Optimality theory

							Optimality theory


April 1998
 Optimality theory
UR (underlying representation)




         Gen


Candidate Set (1…n)
Select the winner from the candidate set
 by means of a tableau.
See word tableau.
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.
 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.
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.
 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.
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.
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...
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.
 Yawelmani CV distribution
1. All words: [C
2. *[CC , * CC]
3. *VV
4. *CCC
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.”
 Violated in Yawelmani?
Peak: never
Onset: never
*Complex: never
NoCoda: sometimes

The grammar of a language specifies a
 language-particular ranking of
 constraints.
 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?
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
 More Yawelmani
Xat+ en = xaten
logw+ en = logwen
but
xat+ hin = xathin
logw+ hin = logiwhin. Why? How?
See tableau.
 Spanish
absorber absorto *absorbto
esculpir escultor *esculptor
distinguir dintinto *distingto

Spanish deletes the non-coronal
 obstruent in a cluster.
 English
Permits more complex codas than
  Spanish or Yawelmani Yokuts
limpness
softness
crispness
strangeness
Tableau...
More generally
Faithfulness >> Onset, NoCoda
(C)V(C)
Onset, NoCoda >> Faithfulness
CV
Onset>> Faithfulness >> NoCoda
CV(C)
NoCoda>>Faithfulness >> Onset
(C) V
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...)
 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‟
Ulwa: -ka- „his‟ falls immediately after the
  head foot of the word:
bás ka    „hair‟
siwá ka nak      „root‟
English: Align (Prosodic Word, L, Foot, L)
Tagalog: -um- Align ( [um], L, Stem, L)
Ulwa: Align ([ka], L, Foot‟, R) where Foot‟
  = head foot.
 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.
 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)
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.
 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‟
 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.
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.
 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)
 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)
 Non-iterative stress assignment
If Alignment >> Parse-syllable, then we
   get non-iterative footing:
see Word: