Introducing OT

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Introducing Optimality Theory

Author(s): D. B. ArchangeliSource: Annual Review of Anthropology, Vol. 28 (1999), pp. 531-552Published by: Annual ReviewsStable URL: http://www.jstor.org/stable/223405

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Annu.Rev. Anthropol.1999. 28:531-52Copyright? 1999 by Annual Reviews. All rightsreserved

INTRODUCING OPTIMALITY THEORYD. B. ArchangeliDepartmentof Linguistics,Douglass Building200E, UniversityofArizona, Tucson,Arizona85721-0028; e-mail:[email protected] Words: phonology, constraints,universal grammar, linguistics, Tibetan,Tonkawa* Abstract Optimality theory was introduced in the early 1990s as analternative model of the organization of natural humanlanguage sound systems.This article provides an introduction to the model for the nonlinguist. Thebasic principles of optimality theory are introduced and explained (GEN, CON,and EVAL). Three important constraint families are explored (Faithfulness,Alignment, and Markedness). Illustrations are provided involving syllabifi-cation and vowel harmony in Tibetan and prosodic phonotactics in Tonkawa.The article closes with two general discussions. The first addresses recurringissues in phonological and linguistic analysis and sketches how optimalitytheory might account for these. The second points out how the explanationsarrived at through optimality theory are providing new answers to familiarquestions, as well as raising new questions for study.

CONTENTSIntroduction ................................................... 532Background .................................................. 533The Structure of Optimality Theory ................................ 534Universal, Yet Violable, Constraints ............................... 535Faithfulness Constraints ..................................... ....... 535MarkednessConstraints ............ .......................... 536FurtherInteractionsof Faithfulnessand Markedness ...................... 536GEN ............................................................. 538EVAL ............................................................ 538A Returnto Tibetan........... ................................. 539

Consequences ..................................................... 540Other Domains of Explanation ................................... . 540VowelHarmony .................................................... 541

0084-6570/99/1015-0531$12.00 531


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532 ARCHANGELIVowelHarmonyvia Alignment ........................................ 541VariableLow Vowels via Faithfulnessand ConstraintRanking ............. 542Markednessand FeatureAlignment .................................... 543

Empirical Extensions ........................................... 543Conclusions ...................................................... 546Consequences ..................................................... 546Some MarkednessConstraints ....................................... 547

Phonological Issues and How OT Addresses Them ................... 547Phonotactics and Alternations ....................................... 547Inventories ....................................................... 547MorphemeStructureConstraints ..................................... 548Contexts(or Environments) ......................................... 548Exceptions ....................................................... 548ExtralinguisticPhenomena .......................................... 549OTBeyondPhonology .............................................. 549New Questions; New Answers .................... ................ 549Representations.................................................. 549Nature of Constraints .............................................. 550Natureof Languages ................................................ 550Evaluationof Analyses .............................................. 550C onclusion ................................................... 550

INTRODUCTIONOptimality theory (OT), first introduced in Prince & Smolensky 1991, has sweptthrough formal linguistic research. On encountering the formally simpleconstraint-based optimality model, phonologists abandoned rules with alacrity toexplore the hypothesis that universal constraints alone, rather than a mix of con-straints and rules, account for linguistic phenomena. Phonology suddenlyemerged as focusing on universals, rather than on the specific language-particulardetails of rules. Research into phenomena in other domains-morphology, syn-tax, language acquisition, and change-has also been considered in terms of OT.A wide-spread change in paradigm happened with remarkable speed.In this article, I discuss the new paradigm and show how the model works andhow it characterizes the nature of language. I hope that the examples used not onlyare clarifying but that they provide the reader with a sense of why this model hasinspired such enthusiasm. I also aim to prepare the reader to understand moreadvanced work in the model and perhaps even to feel encouraged to experimentwith the optimality paradigm in domains outside of theoretical linguistics.OT is a theory of linguistics. Before delving into the model itself, this reviewoffers a brief and general discussion of formal linguistics. Most work in OTexplores phonological phenomena and the interface between morphology andphonology; thus, the discussion focuses primarily on those domains. By neces-sity, I assume some prior understanding of principles of phonological analysis.The remainder of the article provides examples of the ways OT explains phenom-


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ena,reviews some of thenonphonologicalapplicationsof OT,and raises some ofthe issues OT faces as a theoryof grammar.

BACKGROUNDLinguistics, broadlyspeaking, explores all aspects of natural anguage.Currentlinguistictheorytakes the Chomskyanview that there is a geneticpredispositionin humans to learn language, and that this predispositionresults in languagesbeing fundamentallysimilar (e.g. Chomsky 1957, 1975, 1986; Pinker 1994).Nonetheless, only a little experiencewith differentlanguagesmakesit clear thatlanguagesareby no means identicalto each other. The similarity,then, is at anabstract evel. Linguistsattempt o developa formalmodel of the linguistic capa-bilities of humans,a model that characterizes he fundamental imilarities whilepermitting hemyriadvariations hatappear n natural anguage.The termuniver-sal grammar efersto theinnate inguisticcapabilitiesof humans.Thegrammar feachspecific language s one of thepossibilities permittedby universalgrammar.The linguist attemptsto develop a theoryof universalgrammar hatclearlyandcorrectlydelineatespossible andimpossible grammars.Inthe domainof phonology, universalgrammars intendedto accountfor theregularitiesand variations found in the linguistic organizationof sound. Thisincludes means for expressingthe following propertiesof the speaker'sknowl-edge of his/herlanguage: a) phonotactics, he overallsoundpatternof wordsin alanguage; b) alternations, ariations nthe form of amorpheme n differentsitua-tions; (c) segmentinventories,the segmentsusedby a language,bothunderlyingand surface; (d) morpheme structureconstraints,the sound patternsof mor-phemes in a language;(e) contexts (or environments), he characterof the situa-tions that conditionalternations;and(f) exceptionsto any of the above.Inthe linguisticdomains,the ideal model will providea means of characteriz-ing the fundamentalsimilarities among languages, of expressing the variationthatdifferentiates anguages,and of predicting types of patterns hat shouldandshouldnot exist. It is always tempting o tryextendingamodel to includeextralin-guistic phenomena,propertiesof the linguisticorganizationof soundthatarenotpropertiesof the adultgrammar, or examplefirst or secondlanguageacquisitionpatterns,historicalchange,and dialectalvariation.OT, proposed as a universal grammar or phonology (Prince & Smolensky1993, McCarthy& Prince 1993a),meets the challengesabove moredirectlythanany othermodel of phonology. At the heart of OT is the idea of universalcon-straints, which are nevertheless violable. By being universal, the constraintsthemselvesprovidean explicit meansof characterizinghe cross-linguisticsimi-larities that exist. By being violable, there is a means of expressing languagevariation: he degreesof violationtolerated or each constraintareuniqueto eachlanguage.OTproposesa single meansof expressingwhich constraintsare viola-ble, namelyconstraintranking-violations of lower-ranked onstraintsare toler-ated in orderto satisfy higher-ranked onstraints.


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THE STRUCTURE OF OPTIMALITY THEORYGrammar s deceptively simpleunderOT. At the universal evel, there is a set ofconstraintson phonological representations CON). There is also a means forgeneratingrelationshipsbetweenanactualinputand all potentialoutputs(GEN).Finally,there is a mechanismfor simultaneouslyevaluating hepotentialoutputsagainstthe set of rankedconstraints n orderto select the optimaloutputfor theinputin question(EVAL).At the language-particularevel, each languageneedsto identify its set of inputsand an appropriate ankingof CON, called the con-strainthierarchy.The informationencoded for a specific language works withuniversalgrammarFigure1).Onencounteringaninput,GENcreatesa candidateset, showing correspondencesbetweenelementsinthe candidatesandelementsinthe input.EVAL thentakesover,usingthe constrainthierarchyof the languagetoselect the optimaloutputfor thatinput.Exploringsome aspectsof syllabificationwill makethismodel concrete.Pho-nologists generallyassumethatin all languagesthe soundsof wordsareincorpo-rated into some syllable, the exhaustive parsing hypothesis (see Ito 1986):Consonants Cs) andvowels (Vs) thatarenot syllabifiedarenotpronounced.Thishypothesisclaimsthat the syllable structuredeterminessurfacesequencingof Csand Vs. For example, a languagewith CV syllable structureallows stringslikeCV, CVCV, CVCVCV,etc butdoes not allow stringslike VCV, CVC, CVCVC,etc. (for otheradvantages o syllabification,see Clements& Keyser 1983, Blev-ins 1994).A general observation about syllable structureuniversals is that althoughmany languagesdesignateCV or CV(C) as the syllable template, sequences likeC, VC, and(C)VCare neverso designated.The contrast s characterizedby fouruniversal constraints(by convention given in small caps): ONSET,a syllable-initial consonant;PEAK, he most sonorous part of the syllable; NOCODA, o

KEYoval: grammarf languageLG)box: UniversalGrammarcircle:derivedbyinteraction /of UGandLG

Figure 1 A schematicgrammar t work.


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syllable-finalconsonant;andCOMPLEX,yllable margins(onsets, codas) containat most one consonant.These four constraintsdo not conflict with each other:every CV syllable satisfies them all, e.g. [mi.co] "mico,"[ma.ri.ne] "marina"(the period separates two syllables). Furthermore, hese constraints are goodcandidatesforbeing universals,for two reasons.First,togetherthey characterizethe most common type of syllable, CV: Every language allows this syllableregardless of the othertypes of syllables that occur in the language. Second, ifa language allows only one type of syllable, that syllable is CV (e.g. Blevins1994).However,these constraintsare notparamountn all languages.Numerous an-guages, includingEnglish, allow syllables with codas (e.g. [lan] "lawn"),sylla-bles without onsets ([an] "on"),or even syllables without vocalic peaks (e.g. thefinal sound in [dap,l] "dapple").The existence of such languages demand thatthese constraintsbe violable.

UNIVERSAL, YET VIOLABLE, CONSTRAINTSThis section explores the centralOT hypothesis:Universal constraintsare vio-lable;theydo nothold absolutelytruein all languages.First,two generalfamiliesof constraints,faithfulness and markedness,are discussed. These, along withalignment constraints, form the core constraints in OT. Second, the modelsketchedin Figure 1, showingthe effects of GENandEVAL, is detailed.Finally,a fragmentof theTibetangrammar, elying primarilyon Dawson (1980) fordata,is analyzed.

Faithfulness ConstraintsOne general propertyof phonological systems is that the input,or mentalrepre-sentation,and the output,or surfacerepresentation,are largely and essentiallyidentical.With an inputof/fals/ ("false"),we expect (andare rewardedwith) anoutput hat is similar,i.e. [falts],rather hansomethingbearing ittle resemblanceto the input(suchas [kaet] r [tru]).Thesimilaritiesareexpressed nOT via a fam-ily of faithfulness(or correspondence)constraints,constraints hatrequirecorre-spondencebetween the inputand the output.Althoughthis might in principlebeviewed as a symmetricrelation(inputandoutputare identical),there is substan-tial evidence supportingasymmetric correspondencerelations. The example of/fals/ X [falts] is illustrative.Every input sound has an output correspondent(f,a,l,s), but thereis anoutputsound(t) that does nothave aninput correspondent.Examples illustrating he opposite asymmetryexist as well. These involve inputsoundswith no outputcorrespondent,llustratedby theV/0 alternationn the twopronunciationsof "separate," sspeart/[s?pret].These correspondencesare formally characterizedby the faithfulness con-straints. The class of faithfulness constraintsthat insists that propertiesof theinput correspond o propertiesof the outputare called MAX (maximizethe input)


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536 ARCHANGELIconstraints.Those demanding hat the outputcorrespond o the inputaredubbedDEP outputdependson input)constraints.TheMAXand DEPconstraint amiliesarerelativized to every type of phonological structure-features, segments, andprosody.1As shown in particularby the alternatepronunciations[ssperat/[sEpr9t]"separate," aithfulness is violable. In fact, were faithfulness inviolable, therewould be no phonology: inputand outputwould always be identical.However,alternationsabound, nEnglishandelsewhere. Additional ypesof constraintsarenecessaryin order o account forthetypes of alternations ound. We exploretwoadditionalconstraint amilies in thisarticle.The first is themarkednessconstraintfamily, a set of constraints hatpreferunmarkedconfigurations.

MarkednessConstraintsMarkednessconstraintseither demandunmarkedconfigurations,such as ONSETand PEAK,or prohibitmarkedconfigurations,such as NOCODA nd COMPLEX(definedabove). These constraintsresultin a preferencefor CV syllables (Table1). Any othertype of syllable violates at least one of these constraints.Table 1 shows that,with respectto thismodel, Englishis lenient in its syllablestructure:Violations of each of these markednessconstraintsare tolerated.As iswell-known, this is not universal.Many languages permit only limited types ofsyllables (see Blevins 1994 for a typology). UnderOT,these differences are char-acterizedby the relative mportanceof the variousmarkedness onstraintsandthedifferent faithfulness constraints[this typology is due to Prince & Smolensky(1993)]. Table2 illustrateshow differentrankingsof ONSET, OCODA,ndfaith-fulness resultin differentsyllable types.

FurtherInteractionsof Faithfulnessand MarkednessWheninputstringsdo not conformto the syllable structure onstraintsof the lan-guage, the differentrankingsof the two classes of faithfulnessconstraints,MAXand DEP,have different effects. In addition, it is important o understandhowGEN andEVAL each work. ConsiderTibetansyllabification(Dawson 1980).1MAX ndDEPwere introduced n McCarthy& Prince(1995) to replacethe faithfulnessconstraintsPARSE nd FILL rom earlierwork (Prince& Smolensky 1993, McCarthy&Prince 1993a). There are two chief differences.First,the MAX/DEPmodel uses the samemeans to relate inputsand outputsthat it uses to relatereduplicantsand bases. Thus, theMAX/DEPmodel unifies the formal treatmentof correspondingrelationsin phonology,rather hanrequiringone type of relationfor input-output orrespondenceand a differenttype forbase-reduplicant orrespondence.Second,theMAX/DEPmodel abandons hecon-tainmenthypothesis, hateverycandidate ora given input iterallycontains hat nput,ahy-pothesis that led to a varietyof very complex mechanismsthat servedonly to satisfy thehypothesis,as well as failing utterly o explainmetathesis see McCarthy1995).UndertheMAX/DEPmodel,relationsbetweeninputandoutputare indicated oreverycandidate theconvention is to use subscripts;matchingsubscripts ndicatecorresponding lements).


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TABLE 1 The universalpreferencefor CV syllablesONSET PEAK NOCODA COMPLEX

CV [ra]"raw"V [ae.pl]"apple" *C [ae.pl]"apple"CVC [kaet]"cat"CCV [spa] "spa" *VC [aet]"at *CCVC [flaep]"flap" * *CVCC [taesk]"task" * *VCC [ask] * * *CCVCC[flaesk]"flask" **

TABLE 2 Syllable typology underoptimality theoryaONSET >> FAITH FAITH >> ONSET

NOCODA > FAITH CV (Hua) CV, V (Hawaiian)FAITH > NOCODA CV, CVC (Cairene) CV, V, CVC, VC (Mokilese)aMAXand DEPare collapsed togetheras a single constraintFAITH.Example languagesaretaken fromBlevins 1994.

Tibetan syllables allow single onsets and at most a single coda, which suggeststhat ONSET,COMPLEX outrank faithfulness, which in turn outranks NOCODA.Whennumberscombineto formteensandtens,an"intrusive onsonant" s foundat the boundarybetween the two morphemes (Table 3). The varietyof types ofintrusiveconsonantsarguesthatthey arein fact partof the input representation.Thedatahere arecompatiblewithananalysisin which the intrusiveconsonantis the initialconsonantof the secondmemberof thecompound e.g. /pu/ -> [cu],"ten"; /ija-pcu/ -> [rapcu], "fifty"; but /pcu-i-a/ -- [cuia], "fifty"). Theessence of the analysis is thatthe initial/p/ of/pcu/ survivesonly when it cansyl-labify-and it can only do so when it follows a vowel. Undermorphemeconcate-nation, the CC sequence survives if a vowel-final morpheme comes first(/ia-pcu/ -- [iapcu]). However,whenthe CC sequenceis word-initial,syllabi-fication fails to rescue/p/, so it does not surface(/pcu/ -> [cu]).


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TABLE 3 Tibetannumbersshowing the "intrusive" onsonantappearingbetween two numberswhen they areconcatenatedwith eathotheraTeens TensSimplex Gloss (10-#) Gloss (#-10) Gloss

cu Tencik One cukcik ElevenIsi Four cupsi Fourteen sipcu Fortysipsi Forty-fourqu Nine curqu Nineteen qupcu Ninetyia Five cuia Fifteen r apcu FiftyaSimplexnumbers surfaceas CV or CVC. When numbersconcatenateto forma complex number,aconsonantoften appearsbetweenthe two morphemes.In the "tens," his consonantis always [p], butin the teens, the consonant variesdependingon the second number [k] with"one,"[p]with "four," r]with "nine,"andnothingat all with "five").Dataare fromDawson 1980 and Halle & Clements 1982;the Halle/Clementstranscriptionhas been modifid to match that of Dawson.

GENInOTanalysisof the surfaceformsof/pcu/, (asdepicted nFigure1),the firststepis theinput, pcu/,"ten."GEN matchesthis inputwithoutputcandidatesby show-ingcorrespondencesvia subscripts)betweenthesegmentsof/pcu/ and thecandi-dates(Figure2).The mappingsshownin Figure2 arerepresentativeof the kindsof thingsthatGEN can do. GEN can show correspondenceswith an outputcandidatethat iscompletely faithful, [plC2U3], ut it can also show correspondenceswith outputcandidates hatarenot completely faithful.Differencescan occur in a varietyofways:by the featuresof the corresponding lements, [klr233];by the orderof thecorresponding lements, [c2u3pl];andby a mismatch n the numberof elements,['2u3] and [pli'2u3]. Additionally, it is formallypossible to have outputcandi-dates thatbearno correspondence elation o the inputatall, regardlessof the seg-mentalmakeupof the string, [c7u9].Inprinciple,GENprovidescorrespondencesto an infinite numberof candidates;2n practice,linguiststryto select the candi-dates that are closest to the winner and to show how these are eliminatedbyEVAL.

EVALThedevice used in OTresearch o provethat a given constraint anking ucceedsin selectingthe optimaloutput ormis called a tableau.Thetableauhasa specific21nhercomputationalmodel,Heiberg(1999) proposesanalgorithm o avoidtheproblemofGENproducingan infinite set of candidates.


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PI23 kr233Figure 2 Theresultof feeding pcu/intoGEN.

form,with constraints isted acrossthetop andcompetingcandidates isted downthe left side (Tableau 1, online only; also available throughhttp://AnnualRe-views.org,ElectronicMaterials).Theconstraint anking s depictedby the left-to-rightorder of constraints,with the leftmostbeing the most dominant.Wheretherankingof constraints s critical,a solid verticalline separates he constraints e.g.between FAITH ndNOCODAn Tableau 1). Wherethe rankingof constraints snot critical(i.e. neithercruciallyoutranksheother),eitheradashed ine orno lineat all separates the constraints (e.g. between ONSETand COMPLEX).Fatalviolations are violations of the highestrelevant constraint. n Tableau1,both candidatessucceed with ONSET nd COMPLEX;hese two constraints, hen,arenot relevant forselectingbetween the candidates.Candidatebviolates FAITH,a constraint hat candidatea satisfies. Cells forNOCODAreshaded,becausesuc-cess or failure with this constraintis irrelevant:The contest has alreadybeendecided.

A Return to TibetanIt was shown abovethatwhen/pcu/compoundswith/ra/, "five," hefully faithful[ijapcu]surfaces because of the subordinatestatus of NOCODA.Why does theconsonantnot surfaceeverytime? Tableau2 (online only; also availablethroughhttp://AnnualReviews.org,ElectronicMaterials) selects the unfaithful CV-syllable candidate[cu], because of the absenceof a COMPLEXiolation.The two candidatesin Tableau2 are equivalentwith respectto ONSET,but thefaithfulcandidatea violates COMPLEX, constraint hatthe unfaithfulcandidatebsatisfies. Here, then, the output s not identical to the input.There is a further candidate to consider. The COMPLEXiolation can beavoided through epenthesis (the additionof a vowel), giving a form like [pi.cu](Tableau3, online only; also available through http://AnnualReviews.org,Elec-tronicMaterials).The completely faithfulcandidatea is eliminatedby COMPLEX.andidatesband c, however, tie in their violation of FAITH:How will the grammarselectbetween them? The answer is that faithfulness is asymmetric.The unattested*[pi.cu](withvowel epenthesis)violates DEPwhereas the attested[cu](withcon-sonantdeletion)violates MAX.As Tableau4 (online only; also availablethrough


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http://AnnualReviews.org,ElectronicMaterials)demonstrates, ankingDEPoverMAX dentifies the correctcandidate.3WereMAX o outrankDEP, he surfacepatternwould show epenthesisratherthandeletion. This is a desirableresult.Epenthesisoccursinnumerous anguages(possibly including English:Epenthesismightbe invoked to accountfor the con-trast between past-tense [t/d] in [kist], "kissed,"and [fizd], "fizzed,"and past-tense [ad] in [fited], "fitted").

ConsequencesUniversal constraints,constraintviolability, and constraintrankingprovide theexplanatorypower of OT, giving the means to explain strong cross-linguisticsimilarities (universals),cross-linguisticvariation(violability), and typologicaldifferences(ranking).This section examines the impactof hypothesizinguniver-sal andviolable constraints, pecificallymarkednessandfaithfulnessconstraints.First, universal constraintsprovide a means of characterizing he similarityamong the phonologies of the world's languages. The phonologies are similarbecause they areexpressedin terms of the same set of constraints.Second,the violability hypothesisallows languagesto differ from each other.The degree of violation toleratedfor any given constraint s a propertyof eachparticular anguage. In this way, OT characterizes he two key factors of lan-guage:thehighdegreeof cross-linguisticsimilaritycombinedwith thepossibilityof certaintypes of differences between languages, namely differences attribut-able to differentrankingsof CON.Finally, rankingdifferences provide a means of characterizing ypologicalvariationamongthe world's languages.As shown in the examplesabove, differ-entrankingsof the syllablemarkednessconstraintswith faithfulnessproducetheattested ypology of languagesbasedon surfacesyllablestructure.Different rank-ings of the two classes of faithfulness constraints,MAXand DEP,divide lan-guages in a differentway, those thatavoid violationof higher-ranked onstraintsthrough insertion (MAX > DEP) and those that do so through deletion (DEP >MAX).

OTHER DOMAINS OF EXPLANATIONExtensions to other domains involving prosody, such as prosodic morphology[reduplicationandtemplaticphenomena McCarthy& Prince 1993a, 1995;Hen-dricks 1999)] andmetricalphenomena[stressand otherfoot-basedalternations(Hung 1995, Hammond1997, 1999)] arerelatively straightforward, articularly

3A urtherandidatehallengesEu]:pu]hasan denticaletof violations. he ie is brokenbyafurtherorrespondenceonstraint,ONTINGUITY,hichdemandshat ontiguousle-ments n the inputbe contiguousn the output. n /pcu/, p/ and u/ arenotcontiguouswhereasc/ and u/ are.Thus, cu]winsover[pu] seeMcCarthy Prince1995).


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when an additional family of constraints is introduced, namely alignment(McCarthy& Prince 1993b). In an effort to provide a broaderunderstandingofhow OTaddressesdifferent ypesof phonological patterns,vowel harmonyratherthanotherprosodic phenomena s used.

Vowel HarmonyThe basic propertyof vowel harmonyis that vowels in a sequence surface assimilar to each other. Thus, within a single word, vowels might be either[+round]or [-round][Hungarian Ringen 1988)], [+back] or [-back] [Turkish(Clements& Sezer 1982)], [+high]or [-high] [Tibetan Dawson 1980)], [+ATR](advancedtongue root), or [-ATR] [Pulaar Paradis1986, Archangeli& Pulley-blank 1994)].In Tibetan,nonhigh vowels rase to become high vowels when concatenatedwith a high-voweled morpheme.Table 4 shows compoundswhere the secondmembercontains ahighvowel, andTable 5 shows compoundswith anunderlyinghigh vowel in the first member.There are three importantgeneralizationsabout Tibetan [+high] harmony:[+high] regressesfromrightto left; [+high]progressesfrom left to right;andpro-gression does not affect long, low vowels.

