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A hands-on introduction to Optimality Theory

John Alderete, alderete@sfu.ca Simon Fraser University

Focus: learning how Optimality Theory works by doing problems in it Goals:

1. Grasp some of the core motivation for Optimality Theory 2. Learn the core principles 3. Learn to do OT: ranking constraints, determining the correct constraints, reranking constraints in

factorial typologies 4. Introduce the software tools for doing OT

Table of contents:

1. Some common problems in phonology (and elsewhere) .................................................................... 2  2. Do something, except if … ................................................................................................................. 2  3. Same target, different repair ............................................................................................................... 4  4. Core assumptions ................................................................................................................................ 5  5. Linguistic typology in OT ................................................................................................................... 6  6. The duplication problem and the richness of the base ........................................................................ 8  7. Optimality Theory since 1993—further reading ................................................................................. 9  8. Japanese velars: building a linguistic system .................................................................................... 10  9. Japanese velars again: ranking constraints ....................................................................................... 11  10. Athabaskan laryngeals: a mini factorial typology .......................................................................... 13  11. Doing OT with software ................................................................................................................. 15  12. Syllable universals: more complex typology .................................................................................. 16  12. References ....................................................................................................................................... 17  

Useful readings to get started: Kager (1999), Optimality Theory. Cambridge University Press. The first three chapters give an excellent introduction to the core theory and syllabification. Blevins (1995), ‘Syllable in phonological theory’. Blackwell handbook article. A nice introduction to the syllable in generative phonology, useful for understanding many illustrations here and the final problem set. Itô (1989), ‘A prosodic theory of epenthesis’, NLLT article. An important early approach to syllables that pre-figures OT in that it anticipates the use of well-formedness constraints in phonology.  

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1.  Some  common  problems  in  phonology  (and  elsewhere)   (1) Do something, except if … Latin stress Stress assigned by ignoring the final syllable Unless final syllable only syllable! (L L) <σ> (H) cá.me.ran ‘(bed)room’ mél ‘honey’ L (H) <σ> Or in two syllable words!

a.míi.cum ‘friend’ (L σ) má.lum ‘misfortune’ . Observation: the normal application of stress assignment ignores the final syllable, unless doing so would result in no stress at all mél or a subpart foot, málum. Phonological processes have upper bounds. (2) Same target, different repair to achieve target: how unify the analysis?

Target: languages dislike initial clusters Some languages resolve them with deletion, e.g., Tibetan /gjij/ à _jig ‘one’ Others resolve them with epenthesis, as in Spanish, /ski/ à eski ‘ski (loan)

Question: what do Tibetan and Spanish have in common, if not the phonological processes? (3) Duplication problem: the output of phonological rules seem to be structured by the same constraints that shape the inventory; but these are different mechanisms in some models.

Lexical restriction in Thai: no morphemes end in voiced obstruents. Phonological process in German and Russian: morphemes have a contrast in voicing finally, but this is neutralized by syllable/word-final devoicing, e.g., Bun[t], cf. Bun[d]-e

Question: how could the two types of constraints be unified? (4) Linguistic typology from language particular analysis Question: when you have constructed an analysis of a particular phenomena, in a particular language, what predictions does that make for other languages, and even other phenomena? Indonesian nasal substitution

/məәN + pilih/ à məәmilih ‘to vote’

Assume: N+p merges to m because of a general ban on nasal + voiceless stop clusters. Question: what predictions does that make about other languages? Are there other ways to satisfy

the same constraint?  

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2.  Do  something,  except  if  …   (5) Various blocking effects in phonology

a. Latin stress: the final syllable is extrametrical, except if it is the only syllable or the last syllable of a two syllable word

b. Dutch epenthesis: insert ʔ in VV sequences, unless the second vowel is unstressed

c. Berber delabialization: delabialize m to n in a prefix, unless it it attached to a stem that begins with a coronal sonorant.

