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Optimality theory

Optimality theory. April 1998. Optimality theory. UR (underlying representation) Candidate Set (1…n). Gen. Select the winner from the candidate set by means of a tableau. See word tableau.

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Optimality theory

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  1. Optimality theory April 1998

  2. Optimality theory • UR (underlying representation) • Candidate Set (1…n) Gen

  3. Select the winner from the candidate set by means of a tableau. • See word tableau.

  4. Optimality theory: a language specifies a ranking of constraints; select the optimal candidate from among the set of candidates with the following algorithm: • For a given set of candidates, iterate through the constraints: I=0; • Loop: I= I + 1; • for constraint I, find the lowest number of violations V of the constraint I; eliminate all candidates that violate it more than V times; • if more than 1 candidate remains, proceed through loop again; otherwise, the remaining candidate is the winner.

  5. Optimality theory • Bare bones, subject to modifications as needed: • A theory relating underlying forms to surface form(s). • To each input (=underlying) form, associate a (potentially infinite) candidate set, produced by GEN. • Choose the output by means of a tableau.

  6. Alternatively put: • Assign a decimal fraction to each candidate thusly: • Optimality score: 0.a1 a2 a3 a4 … • where a1 is the number of violations of the 1st constraint, etc. • If ai is always < 10, then: • the winning candidate is the one with the lowest optimality score.

  7. Issues and concepts in OT • Constraints are said to be universal, but nobody acts as if they were a fixed set from a research point of view. What this belief means in practice is that we do not need to think about how they could be learned • Constraints divide into two important subgroups: Faithfulness constraints and phonotactic constraints.

  8. Faithfulness constraints measure the degree of difference between UR and SR (surface). • However important that difference is conceptually, it is not a theoretical difference: all constraints are ordered in the same ranking.

  9. Early on, the critical or essential claim of OT was the strict hierarchical ranking of constraints: this meant that no coalition of lower ranked constraints c1, c2 could get together and be more important than a single constraint D, if D outranks C1 and C2 individually. • This is the primary difference between early OT and harmonic phonology, and...

  10. This claim was abandoned by Smolensky in 1995, for constraint conjunction, which allowed the conjunction of two constraints to be ranked separately from (and higher than) either of the constraints individually.

  11. Yawelmani CV distribution • 1. All words: [C • 2. *[CC , * CC] • 3. *VV • 4. *CCC

  12. 1. Onset: syllables begin with a consonant • 2. Peak: syllables have one (‘a’?) vowel • 3. NoCoda: syllables end with a vowel. • 4. *Complex: syllables have at most one consonant at an edge. • 5. Syllables are composed of consonants and vowel (Onset & peak). • “general tendencies, not laws.”

  13. Violated in Yawelmani? • Peak: never • Onset: never • *Complex: never • NoCoda: sometimes • The grammar of a language specifies a language-particular ranking of constraints.

  14. Faithfulness constraints • Faithfulness constraints require that the output be identical to the input. • In Yawelmani, “as a violable constraint, NoCoda must be outranked by some more important constraint … Faithfulness…” • How is it that NoCoda could in principle be satisfied?

  15. Syllabify the consonant in question as a peak. Xa.ten. -> xa.te.n. English: meter, metric. • Delete the C in question. • Insert a vowel. Xaten -> xateni. • See Word tableau

  16. More Yawelmani • Xat+ en = xaten • logw+ en = logwen • but • xat+ hin = xathin • logw+ hin = logiwhin. Why? How? • See tableau.

  17. Spanish • absorber absorto *absorbto • esculpir escultor *esculptor • distinguir dintinto *distingto • Spanish deletes the non-coronal obstruent in a cluster.

  18. English • Permits more complex codas than Spanish or Yawelmani Yokuts • limpness • softness • crispness • strangeness • Tableau...

  19. More generally • Faithfulness >> Onset, NoCoda • (C)V(C) • Onset, NoCoda >> Faithfulness • CV • Onset>> Faithfulness >> NoCoda • CV(C) • NoCoda>>Faithfulness >> Onset • (C) V

  20. Generalized Alignment (McCarthy and Prince 1993 Yearbook of Morphology) • Align (category 1, L/R, • category 2, L/R): • Constituent type: could be: • Prosodic word; stress foot; syllable; mora; • For all (L/R) edges of Cat 1, there is a Cat 2 edge of (L/R) (you might think: Cat 1 is bigger than Cat 2 -- but...)

  21. Reference to edge: • Secondary stress on first syllable: • Tátamagouchi, not Tatámaguchi • Tagalog: the affix -um- falls as near as possible to the left edge of the stem subject to coda restriction: • u ma ral ‘teach’ • su mu lat ‘write’ • gru mad wet ‘graduate’

  22. Ulwa: -ka- ‘his’ falls immediately after the head foot of the word: • bás ka ‘hair’ • siwá ka nak ‘root’

  23. English: Align (Prosodic Word, L, Foot, L) • Tagalog: -um- Align ( [um], L, Stem, L) • Ulwa: Align ([ka], L, Foot’, R) where Foot’ = head foot.

  24. Align 2 phonological cat’s • Ft-Binarity: Feet must be binary under syllabic or moraic analysis. • (unviolable) • Trochaic: Ft -> Syllstrong Syllweak • Parse-syll: All syllables must be parsed by feet. • It follows: parsing is unambiguous in the case of words of even # of syllables.

  25. Odd number of syllables: • L->R: Wankumara: • á a á a á a = (á a)(á a)(á a)a • R->L Warao • a (á a) (á a) (á a) • Initial dactyl = initial trochee plus R->L • Garawa (á a) a (á a)(á a) • L->R plus final trochee (Polish) • (á a) (á a)(á a) a (á a)

  26. Parse syllable is violated, minimally, in all these cases. • Garawa: • Main stress falls on initial syllable; • Secondary on the penult; • Tertiary on every other syllable leftward from the penult, but not on the 2nd.

  27. Garawa • yá mi eye • púnja la white • wá tjim pà ngu armpit • ká ma la rì nji wrist • yá ka lâ ka làmpa loose • ngár ki ri kî rim pà yi fought with boomerangs • ngá mpa lâng in mûkun jìna ‘at our many’ • nár ngin mûkkun jîna mìra ‘at your own many’

  28. Garawa • Align Prosodic Word: • Align (ProsodicWord, Left, Foot, Left): • Left edge of each prosodic word must match the left edge of some foot. • Right edge? • Align Foot: • Align (Ft, R, ProsodicWord, R) • Every foot stands in final position in PrWd.

  29. Conflict in Trisyllables: • (Ss)S Align PrWd:OK AlignFt:NO • s(Ss) Align PrWd: NO AlignFt: OK • In general, minimal violation, together with Align Ft, means squeezing the singleton (nonfooted) syllable to the “opposite” side. • See Word page.

  30. Other rankings to yield trochees: • Left to right: • Align (Foot, L, PrWd, L) >> • Align (PrWd, R, Ft, R) • Right to Left • Align (Foot, R, PrWd, R) >> • Align (PrWd, L, Ft, L)

  31. More... • Initial dactyl: • Align (PrWd, L, Ft, L) >> • Align (Fot, R, PrWd, R); • Left to Right plus Final Trochee • Align (PrWd, R, Ft, R) >> • Align (Ft, L, PrWd, L)

  32. Non-iterative stress assignment • If Alignment >> Parse-syllable, then we get non-iterative footing: • see Word:

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