Optimality Theory(Prince & Smolensky 1993)

Outline

• Phonetics and Phonology

• OT Characteristics• Output-Oriented• Conflicting Soft Well-formedness Constraints

• OT Grammar • Families of Constraints• OT-Tableau• Example: Cluster Reduction in First Language

Acquisition Data

• The Merits of OT

Concept Derivationally-

based Phonology (Chomsky & Halle 1968)

• Structural Description (SD):identifies class of inputs (= stored lexical forms)

• Structural Change (SC):specifies operations that change the input

Chomsky (1976): writing a rule does not constitute a solution

to a problem; writing a rule is merely a statement of a problem

A B / X __ Y SD: XAY SC: XAY XBY

Optimality Theory (Prince & Smolensky 1993)

• Optimality Theory is a theory of language and grammar in which well-formedness constraints on outputs determine grammaticality

If you don’t want phonology to be just a technique for data-compression, you have to seek the locus of explanatory action elsewhere(Prince & Smolensky, 1993)

Why output-oriented?Not all phonology is derivationally-basedAlternations in Turkish (Clements & Keyser, 1983):

Accusative Nominative AblativeDegemination:‘feeling’ hiss+i his his+ten ‘right’ hakk+i hak hak+tan

Epenthesis:‘transfer’ devr+i devir devir+den‘abdomen’ karn+ karn karn+dan

Vowel shortening:‘time’ zama:n+i zaman zaman+dan‘proof’ isapa:t+i ispat ispat+tan

Why output-oriented?Not all phonology is derivationally-basedAlternations in Turkish (Clements & Keyser, 1983):

Accusative Nominative AblativeDegemination:‘feeling’ hiss+i his his+ten ‘right’ hakk+i hak hak+tan

Epenthesis:‘transfer’ devr+i devir devir+den‘abdomen’ karn+ karn karn+dan

Vowel shortening:‘time’ zama:n+i zaman zaman+dan‘proof’ isapa:t+i ispat ispat+tan

Output Constraint: Turkish syllables cannot exceed the structure CVC/CVV

Potentially Conflicting, Soft Constraints

• Optimality Theory is a theory of language and grammar in which well-formedness constraints on outputs determine grammaticality

• Optimality Theory is a theory of language and grammar in which well-formedness constraints on outputs determine grammaticality

• These constraints apply simultaneously to representations of structures. They are potentially conflicting and they are soft, which means violable

Potentially Conflicting, Soft Constraints

• These constraints apply simultaneously to representations of structures. They are potentially conflicting and they are soft, which means violable

Potentially Conflicting, Soft Constraints

Example

Foot ()

Syllable () Syllable ()

p pa

Conflicting Constraints

• Nonfinality: stress never falls on the last • Peak Prominence: stress falls on the heaviest

constraints nonfinality peak prominence

candidates

.

. *!

*

stress application

Conflicting Constraints

• Nonfinality: stress never falls on the last • Peak Prominence: stress falls on the heaviest

constraints peak prominence nonfinality

candidates

. *!

. *

stress application

OT-grammar

• GENgenerates a set of candidate outputs• e.g. stress assignment papapa• candidates: pápapa; papápa; papapá

OT-grammar

• GENgenerates a set of candidate outputs• e.g. stress assignment papapa• candidates: pápapa; papápa; papapá

• H-EVAL determines the relative harmony of the possible output structures and evaluates which one satisfies the relevant constraints best: the optimal output (indicated by ‘’)

OT-tableau

constr 2 constr 3constr 1 constr 4 input

output 1

output 2

output 3 *!

*!

*

*

*

vertical: all output candidates ( is optimal output)

horizontal: constraint 1 dominates constraint 2; 2 >> 3, etc.

*: output violates constraint (*!: violation is fatal)

grey cell:evaluation is irrelevant.

Families of Constraints• Markedness (prefers unmarked structures):

• ONS: syllables must have onsets• *CODA: syllables must not have a coda

more harmonic than one of lower/higher sonority• Hnuc/Hmar: A higher/lower sonority nucleus is

• Correspondence (ensures diversity): relates elements of different strings (e.g. inputs and outputs)

• MAX-IO: every segment of the input has a correspondent in the output (prohibits deletion)

• DEP-IO: every segment of the output has a correspondent in the input (prohibits epenthesis)

• Alignment (refers to constituent edges)

• Markedness (prefers unmarked structures):• ONS: syllables must have onsets• *CODA: syllables must not have a coda• *COMPLEX: no clusters of consonants

(1;2) (1;3)

Families of Constraints

• Correspondence (ensures diversity): relates elements of different strings (e.g. inputs and outputs)

• MAX-IO: every segment of the input has a correspondent in the output (prohibits deletion)

• DEP-IO: every segment of the output has a correspondent in the input (prohibits epenthesis)

(3;0)

Families of Constraints

• Alignment (refers to constituent edges)