(6) Berber delabialization problem (C! is an emphatic consonant)

a. m-xazar √xzr ‘scowl’ b. n-fara √fra ‘disentangle’

m-saggal √siggl ‘look for’ n-Haššam √ ħššm ‘be shy’

m-!šawar √!awr ‘ask advice’ n-xalaf √xalf ‘place crosswise’

mm-žla √žla ‘lose’ n-kaddab √kddb ‘consider a liar’ Assumptions: the reflexive prefix has two forms, m- and n-, depending on the composition of the stem it attaches to. If the stem contains one of the primary labial consonants /b f m/, then the allomorph is n-, otherwise it is m-. We assume therefore that the underlying form of the prefix is /m-/ and that it changes in the presense of another labial. Delabialization: the derivation prefix m- is changed to n- when in the same stem (which includes the prefix) another primary labial consonant exists. Technical implementation: delink the [labial] specification and insert a [coronal] specification to give the alveolar. (7) Exceptions to labial dissimilation

/m-laqqaf/ à mlaqqaf ‘attraper en l’air’ /m-lkm/ à nyalkam ‘atteindre’

Question: what do these exceptions have in common, and how are they different from the cases that undergo labial dissimilation? Below consider all the logical possibilities for the forms below and make a proposal about why delabialization is blocked here. Delabialized Left alone (*Lab-Lab) /m-fara/ /m-xalaf/ /m-kaddab/ /m-laqqaf/ Take home message: phonological processes seem to be blocked by certain well-formedness constraints that place an upper bound on the scope of a process.  

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3.  Same  target,  different  repair   (8) Nasal substitution in Indonesian

/məәN + pilih/ məәmilih ‘to choose, vote’ /məәN + tulis/ məәnulis ‘to write’ /məәN + bəәlih/ membəәlih ‘to buy’ /məәN + dapat/ məәndapat ‘to get, receive’

Observation: when the input contains a nasal plus a voiceless obstruent, these segments coalesce into a nasal that has the same place as the obstruent; otherwise the nasal assimilations in place. (9) NC̥: no nasal + voiceless obstruent clusters. Proposal (Pater 1999; Pater 2001): assume that the reason for nasal substitution is a constraint that is active in Indonesian phonology, NC̥. This constraint is well-motivated phonetically, because nasal airflow leaks into the following obstruent, which facilitates voicing, and velum raising rarefies the air column above the glottis, which also facilitates voicing. Formalizing this intuition as a constraint on phonological structure, the merging of the nasal and the obstruent avoids this sequence. Leading question: what other ways might a language avoid nasal + voiceless obstruent clusters? (10) Denasalization in Mandar (Austronesian)

a. N + voiced stop: /maN + dundu/ à mandundu ‘to drink’ b. N + voiceless stop: /maN + tunu/ à mattundu ‘to burn’

Observation: denasalization also satisfies NC̥ by eliminating the initial nasal. (11) Post-nasal voicing in Puyu Pungo Quechua

/kam + pa/ à kam-ba ‘yours’, cf. sinik-pa ‘porcupine’s’ /wakin + ta/ à wakin-da ‘the others’ cf. wasi-ta ‘in the jungle’

Observation: post-nasal voicing also removes the shunned sequence. (12) Nasal deletion: N + voiceless obstruent à Ø + voiceless obstruent Kelantan Malay, Venda, Swahili, Maore, common in child language Observation: deletion removes the shunned sequence too. (13) Summary

Input Output Description N + K ŋ Nasal substitution N + K k-k Denasalization N + K n-g Post-nasal voicing N + K Ø-k Nasal deletion

Take home message: a natural way to relate all of these examples is that each case is doing something to remove the shunned nasal + voiceless obstruent sequence. Each languages does something different (different repair), but they all have the same goal (same target). Another slogan: “homogeneity of target, heterogeneity of process”

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4.  Core  assumptions   Objective: how to account for constraint-based blocking and the typological convergence in ‘same target, different repair’? (14) Core ideas (McCarthy & Prince 1995; Prince & Smolensky 1993/2004) Targets as constraints: markedness constraints require target output form; processes are just unfaithful mappings motivated by markedness

Recoverability via constraints: different types of input-output constraints, called faithfulness constraints, require different types of input-output matching, effectively requiring recoverability of input structure

University of constraints: markedness and faithfulness constraints are present and potentially active in all OT grammars; essential part of UG

Language particular prioritization: the constraints are ranked on a language particular basis to account for language variation

Input-output mappings as optimization over entire constraint hierarchy: selecting the observed surface form is a matter of picking the winning candidate that is ‘most harmonic’ w.r.t. the constraint hierarchy

(15) The Model CON set of all well-formedness constraints (markedness, faithfulness, etc.), rich in internal structure

GEN function that maps a linguistic input onto a set of candidate forms, altered in all possible ways (via ‘freedom of analysis’)

EVAL function that takes as input the candidate set and returns an ordering of that set that ranks output forms based on their overall harmony

Anatomy of EVAL: think of EVAL as a composed function, e.g., F(G(x)). Individual constraints can be thought of as functions that take the candidate set as input, and output an ordered set of candidates, where the ordering reflects how well the candidates satisfy the constraints. All constraints are functions in this sense. EVAL, then, is just a composed function made up of these basic functions, where the most deeply embedded function is the topmost in the hierarchy, the next one is the second highest constraint, etc.

Task: consider the composed function FRounding(FFahr>Cel())

(16) Markedness and faithfulness for Berber

Markedness: *[Lab – Lab ]Stem. Two or more labial specifications are not allowed in a stem. Faithfulness: Ident[Place]. Do not change the place of the input segments.

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(17) Delabializaiton as markedness over faithfulness Input: m + xalaf *[Lab – Lab ]Stem Ident[Place] a. m-xalaf *! b. → n-xalaf * Conventions: constraints are ranked from left-to-right, violations marked with ‘*’, and fatal violation (one that knocks a candidate out of the running) is ‘*!’. Task: provide the outputs of Gen and Eval here. Hint: the work of Gen() is shown in the first column, the work on Eval() in the second column. Gen(m-xalaf) = ? Eval = FIdentPl(F*Lab2(input)), so: Eval(Gen(m-xalaf)) = ? (18) Faithful treatment when markedness not relevant Input: m + xazar *[Lab – Lab ]Stem Ident[Place] a. → m-xazar b. n-xazar *! (19) Delabialize, unless that produces two adjacent coronal sonorants! Input: m + laqqaf *[Cor/Son.Cor/son] *[Lab – Lab ]Stem Ident[Place] a. → m-laqqaf * b. n-laqqaf *! * Take home: it is formally possible to conceive of a grammar as a ranking of constraints. Linguistic processes are unfaithful mappings, motivated by high-ranking markedness constraints. This approach also naturally accounts for the ‘upper bounds’ of processes, i.e., when processes are blocked by other top-ranked constraints, the ‘except if’ clause in some many processes.

5.  Linguistic  typology  in  OT   The argument: The constraints are universal (in standard OT anyway, definitely debatable). Constraints are ranked on a language particular basis. The input is universal, though languages have different lexicons (see below).

ð Languages differ primarily in the way their constraints are ranked. Insight: to understand the predictions of an analysis of a particular language, take the constraints that make up that analysis and permute them into all possible orders. The various possible orders determine the range of structurally different languages.

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(20) Constraint system for nasal substitution, see Pater (1999, 2001) for this and other examples Target High-ranking faith Low-ranking faith

/məәN1 + t2ulis/ NC̥ Max Ident(voice) Ident(nasal) Uniformity

a. No change məәn1t2ulis *!

b. Substitution →məәn12ulis *

c. Denasalization məәt1t2ulis *!

d. Voicing məәn1d2ulis *!

e. Deletion məә_t2ulis *! Constraint names: ‘Max’ is the anti-deletion constraint, Ident(Feature) constraints say that segmental counterparts in input and output have the identical specifications for Feature, Uniformity bans coalescence, the merging of two segments into one. Question: what happens if we mess with the ordering of the faithfulness constraints? (21) Constraint system for denasalization: demote Ident(nasal) Target High-ranking faith Low-ranking faith

/məәN1 + t2ulis/ NC̥ Max Ident(voice) Uniformity Ident(nasal)

a. No change məәn1t2ulis *!

b. Substitution məәn12ulis *!

c. Denasalization →məәt1t2ulis *

d. Voicing məәn1d2ulis *!

e. Deletion məә_t2ulis *! (22) Constraint system for voicing: Target High-ranking faith Low-ranking faith

/məәN1 + t2ulis/ NC̥ Max Uniformity

a. No change məәn1t2ulis *!

b. Substitution məәn12ulis *!

c. Denasalization məәt1t2ulis

d. Voicing → məәn1d2ulis

e. Deletion məә_t2ulis *!