Vowel Harmony via AlignmentIn order o account for theregressiveandprogressivepatternsof height harmony,I use the alignment family of constraintsfrom McCarthy& Prince (1993b).Alignmentconstraintsprefer hattheedges of two categories,eitherphonologicalormorphological,match.Thepattern een here canbe expressedby matching heedge of thefeature[+high]with therightand left edges of the word.As withfaith-fulness, alignmentis asymmetric:Separateconstraintsenforce alignmentto theTABLE4 Tibetan+high]harmonyncompounds:hesecondmember f thecompoundsintrinsically [+high]aN1 Gloss N2 Gloss NJ + N2 Gloss

me Fire siri Wood misii FirewoodJIEl Sleep qhuu Tent pIIlquu Mosquitonetto Stone puu Pile tupuu Pile of stonesloo Electricity rii Price luurii Price of electricityqhaa Snow ri Mountain qhaari Snow-mountainaThecompound surfaceswith high vowels throughout.An affected low vowel surfaces as [a]. Following Dawson 1980,this is a [+high] vowel.


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542 ARCHANGELITABLE5 Tibetan+high] armonyncompounds:he irstmember f thecom-pounds intrinsically+high]aN1 Gloss N2 Gloss N1 + N2 Gloss

ri Mountain tse Tip,peak ritsi Mountaineaku Head Jpee Pillow upII Pillowmi Person tho List mitu Listof peoplequ Body loo Lungs quluu Lungsu Head ta Hair ute Hair

ripaa, Wildboar*ripaeaThesecompoundsalso show high vowels throughout; ee footnote in Table 2. However,when the secondvowel is a long /aa/, this vowel does not raise but surfaces intact as [aa].

right and to the left. Thus, underthis hypothesis, Tibetanmust have two con-straints aligning [+high], one to the right and one to the left. ALHIR,akaALIGN([+high],ight,word,right),wheretherightedge of every [+high]alignstothe right edge of some word; and ALHIL,akaALIGN([+high],eft, word, left),wherethe left edge of every [+high] alignsto the left edge of some word.Tableau5 demonstrates he role of ALHIL,and Tableau6 shows ALHIR tableauxonlineonly; also availablethroughhttp://AnnualReviews.org,ElectronicMaterials).These constraintscover the first two generalizationsabout Tibetan [+high]harmony: [+high] shows both progressive and regressive harmony.But whataboutthe thirdproperty, he variablebehavior of the long, low vowels?

VariableLow Vowelsvia Faithfulnessand ConstraintRankingLow vowels show faithfulness o their nputvowel heightin away thatothervow-els donot:Long, low vowels areexemptfromtherightwardalignmentof [+high],although heyare not exemptfromleftwardalignment.The faithfulness o [+low]suggests a constraintMAxLow (every input[+low] vowel has some [+low] out-put correspondent), orcingthe preservationof input[+low]. MAxLow mustberanked between the two alignment constraintsso that leftward alignment isoblivious to [+low] specifications and rightwardalignmentis sensitive to them(Tableaux7 and8, onlineonly; also availablethroughhttp://AnnualReviews.org,

ElectronicMaterials).Tableau 7 shows that leftward harmony is obtained in [qhoeri] becauseMAxLo is subordinateto ALHIL. By contrast, because MAxLo dominatesALHIR, ightwardharmonydoes not alter aa/ in [ripaa] Tableau8). Statedmore


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TABLE 6 Harmonytypology via constraintrankingaRanking Effect Examples

ALIGN >> MARKEDNESS Harmony proceeds regardless Maasai, Turkana, Wolof, Nezof the type of sound created Perce, ChukcheeMARKEDNESS>> ALIGN Harmony is prevented from Pulaar, Yoruba, Wolof,creatingmarkedfeature Menomini,Maasai, Turkana,combinations TibetanaLanguages hat fall into both categoriesare like Tibetan:Harmonyproceedsin two directions and is blocked in one direc-tion but not in the other. Examplesother thanTibetan are fromArchangeli& Pulleyblank 1994.

generally, harmony is obtained when ALIGN> FAITH;harmony is blocked whenFAITH> ALIGN.4Markedness and Feature Alignment

There are other ways in which harmony might be prohibited, for example throughfeature markedness. Feature markedness refers to the likelihood (or the unlikeli-hood) of certain features co-occurring. For instance, vowel height features andtongue root features have a close connection (see Archangeli & Pulleyblank1994): Tongue root advancement, [+ATR], and [+high] are compatible, as are[+low] and tongue root retraction (or [-ATR]). The opposite combinations are notcompatible. These constraints interact with alignment of [ATR] predicting atypology of tongue root retraction harmony (Table 6).

EMPIRICAL XTENSIONSAlignment can readily be extended to other empirical domains, such as prosodicphenomena. Alignment of the word edge to a foot edge forces initial or final stress(Hung 1995; Hammond 1997, 1999). Alignment of a reduplicative morpheme toa particular prosodic category forces the reduplicant to take on that prosodicshape (McCarthy & Prince 1993b, 1995). Interactions between alignment andother constraints can force infixation rather than prefixation or suffixation (Hen-dricks 1999). The list goes on.

4Thedifferencebetweenlong, low vowels andshort, ow vowels is that heshort, ow vowelalwaysharmonizes,even wherethelong, low vowel fails to. This introducesa further om-plexity to the constraint amilies:the need to limit constraints o a subset. Here,MAXLOmustbe restricted o long vowels (MAxLO0,).This constraintoutranksALIGNHIR,hichin tur outranks he genericMAXLO:MAxLot > ALHIR>MAXLO.>


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544 ARCHANGELI

Cases involving the interaction of faithfulness, alignment, and markednessillustrate the complex patterns that result from the interaction of relatively simpleconstraints. A case in point is syllabification in Tonkawa. The analysis hereassumes the input forms motivated in the work of Kenstowicz & Kisseberth(1979), shown in the leftmost column in Table 7. Of interest is the observationthat although Tonkawa roots have three vowels in the input form, there are no sur-face forms in which all three vowels surface simultaneously.The challenge is to characterize not only the syllable structure but also the pat-tern of vowel loss in Tonkawa verbs. The first step is to determine which of thesyllabification and faithfulness constraints are inviolable and which are violable.To do so, it helps to make further observations about the Tonkawa data. First, sur-face syllables are either CV or CVC (pi.cen). No syllables start with a vowel, nosyllables have a complex margin, and no syllables have a consonantal peak. How-ever, codas are permitted.Second, the only alternation seen is between the presence and absence of vow-els. As observed in Kenstowicz & Kisseberth (1979), the quality of the vowels isidiosyncratic. This fact suggests that they are present in the input and that in

TABLE 7 Tankawaverb paradigmsshowing vowel/0 alterationsaRootb Gloss Active Progressive Gloss

picena Cut picn-o? picna-n-o? He...itwe-pcen-o? we-pcena-n-o? He...themke-pcen-o? ke-pcena-n-o? He...me

