatec

Paradigm entropy (bits)

Per

cent

of T

otal

0

5

10

15

20

0.7 0.8 0.9 1.0 1.1 1.2

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Language Cells Realiza&ons Declensions Declensionentropy

Expectedentropy

Paradigmentropy

BootstapAvg Bootstrapp

Amele 3 31 24 4.585 2.882138071081.105330679521.32749714946 0.001Arapesh 2 41 26 4.700 4.070538035410.6299016827340.629901682734 1Burmeso 12 24 2 1.000 1 0 0 1Fur 12 80 19 4.248 2.394762454520.5168808443561.31619569963 0.001Greek 8 12 8 3.000 1.621 0.644 0.891 0.001Kwerba 12 26 4 2.000 0.8639723955630.428030303030.522673331721 0.001Mazatec 6 356 109 6.768 4.92 0.709 1.1 0.001Ngi+ 16 68 10 3.322 1.936641648330.4839928968691.01926185459 0.001Nuer 6 12 16 4.000 0.8636758201390.7926130922220.810940247458 0.16Russian 12 26 4 2.000 0.9111528644480.5375256392580.541181039402 0.383

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Externalfactors

Amele(Roberts1987)isdescribedinWALSashaving31differentclassesofpossessivesuffixesplusapostposi+on

HeinandMüller(2009)arguethatfactoringoutphonologicallypredictablealterna+onsreducesthisto23suffixedclasses

H&M’sparadigmshaveanentropyof1.105bits!

But,somefacts:

Possessivesuffixesonlyapplytoaclosedclassof109inalienablypossessednouns

Acombina+onofalmost(butnotquite)categoricalseman+candphonologicalpa\ernsgeneratemostoftheclasses

Manyclasseshaveonlyasinglemember

63

Prospects

ParadigmentropymeasuresthecomplexityofaparadigmwithrespecttotheParadigmCellFillingProblem

TherearemanywaysthatmorphologicalsystemscanbeE-complex,but(perhaps)onlyonebasicprincipleofI-Simplicity,thoughmanywaystogetthere.

Ques+ons:

Whatistherangeofparadigmentropiesinrealtypologicallydiverselanguages?

Whatarethewaysthatparadigmscanbeorganizedtomanagecomplexity(andkeepparadigmentropylow)?

Arethereotheraspectsofmorphologicalsimplicitythatcanbequan+fied?

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