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(23) Constraint system for deletion: Target High-ranking faith Low-ranking faith

/məәN1 + t2ulis/ NC̥

a. No change məәn1t2ulis *!

b. Substitution məәn12ulis

c. Denasalization məәt1t2ulis

d. Voicing məәn1d2ulis

e. Deletion → məә_t2ulis Take home: same target, different repair is a natural outcome of the contention that all languages have the same targets (=markedness constraints), but they rank the constraints differently. Different rankings of faithfulness constraints produces different ways of satisfying the target, and either the target is satisfied at all.

6.  The  duplication  problem  and  the  richness  of  the  base   Observation: the restrictions on lexical items are often repeated in phonological processes. Thai: no morphemes end in a voiced obstruent; isolating nature of the language does not provide examples that would create alternations German: morphemes may end in voiced obstruents, but at the surface, no word ends in a voiced obstruent; e.g., Bun[t], cf. Bun[d]-e (24) The duplication problem: restrictions in the lexicon are duplicated in phonological rules. (25) Example based on Old English (though not exactly) Restriction in the lexicon: if [-back], then [-round] (i.e., no front rounded vowels) [-back] à [-round] (context-free redundancy rule) Hypothetic fronting rule (cf. i-umlaut): vowels are fronted and unrounded after Ci V à [-back, -round] / ___Ci Problem: it would be simpler if the fronting rule just matched the [back] specification of the following i, but the actual fronting rule has to duplicate the effects of the lexical restriction. A generalization is missed.

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(26) OT approach to the duplication problem: ‘richness of the base’ The input set is universal. That is, the grammar of a language has to contend with all possible inputs. This does not entail that the lexicon of a language has inputs with sounds and sound sequences; that is a matter finding the appropriate lexical representations for actual words. Since there are no restrictions on the input, there is not duplication of effort.

Practical implication: it is absolutely necessary to consider all relevant inputs for a given problem, otherwise, the rankings may not be right. In the Old English example, the OT analysis has to reckon with front rounded vowels because the restrictions on them in English are due to surface constraints, not constraints on the inventory. Insight into OT: in a sense OT is a theory of constraints on inventories, and alternations unfaithful mappings that happen when these same constraints are applied to polymorphemic words. Contrast this with SPE phonology, which is really a theory of alternations.

7.  Optimality  Theory  since  1993—further  reading   Learnability A considerable amount of research has taken the core ideas of OT and shown how they are can be employed in tackling tough problems in language acquisition. For example, the idea that a grammar of a language is a language-particular ranking of universal constraints focuses language learning on learning constraint rankings, and early work on stress typology showed learning stress can be viewed as learning the correct rankings of prosodic well-formedness constraints (Tesar 2007; Tesar & Smolensky 2000). Other problems include learning underlying representations (Tesar et al. 2003), learning phonotactic distributions (Prince & Tesar 2004), and learning biases that make language learning more computationally tractable (Tessier 2007). Harmonic Grammar and MaxEnt Grammars Influenced by connectionism, Harmonic Grammar is a style of OT that uses the same constraints of standard OT but instead of constraint orderings the constraints are weighted (Farris-Trimble 2008; Legendre et al. 1990; Pater 2009). Harmonic Grammar allows ‘ganging up’ effects where two otherwise unimportant constraints can conspire to produce a result, and it significantly changes the learning problem. MaxEnt grammars (for Maximum Entropy) are related to Harmonic Grammars, but there is a smart algorithm for selecting constraints from a vast universe of constraints (Hayes & Wilson 2008). Levels of explanation In an effort to understand how OT grammars relate to the fine-grained detail of neural networks (and thus the human brain), Paul Smolensky and his colleagues have worked on way of relating the macrostructure of OT grammars to the microstructure of connectionist networks (Smolensky & Legendre 2006). Parallels between ‘hard constraints’ and ‘soft constraints’, the notion of harmony, and even learning have been made, suggesting that OT has a place in connection science.  

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8.  Japanese  velars:  building  a  linguistic  system   Goal: given a linguistic pattern, build a linguistic system of inputs and outputs that can be assessed by constraints. Dataset (from Kager 1999: 50) impossible words geta ‘clogs’ *ŋeta giri ‘duty’ *ŋiri guchi ‘complaint’ *ŋuchi kaŋo ‘key’ *kagi kaŋo ‘basket’ *kago kaŋŋae ‘thought *kaŋgae Observation: [g] appears word-initially but not word-intially, while [ŋ] is the opposite. Question: given this pattern, what are the logical inputs and outputs for your OT system? What input representations of these words will an OT grammar need to consider, and what are the logically possible candidates for each of these inputs. Inputs: Outputs: Question: did your inputs include words like ŋeta? What principle is relevant here? What analytical assumption do you make about a logically possible input /ŋeta/? Task: now arrange the inputs and outputs into two columns, showing which outputs are from which inputs.  

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9.  Japanese  velars  again:  ranking  constraints   Goal: given a linguistic system and set of constraints, rank the constraints so they account for the data. Task: use the linguistic system above (4 inputs * 2 outputs) for Japanese velars to figure out the ranking of the constraints below. Constraints

*g: context free markedness constraint, violated with every instance of [g] *#ŋ: context sensitive markedness constraint, violated with every instance of an initial [ŋ]

Ident(nasal): corresponding segments agree in the feature [nasal]. Violation tableau: a tableau that records the constraint violations of each output form; if the constraint system has the right constraints, and constraints are ranked properly (convention: left-to-right ordering), the winner is the attested form. Task: fill out the violations of the tableau below. What rankings are crucial?

Inputs Outputs *#ŋ *g Ident(nasal)

a. /gV/ > gV *

ŋV * *

b. /ŋV/

c. /VŋV/

d. /VgV/

Problem: with complex constraint systems with more than five input-output mappings and more than four constraints, the ranking problem is hard to do by hand. Comparative tableau enable people to do more complex rankings even with pencil and paper, and they are used in the OT approach to language learnability. Comparative tableau (Prince 2002): constraints evaluate winner-loser pairs instead of individual candidates. The values in a comparative tableau show whether a constraint: (1) favors the winner (W), (2) favors the loser (L), or doesn’t decide between the two. The result is a robust set of ‘elementary ranking conditions’ that show all the ranking requirements of a constraint system. Valuable for: linguistic analysis, understanding learning.

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Task: make a comparative tableau from the violation tableau of Japanese velars.

Inputs Winner ~ Loser *#ŋ *g Ident(nas)

a. /gV/ gV ~ ŋV W L W

b. /ŋV/ gV ~ ŋV

c. /VŋV/ VŋV ~ VgV

d. /VgV/ VŋV ~ VgV

Rationale: for every winner-loser pair, the constraints that favor the loser must be dominated by a constraint that favors the winner; otherwise the incorrect outcome is predicted. In (a), either *# ŋ or Ident(nas) must dominate *g, either will do. Recursive constraint demotion (Tesar 2004): an algorithm that works on comparative tableau and is guaranteed to find the correct ranking, if indeed a ranking exists.

Step 1: examine all constraint columns and find all constraints that do not favor a loser. Insert them in the constraint hierarchy (i.e, the next stratum down).

Step 2: for all constraints just ranked in Step 1, eliminate all rows where the just-ranked constraint favors a winner (this data has been accounted for).

Step 3: with the remaining forms, return to Step 1 and repeat the process iteratively until all the constraints are ranked.

Task: use this method to give the ranking for the constraints above.  

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10.  Athabaskan  laryngeals:  a  mini  factorial  typology   Goal: given a pattern, determine what the correct constraints are for that pattern using linguistic typology Part A. Consider the often assumed implicational relation: if a language has a voiced obstruent series, it also has a voiceless obstruent series. Using the obstruent system below as an example, this statement means that the existence of 1b and 2b entails the existence of 1a and 2a.

1a. p t k 1b. b d g 2a. s x 2b. z ɣ

Show how this implicational relation is ensured in an OT framework if CON has the constraints below. Assume in your ranking results that [son] specifications are held constant. Just use simple input-output mappings with single segments, and consider the free combination of features in inputs.

*VoicedObstruent: segments with [+voice, -son] are prohibited. Ident(voice): corresponding segments agree for [voice]

Part B. Many Athabaskan languages have a contrast in [voice] in fricatives, but no corresponding contrast in stops. For example, Navajo obstruents (ignoring laterally released segments) have a three-way contrast in stops, without voiced stops, and a two-way contrast in fricatives (note that /d/ is voiceless, and /t/ is voiceless aspirated, consistent with Athabaskan transcription):

3a. (plain stops) d dz dʒ g 3b. (aspirated stops) t ts tʃ k 3c. (ejectives) t’ ts’ tʃ’ k’ 4a. (voiceless fricative) s x 4b. (voiced fricative) z ɣ

Assume that CON only has the markedness and faithfulness constraints introduced in Part A. Explain why this system is impossible. In giving your answer, concentrate only on 3a, 4a, and 4b (so ignore the issue of accounting for the aspirated stops and ejectives). Part C. Consider the following two hypotheses for accounting for voicing in Navajo obstruents:

Hypothesis X: in addition to *VoicedObstruent, CON has the constraint: *VoicedStop: segments must not have [+voice, -son, -cont] specifications.

Hypothesis Y: instead of *VoicedObstruent, CON has the following two constraints:

*VoicedStop: segments must not have [+voice, -son, -cont] *VoicedFricative: segments must not have [+voice, -son, +cont]

First, show how each hypothesis accounts for the series 3a, 4a, 4b in Navajo. Show all relevant winner-loser data in a comparative tableau for each theory, and give the ranking predicted by recursive constraint demotion for each theory.

Next, describe the different cross-linguistic implications of each hypothesis. Do this by constructing a factorial typology for each hypothesis, and explain precisely where the predictions differ. Which hypothesis is more restrictive? Finally, use the phoneme inventories on the next page to decide the matter.

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11.  Doing  OT  with  software   Preamble: some problems don’t require software. If you have a simple linguistic system, and up to eight constraints, you can rank the constraints straightforwardly by creating a comparative tableau and applying recursive constraint demotion. However, more complex systems test the limits of this, and it’s virtually impossible to do a factorial typology with more than four constraints. OTSoft (Hayes et al. 2003) The first software tool for ranking constraints and doing factorial typology. It also provides tools for different kinds of ranking assumptions and how to structure the display of ranking arguments. It is a little more user friendly that OTWorkPlace, but since it doesn’t use winner-loser data, it’s hard to visualize a problem space with ERCs. Limited to PC computers. Procedure: prepare an excel spreadsheet in a particular form (first column input, second outputs, third ‘1’ for winner, then constraints). OTWorkPlace (Prince et al. 2013) A macro that is an add-on to Excel, and also limited to PC computers. Works directly in Excel and provides a number of specific processes as pull-down menu options. It can both rank constraints and produce factorial typologies, along with a number of other ways of organizing your data that are explained in (Brasoveanu & Prince 2011). A very useful feature of this OT environment is that it displays full comparative tableau, even when there is not possible ranking of constraints. This enables problem solving because you can see visually the ranking requirements that need to be resolved, and it leads new hypotheses about what the constraints are and how to classify your data with hidden structure.  