Castratedone, picensteernotoxo Hoe notx-o? notxo-n-o? He.. it

we-ntox-o? we-ntoxo-n-o? He...themke-ntox-o7 ke-ntoxo-n-o? He...meHoe (noun) notox

netale Lick netl-o? netle-n-o? He...itwe-ntal-o? we-ntale-n-o? He...themke-ntal-o? ke-ntale-n-o? He...me

naxace Make into a fire naxc-o? naxce-n-o? He...itwe-nxac-o? we-nxace-n-o? he...themke-nxac-o? ke-nxace-n-o? he...me

aTheroots in the active take eithera monovocalic CVCC or CCVC shape (e.g. picn- or -pcen-), whereasthose in the progressiveshow up as the bivocalic CVCCVor CCVCV(e.g. picna- or -pcena-). Whether hesurfaceform of the root itself startswith CV or with CCdependson whether t is word-initial(picno?)or fol-lows a prefix (wepceno?), respectively.bInput orms motivatedin the work of Kenstowicz & Kisseberth.


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OPTIMALITYHEORY 545Tonkawathereare restrictionson where vowels may surface.To account for theability of vowels, but not consonants,to delete, it is necessary to do somethinghintedat above-to separateMAX nto faithfulnessconstraints argetingspecifictypes of segments.Here,MAXV s violated whereasMAXC,DEPC,and DEPVareinviolable (Table 8).From Table 8, we can extracta working hypothesis that the inviolable con-straints outrank the violable ones: ONSET,PEAK,MAXC, DEPC, DEPV > MAXV,NOCODA. ote how faithfulness(MAxC,DEPC,DEPV,MAXV)and markednessinterweavein this hierarchy.This intricate nteraction s expectedunderthe OThypothesis,which allows each languageits own individual constraintranking.This constrainthierarchy ails to select the correct candidate n certaincases,such as [pi.cen] < /picena/, rather than the well-syllabified by unattested[pi.ce.na](Tableau9, online only; also availablethroughhttp://AnnualReviews.org,ElectronicMaterials).The tableaualso demonstrates hatgiven an an inputlike /picena/, thereis no way to rank markednessand faithfulness constraints oprefer[pi.cen] over [pi.ce.na].A faithful stringof CV syllables is exactly whatthese two constraint amilies prefer.Somethingis necessaryto force vowel loss,incurringMAxV andNOCODAiolations.Further examination of the data reveals two critical generalizations. First,all words are consonant-final. Effects of this sort, where two edges match(here the wordedge and the consonantedge), arethe hallmarkof alignmentcon-straints,alreadyfamiliar nphonology:ALWDCR, kaALIGN(word,ight,conso-nant,right),where the rightedge of every word aligns to the right edge of someconsonant.This constraint s violated by words thatend with vowels and is not violatedby words thatend with consonants. As shown in Tableau 10 (online only; alsoavailable through http://AnnualReviews.org,Electronic Materials), whereALIGNWDCRutranksbothMAXVandNOCODA, word-finalconsonantresults,violatingNOCODA,hroughvowel loss, violating MAxV.

TABLE8 Tonkawa onstraintiolabilityViolability Constraint Example of violationInviolable ONSET Not applicable

PEAKMAXCDEPCDEPV

Violable MAXV pic.no? "He is cuttingit"*pi.ce.na.no?

NOCODA pic.no? "Hecuts it"


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OPTIMALITYHEORY 547althoughfaithfulnessandalignmenthave generalforms,theformulationofmark-edness constraints is not as rigorously defined. Categorizing the constraintsbelow as markednessconstraintsmakes sense from the point of view of strongcross-linguistictendenciesand/orphoneticproperties,but the formalstatementsarenot obviously cohesive.

Some Markedness ConstraintsThe following are examples of markednessconstraints:ONSET,syllables haveonsets; HI/ATR,f [+high] then [+ATR]; and ICC[voice], a sequence of conso-nants must be identical in voicing (see Pulleyblank 1997). Whetheranalyzingdataorstudyingsomeone else's analysis,it is notalwaysobvious whenonepositsa markednessconstraint hat t is indeed a constraintof thatclass. This is differentfromfaithfulness andalignmentconstraints.

PHONOLOGICAL ISSUES AND HOW OT ADDRESSESTHEMThis section sketchesbrieflyhow OTmighthandlethe linguisticorganizationofsounds.

Phonotactics and AlternationsPhonotacticsandalternationsgo hand-in-handunderOT.Theanalysisof the C/0alternation n Tibetanrelies on the overallsyllabificationphonotacticsof the lan-guage; the analysis of the V/0 alternation n Tonkawarelies on the interactionbetween syllable phonotacticsand on two alignmentconstraintsdefining phono-tactics of Tonkawa word edges. The [+high]/[-high] alternation in Tibetanresulted from alignmentoutranking aithfulness.In short,the overall patternofsounds in words will follow largely from the highest-rankedconstraints n thatlanguage,and alternationsresultwhen markednessor alignmentoutranks aith-fulness.A second result of OT is called the emergenceof the unmarked McCarthy&Prince 1994). The point is that subordinatemarkednessconstraintsnonethelesscanmakedecisions about heoptimalcandidate,providedthathigher-rankedon-straints fail to decide. In these cases, an unmarkedconfigurationarises, evenwhen thatconfiguration s not centralto the language.Tableau 13 illustrates hisphenomenon.

InventoriesUnderOT, all constraintsare in the constrainthierarchy.The inventoryof seg-mentspossible in the outputof a languagearethus the set of segmentspermittedby the constrainthierarchy,which evaluatesoutputs.In general,the constraintsmost responsiblearethe highest-ranked egmentalmarkednessconstraints.


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548 ARCHANGELI

In constrastto the straightforwardway in which OT handlesoutputinvento-ries, OT has no direct means for expressing the inventoryof input segments.Because all constraints n OT arein the constrainthierarchy,no constraintsholdover the set of inputs.Thereare, however, devices proposedin the literature oprovide covert limits on the input. The most popularof these is called lexiconoptimization Prince& Smolensky 1993;see also Itoet al 1995).Lexicon optimi-zationcomes intoplaywhen eachof avarietyof inputsproduces he sameoutput;lexicon optimizationthen selects among these inputsfor the one that incurs thefewest violationsof thehighest-ranked onstraints see inparticular to et al 1995for more on lexicon optimization;see Archangeli& Langendoen1997b for dis-cussion of alternatives).