(1;11)

violation of alignment:

morphology: aard # appel

phonology: aar $ dap $ pel

Align (Cat1,Edge1,Cat2,Edge2) =def Cat1 Cat2

in such a way that Edge1 of Cat1 and Edge2 of Cat2 coincide

Families of Constraints

OT and UG

• At least an important subset of constraints is shared by all languages, forming part of Universal Grammar

OT and UG

• At least an important subset of constraints is shared by all languages, forming part of Universal Grammar

• Individual languages rank these universal constraints differently in their language-specific hierarchies in such a way that higher ranked constraints have total dominance over lower ranked constraints

OT-tableau Berber

constraints ONS Hnuc

candidates

Ul *!

wL

input /ul/

/u/

/l/

OT-tableau Dutch

constraints Hnuc ONS

candidates

Ul /u/

wL /l/!

input /ul/

*

First Language Acquisition in

Optimality Theory

Learning First Language

Learning a language comes down to

resolving possible constraint conflicts by ranking the unordered

UG-constraints in a strict dominance

hierarchy

Example: Cluster Reduction in First Language Acquisition Data

(1;9)

Tableau Steven Stage (1;9)

*COMPL MAX-IO Hons//

[]

[]

[]

[]

*

*!

*

*

**

/k/

/l/!

ONS

Tableau Steven Stage (1;9)

*COMPL MAX-IO Hons/stul/

[stul]

[ul]

[sul]

[tul]

*

*!

*

*

**

/s/!

/t/

ONS

syllabe

(2;0) onset rhyme

margin nucleus

pre-m. m.core satellite peak satellite coda app.

s x a p

Positional Markedness

Tableau Dutch Ranking

*COMPLMAX-IO Hons/stul/

[stul]

[ul]

[sul]

[tul]

*!*

*!

*

*!

*

/s/

/st/

/t/

ONS

Tableau Dutch Ranking

*COMPLMAX-IO Hons/stul/

[stul]

[ul]

[sul]

[tul]

*!*

*!

*

*!

*

/s/

/st/

/t/

ONS

(2;1)

syllabe

(1,11) onset rhyme

margin nucleus

pre-m. m.core satellite peak satellite coda app.

x t

OT: Hmar: /t/ > /x/

syllabe

(2,2) onset rhyme

margin nucleus

pre-m. m.core satellite peak satellite coda app.

k r s t

OT: Hmar: /t/ > /s/

Merits of OT (1)

Conspiracy of

Different Influences

Hindi Heaviness Scale:• superheavy VVC; VCC• heavy VV; VC• light V

Peak Prominence in Hindi

ki.dhar

ja.naab

as.baab

ru.pi.aa

reez.ga.rii

Nonfinality in Hindi

• avoidance of stress on final syllable

(in event of a tie)trad. analysis: extrametricality/stress shift/destressing

sa.mi.ti

ru.kaa.yaa

aas.maan.jaah

Peak-Prominence >> Nonfinality >> AlignR

conspiracy of different influences

determines the most optimal output

OT ranking

Peak-Prominence >> Nonfinality >> AlignRconspiracy of different influences

determines the most optimal output

OT vs. PARAMETER SYSTEM:Parameters: Choice: Setting:Foot Type: Quantity In-/Sensitive QSFoot Size: Bounded/Unbounded BoundedDirection: Right to Left/L to R RLExtrametricality: Yes/No YesEdge of Extrametr.: Left/Right Rightetc.

OT ranking

Peak-Prominence >> Nonfinality >> AlignRconspiracy of different influences

determines the most optimal output

OT vs. PARAMETER SYSTEM:extrametricality parameter: wrong outputs for

ki.dhar - ja.naab - etc.RL scan sees no difference between final heavy ’s:

ru.pi.aa - ru.kaa.yaa - reez.ga.riiLR scan sees no difference between initial superheavy

’s: reez.ga.rii - aas.maan.jaah

OT ranking

Merits of OT (2)

constraints C1 C2 C3 C4 ... ONS *CODA

candidates

$ * *! *

$ *

*

The Emergence of the Unmarked:If two candidate outputs tie on all dominating constraints, the choice depends on the influence of a low-ranked constraint.

cf. principles & parameters theory: Dutch ONS: not obligatory; Dutch Coda: not forbidden

syllabification

Merits of OT (3)

Relative Grammaticality

constraints /ma/ candidates

IDENT-(place)-IO

IDENT-(voice)-IO

IDENT-(nas)-IO

FEAT-MK

IDENT-(cont)-IO

IDENT-(lat)-IO

IDENT-(rhot)-IO

[ma] ***

[pa] *† * *

[ba] *† **

[ta] *† * *

[da] *† * *

• how to restrict the number of constraints?

• variability• deflective systems• what’s in GEN?• what’s an input?• levels of representation/

cyclicity

OT: Work in Progress