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12.  Syllable  universals:  more  complex  typology   Goal: give a typology of a particular pattern or process, find a system of constraints that can account for universal patterns within that typology; also make new predictions Blevin’s  typology (p. 217 of ‘The Syllable in Phonological Theory’, The Handbook of Phonology)

The  Constraints:  Markedness: NoCoda, Onset, *[CC, CC]* Faithfulness: Max, Dep (may be subdivided by Cs and Vs later in a second attempt)

The  Project  Part  I. Build a linguistic system based Blevins’ syllable typology. In particular, use all of the above syllable types as inputs, excluding CVCCC, and consider the logically possible outputs that result in satisfaction of one or more of the above markedness constraints. Some outputs are pointless in OT, like [CVC] from /CV/, because they are harmonically bounded. You don’t need to include them. Put all inputs and outputs in an Excel spreadsheet and fill in the violations for the above constraints, so the spreadsheet can be fed to OTSoft. Part  II. Next answer the question, how well does the factorial typology match Blevins’ typology? Are there any syllable systems in Blevins’ typology that are not predicted? Are there any predicted types not present in Blevins’ typology? If so, how do you interpret such a mismatch? Answer the first two questions by making a chart of the factorial typology that lists the observed syllables, which language it corresponds to (if at all) in Blevins’ typology, and the number in the OTSoft output file. Also, indicate what processes the languages have to create their syllables. For the other questions, try to state the prediction made by the factorial typology as an implication, and if it appears to contradict known syllabification systems.

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12.  References  Blevins, Juliette. 1995. Syllable in phonological theory. The handbook of phonological theory, ed. by J.

Goldsmith, 206-44. Cambridge, MA: Blackwell. Brasoveanu, Adrian & Alan Prince. 2011. Ranking and necessity: the fusional reduction algorithm.

Natural Language and Linguistic Theory 29.3-70. Farris-Trimble, Ashley. 2008. Cumulative faithfulness effects in phonology: Indiana University. Hayes, Bruce, Bruce Tesar & Kie Zuraw. 2003. OTSoft 2.1, software package. UCLA and Rutgers

University. Hayes, Bruce & Colin Wilson. 2008. A maximum entropy model of phonotactics and phonotactic

learning. Linguistic Inquiry 39.379-440. Itô, Junko. 1989. A prosodic theory of epenthesis. Natural Language and Linguistic Theory 7.217-59. Kager, René. 1999. Optimality Theory Cambridge: Cambridge University Press. Legendre, Géraldine, Yoshiro Miyata & Paul Smolensky. 1990. Can connectionism contribute to syntax?

Harmonic Grammar, with an application. Proceedings of the 26th Regional Meeting of the Chicago Linguistic Society, ed. by M. Ziolkowski, M. Noske & K. Deaton, 237-52. Chicago: Chicago Linguistic Society.

McCarthy, John J. & Alan Prince. 1995. Faithfulness and reduplicative identity. University of Massachusetts Occasional Papers 18, Papers in Optimality Theory, ed. by J. Beckman, S. Urbanczyk & L. Walsh, 249-384. Amherst, MA: Graduate Linguistic Student Association.

Pater, Joe. 1999. Austronesian nasal substitution and other NC effects. The prosody morphology interface, ed. by R. Kager, H.v.d. Hulst & W. Zonneveld, 310-43. Cambridge, MA: Cambridge University Press.

—. 2001. Austronesian nasal substitution revisited: what's wrong with *NC (and what's not). Segmental phonology in Optimality Theory: constraints and representations, ed. by L. Lombardi, 159-82. Cambridge: Cambridge University Press.

—. 2009. Weighted constraints in generative linguistics. Cognitive Science 33.999-1035. Prince, Alan. 2002. Arguing optimality. Papers in Optimality Theory II, ed. by A. Coetzee, A. Carpenter

& P. de Lacy, 269-304. Amherst, MA: GLSA. Prince, Alan & Paul Smolensky. 1993/2004. Optimality theory: Constraint interaction in generative

grammar Malden, MA: Blackwell. Prince, Alan & Bruce Tesar. 2004. Learning phonotactic distributions. Fixing priorities: Constraints in

phonological acquisition, ed. by R. Kager & J. Pater, 245-91. Cambridge: Cambridge University Press.

Prince, Alan, Bruce Tesar & Nazarré Merchant. 2013. OTWorkplace. Rutgers University. Smolensky, Paul & Géraldine Legendre. 2006. The harmonic mind. From neural computation to

optimality theoretic grammar Cambridge, MA: The MIT Press. Tesar, Bruce. 2004. Using inconsistency detection to overcome structural ambiguity in language

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