Morpheme Structure ConstraintsThe most naturalway to expressrestrictions hathold morpheme nternally s toinclude constraints imited to particular exical domains.This approachhas theinteresting consequenceof claiming thatmorphemestructure onstraintsreflectuniversalsthatmaynot hold elsewhereinthe language.(Inkelaset al 1997 arguesagainstthis approachandin favorof not representing his type of generalizationin the grammarat all).Contexts (or Environments)

In many cases, contexts for alternationsare irrelevantunder OT: The putativecontext is handled ndependently.For example,Tibetan[+high] spread s condi-tionedby theexistence of a [+high]vowel in the input.This fact can be character-ized by a high-rankedDEPHI,a constraintentirely independentof the [+high]alignmentconstraints.DEPHIprohibitsinsertion of [+high], so that only input[+high] induces harmony. Similarly, it is the rankingof MAxLo that prohibitsrightward preadof [+high],rather hanincludingthis as a propertyof rightward[+high] alignment. In this way, OT is a theory of conspiracies in the sense ofKisseberth 1970): Surfaceeffects aretheresultof the interactionof several inde-pendentconstraints,not the result of a single, highly complex constraint.Despitethese successes, contextsremainone of the least-understood mpiricaldomainswithin the OT paradigm.

ExceptionsDespite the broadgeneralizationsthatwe can make aboutlanguages, therearenonethelessexceptions.Threegeneralproposalshave beenmadefordealingwithlexical items that areexemptfrompartof the constrainthierarchy.First,alterna-tive constrainthierarchies have been set up for exceptional forms, typicallytreatedas a rerankingof constraints hat are critical for the generalcases (Ito &Mester 1993, Ito et al 1995). Second, exceptional forms are simply lexicallyspecified as such (Inkelaset al 1997). Finally, exceptionalbehavioris encodeddirectlyin termsof OT,lexically enteredas anecessaryconstraintviolation(Gol-ston 1996, Archangeli 1999).


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OPTIMALITYHEORY 549

ExtralinguisticPhenomenaA small but growing body of OT work is examiningfirst- and second-languageacquisition (Demuth 1995, Smolensky 1996), language change (Jacobs 1995,Zubritskaya1995), etc. At the centerof much of this work is the OT hypothesis:Differences will be reflected in different constraint hierarchies. This holdswhether the differences are betweentwo stages in acquiringa language,betweenthe hierarchies of an adult's first and second languages, between diachronicstages of a single language,and so on. OTprovidesa clearparadigm-constraintreranking-so that results from extralinguisticdomains influence the develop-ment of the linguisticmodel.Relatedto this arestudies of the learnabilityof OTgrammars Tesar1995,Pul-leyblank& Turkel1995) as well as the interpretation fpsycholinguistic phonol-ogical studiesin termsof OT (Frisch 1996;Hammond1997, 1999).

OT BeyondPhonologyWork in OT syntax can be found as well (Samek-Lodovici 1996, Aissen 1997,Grimshaw1997, Pesetsky 1997, Speas 1997, Barbosa et al 1998). There is littleconsensus at this point in OT syntax. OT, being built for phonological analysis,makes critical use of familiarphonological devices-the UR/input,the SR/out-put.Withsyntax,the natureof the input s ill-defined,anissue exploredby Arch-angeli & Langendoen (1997b): Is it a concept or a set of words? Does it havestructure?Dependingon the answersto these fundamentalquestions,other ssuesarise.Forexample,if the input s simplya stringof words(suchas Mico, Marina,and loves), multiple outputs might correspondto a single input: Mico lovesMarina;Marina oves Mico; Mico, Marina oves; etc). This contrastswith pho-nology, which traditionallymapseach inputto an unambiguousoutput.

NEWQUESTIONS,NEWANSWERSThis article focuses on three main goals: to enable the reader to understandmechanicallyhow OT works, to understandhow OT handlesdifferenttypes ofphonological data, and to understandthe richness of the domains that OTaddresses.This concluding section addressesareaswhere OT challenges us to rethinkargumentsandconclusions once thoughtto be irrefutable.

RepresentationsFor the past two decades,muchphonologicalresearchhas focused on the natureof the representation.Therepresentationdevelopedfromthe linear,unstructuredrepresentations dvocated nthe late 1960s (Chomsky&Halle 1968)to thehighlyarticulatedrepresentations, ncluding word, foot, syllable and moraic structurelinked to independenthierarchicallyarrangedfeatures (see Goldsmith 1994).Interestingly,with OT, the focus has largely shifted fromrepresentationalssues


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(1997a) provide a deeperintroduction o OT, coveringphonology, morphology,andsyntax.Also, theRutgersOptimalityArchiveoffersa searchablecollectionofcutting-edgeworks in OT (http://ruccs.rutgers.edu/roa.html).

Visit the Annual Reviews home page at www.AnnualReviews.org.

LITERATURECITEDAissen J. 1997. On the syntax of obviation.Language 73:705-50Archangeli D. 1999. Lexical irregularity inOT. DOT vs. variable constraintranking.Presented at Annu. Meet. Linguist. Soc.Am., Los Angeles.Archangeli D, LangendoenDT. 1997a. Opti-mality Theory:An Overview.Maiden,MA:BlackwellArchangeliD, LangendoenDT. 1997b. After-word. See Archangeli & Langendoen1997a, pp. 200-15ArchangeliD, PulleyblankD. 1994. Grounded

Phonology. Cambridge,MA: MITPressBarbosaP, Fox D, HagstromP, McGinnisM,Pesetsky D, eds. 1998. Is the Best GoodEnough. Cambridge,MA. MITPressBlevins J. 1994. The syllable in phonologicaltheory. In TheHandbookof PhonologicalTheory,ed. JGoldsmith,pp. 206-44. Cam-bridge,MA: BlackwellChomsky N. 1957. Syntactic Structures. TheHague:MoutonChomsky N. 1975. Aspects of the TheoryofSyntax.Cambridge,MA: MITPressChomsky N. 1986. Knowledge of Language:Its Nature, Origins, and Use. New York:PraegerChomsky N, Halle M. 1968. TheSound Pat-ternofEnglish. New York:Harper& RowClements GN, Keyser SJ. 1983. CV Phonol-ogy: A Generative Theoryof the Syllable.Cambridge,MA: MITPressClementsGN, Sezer E. 1982. Vowel andcon-sonant disharmony in Turkish. In TheStructure of Phonological Representa-tions, PartII,ed. H van derHulst,N Smith,pp. 213-55. Dordrecht:Foris

Cole J, Kisseberth C. 1994. An OptimalDo-mains Theory of Harmony. Cogn. Sci.Tech. Rep. UIUC-BI-CS-94-02. (Lang.Ser.)Univ. Ill., Champaign-UrbanaDawson W. 1980. Tibetanphonology. PhDthesis. Univ. Washington,Seattle. 143 pp.Demuth K. 1995. Markednessand the devel-opment of prosodic structure.Proc. NELingist.Soc.2:13-25Frisch S. 1996. Similarity and frequency inphonology. PhD thesis. NorthwesternUniv., Chicago, IL. 190 pp.GoldsmithJ, ed. 1994. The Handbookof Pho-nological Theory.Cambridge,MA: Black-wellGolston C. 1996. Direct optimality theory:representationas pure markedness. Lan-guage 72:713-48GrimshawJ. 1997.Heads,projectionandopti-mality.Lingist.Inq. 28:373-22Halle M, Clements GN. 1982. Problem BookinPhonology.Cambridge,MA: MITPressHammond M. 1997. Optimality theory andprosody. See Archangeli & Langendoen1997a,pp. 33-58Hammond M. 1999. English Phonology. Ox-ford,UK: OxfordUniv. PressHeiberg A. 1999. Featural optimality theory:a computationalmodel. PhD thesis. Univ.Ariz., Tucson. 318 pp.Hendricks S. 1999. Reduplication withouttemplate constraints: a study of bare-consonantreduplication.PhDthesis.Univ.Ariz., Tucson. 283 pp.

HungH. 1995. Therhythmicandprosodic or-ganization of edge constituents. PhD the-sis. BrandeisUniv., Waltham,MA. 221 pp.InkelasS, OrgunO,Zoll C. 1997. Theimplica-


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552 ARCHANGELItions of lexical exceptions for the natureofgrammar.In Derivations and ConstraintsinPhonology, ed. I Roca,pp. 393-418. Ox-ford: ClarendonIto J. 1986. Syllable theory in prosodic pho-nology. PhD thesis. Univ. Mass., Amherst.228 pp.Ito J, Mester A. 1993. Japanese Phonology.ConstraintDomains and StructurePreser-vation.Tech.Rep.LRC-93-06, Univ. Calif.SantaCruzIto J, Mester A. 1994. Japanese phonology.See Goldsmith 1994, pp. 817-38

ItoJ,MesterA, PadgettJ. 1995.Licensingandunderspecification in optimality theory.Lingist.Inq. 26:571-613Jacobs H. 1995. Optimality theoryand soundchange.Proc. NELingist.Soc. 2:219-32Kenstowicz M, Kisseberth C. 1979. Genera-tivePhonology. New York: AcademicKisseberthC. 1970. On the functionalunityofphonologicalrules.Lingist.Inq. 1:291-306KisseberthC. 1994.AnOptimalDomains The-ory of Harmony. Cogn. Sci. Tech. Rep.UIUC-BI-CS-94-02, Univ. Ill., Cham-paign-UrbanaMcCarthyJ. 1995. Extensionsoffaithfulness.Rotuman revisited. Tech. Rep. ROA-110,Univ. Mass., AmherstMcCarthyJ, Prince A. 1993a. Prosodic mor-phology I: constraint nteractionand satis-faction. Ms., Univ. Mass. Amherst andRutgersUniv.McCarthy J, Prince A. 1993b. Generalizedalignment. In Yearbook of Morphology1993, ed. GBooij, J vanMarle,pp. 79-153.Dordrecht:Kluwer

McCarthyJ, Prince A. 1994. The emergenceof the unmarked:optimality in prosodicmorphology. Proc. NE Linguist. Soc.24:333-79McCarthyJ, PrinceA. 1995. Faithfulness andreduplicative identity. Univ. Mass. Occ.Pap. 18:249-384PadgettJ. 1999. Partialclass behaviorand na-sal place assimilation.In Proc. SWOptim.Theory Workshop,Ariz. Phonol. Conf 5.WorkshopFeatures Optim.Theory, Univ.

Ariz.,pp. 145-83Paradis C. 1986. Phonologie et morphologielexicales. les classes nominales en pulaar(Fula). PhD thesis. Univ. Montreal,Mont-real, Canada.425 pp.Pesetsky D. 1997. Optimalitytheoryand syn-tax: movement and pronunciation. SeeArchangeli & Landendoen 1997a, pp.134-70Pinker S. 1994. TheLanguage Instinct. NewYork: MorrowPrinceA, SmolenskyP. 1991. Optimality.Pre-sented at Ariz. Phonol. Conf. 3, Univ.Ariz., TucsonPrinceA, SmolenskyP. 1993. OptimalityThe-ory. ConstraintInteraction in GenerativeGrammar.RuCCs Tech.Rep. No. 2, Rut-gers Univ. Center for Cogn. Sci., Piscata-way, NJPulleyblank D. 1997. Optimalitytheory andfeatures. See Archangeli & Langendoen1997a,pp. 59-101Pulleyblank D, Turkel W. 1995. Optimalitytheoryand learningalgorithms. the repre-sentation of recurrentfeatural asymme-tries. Presented at Curr. Trends Phonol.,Abbaye de Royaumont,FranceRingen C. 1988. Transparency n Hungarianvowel harmony.Phonology 5:327-42Samek-LodoviciV. 1996. Constraintson sub-jects. an optimality heoreticanalysis. PhDthesis. RutgersUniv., New Brunswick,NJSmolenskyP. 1995. On the internal structureof the constraint component CON of UG.Presentedat LinguisticsDep. Colloquium,Univ. Ariz., Tucson

Smolensky P. 1996. On the comprehen-sion/production dilemma in child lan-guage. Lingist.Inq. 27:720-31SpeasM. 1997. Optimality heoryandsyntax:null pronounsand control. See Archangeli& Langendoen1997a,pp. 171-99TesarB. 1995. Computationaloptimalitythe-ory. PhD thesis. Univ. Colo., Boulder. 121PP.ZubritskayaK. 1995. Markednessand soundchange in OT. Proc. NE Lingist. Soc.2:249-64

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Introducing OT