what is optimality theory? introduction to optimality theory

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Introduction to Optimality Theory EGG 2011 Peter Jurgec ~ [email protected] What is Optimality Theory? Optimality Theory (OT) is a theory of constraint interaction. Constraints are requirements that forms must meet. Today’s Plan OT vs. Previous Approaches OT Architecture: constraints OT grammar constraint ranking tableaux Why OT?

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Page 1: What is Optimality Theory? Introduction to Optimality Theory

Introduction to Optimality Theory

EGG 2011Peter Jurgec ~ [email protected]

What is Optimality Theory?

• Optimality Theory (OT) is a theory of constraint interaction.

• Constraints are requirements that forms must meet.

Today’s Plan

• OT vs. Previous Approaches

• OT Architecture:

• constraints

• OT grammar

• constraint ranking

• tableaux

Why OT?

Page 2: What is Optimality Theory? Introduction to Optimality Theory

Two approaches

• Rules: “a must turn into b”

• most Generative Phonology, starting from The Sound Pattern of English (1968)

• Constraints: “no a”

• OT, some previous approaches

A real-world example

• Two ways of describing locations

• Example: New York Public Library

Option 1StartLeft

Straight StraightStraightStraightStraightStraightRight

StraightStraight

End

Option I1

NYC, Intersection of 40th Street and 5th Avenue

Page 3: What is Optimality Theory? Introduction to Optimality Theory

Two approachesTarget

NYC, Intersection of 40th Street

and 5th Avenue

Operations

StartLeft

Straight (x 6) Right

Straight (x 2)End

A phonological example

• Tibetan consonant clusters

• Option I:

• C → ∅ / # __

• Option II:

• No initial CC

A phonological example

• Tibetan consonant clusters

• Option I:

• C → ∅ / # __

• Option II:

• No initial CC

A phonological example

• Tibetan consonant clusters

• Option I — A rule:

• C → ∅ / # __

• Option II — A constraint:

• No initial CC

Page 4: What is Optimality Theory? Introduction to Optimality Theory

Rules v. Constraints

• Are the two approaches equivalent or are they fundamentally different?

• Do the two approaches make different predictions?

Optimality Theory

Optimality Theory

• Prince and Smolensky (1993)

• OT is a theory of constraint interaction.

• The main idea is that grammars impose a set of restrictions on what are valid surface forms.

• These restrictions can be formalized in terms of constraints.

What is this course about (and what not)?

• Introduction to Classic OT:

• Basic principles (Prince & Smolensky 1993/2004; McCarthy & Prince 1993b, 1994)

• Correspondence Theory (McCarthy & Prince 1995, 1999)

• Generalized Alignment (McCarthy & Prince 1993a;

Page 5: What is Optimality Theory? Introduction to Optimality Theory

Constraints

Constraints

• Constraints make restrictions on forms (candidates)

• In a nutshell, they require that candidates satisfy some condition: “be like that” or “don’t be like that”

• Constraints can be satisfied or violated.

• What kind of constraints are there?

Pre-OT constraints

• Constraints are a new way of describing and analyzing phonological patterns

• Were there constraints before OT?

• Examples:

• Morpheme Structure Constraints

• Obligatory Contour Principle (OCP)

Markedness constraints

• Languages generally prefer forms that:

• simple

• easy to pronounce

• easy to process

• common

• Some forms are better than others.

• Markedness is a way to formalize this situation.

Page 6: What is Optimality Theory? Introduction to Optimality Theory

Markedness

• an old concept (going back to structuralism)

• Phonology exhibits asymmetries:

• unmarked (common, frequent)

• marked (rare, exotic)

Markedness

• Examples:

• all languages have voiceless obstruents, but only some have voiced obstruents

• all languages have front unrounded vowels, but only some front rounded vowels

• all languages have oral vowels, but only some have nasal vowels

• all languages have C-initial words, but only some have V-initial words

Marked structures

• In OT, marked structures violate some constraint.

• Examples:

• “Obstruents must be voiced.”

• “No front rounded vowels.”

• “No nasal vowels.”

• “Words must start on a consonant.”

Markedness constraints

• Constraints that impose restrictions on surface forms are called markedness constraints.

• Are markedness constraints enough?

Page 7: What is Optimality Theory? Introduction to Optimality Theory

Markedness constraints

• If only markedness constraints existed, we would get only unmarked structures. Marked structures would never appear.

• No languages with voiced obstruents, front round vowels, nasal vowels, or C-initial words.

• We need another type of constraints that offset the effects markedness constraints.

Faithfulness constraints

• Faithfulness constraints mitigate the effects of markedness constraints.

• How?

OT Grammar

OT Grammar

• /input/ → Gen → candidate set → Eval → [output]

Page 8: What is Optimality Theory? Introduction to Optimality Theory

OT Grammar Gen(erator)

• Gen creates a candidate set

• Freedom of Analysis = Any amount of structure may be posited.

• Consistency of Exponence = No changes in the exponence of a phonologically-specified morpheme are permitted. (aka “Input morphemes are output morphemes.”)

OT Grammar Eval(uator)

• Eval selects a single winner from the set of candidates.

• Constraints are part of Eval.

Page 9: What is Optimality Theory? Introduction to Optimality Theory

Constraints

• Two types:

• markedness = impose restrictions on outputs

• faithfulness = mitigate the effect of markedness constraints

Faithfulness constraints

• Faithfulness constraints prefer no change from input to output.

• Faithfulness constraints refer to both the input and the output.

• Faithfulness constraints require identity between input and output.

Two types of constraints

Faithfulness constraints

• Examples:

• “No changes in nasality.”

• “No deletion.”

• “No insertion.”

• “No reordering.”

Page 10: What is Optimality Theory? Introduction to Optimality Theory

Interim summary

• OT background

• OT grammar

• OT constraints

Constraint Ranking

OT Grammar OT Grammar

Page 11: What is Optimality Theory? Introduction to Optimality Theory

Constraints are ...

• universal = all grammars have the same constraints

• violable = no candidate satisfies all constraints

• strictly ranked = a violation of a dominant constraint cannot be offset by non-violation of all other constraints

How do constraints work?

OT tableau OT tableau

Page 12: What is Optimality Theory? Introduction to Optimality Theory

OT tableau OT tableau

OT tableau OT tableau

Page 13: What is Optimality Theory? Introduction to Optimality Theory

An example: Tibetan numerals

Peter Jurgec 615:315 Phonology – Spring 2011

(1) My name is:

(2) Recall the dataset from Tibetan (originally analyzed on February 14) in (3).1

(3) Tibetan Numerals‘-teen (+10)’ ‘-ty (⇥10)’dZ<

u ‘10’dZ<

ig ‘1’ dZ<

u-gdZ<

ig ‘11’Si ‘4’ dZ

<u-bSi ‘14’ Si-bdZ

<u ‘40’

Na ‘5’ dZ<

u-Na ‘15’ Na-bdZ<

u ‘50’gu ‘9’ dZ

<u-rgu ‘19’ gu-bdZ

<u ‘90’

(4) Observation: Tibetan doesn’t allow initial consonant clusters. (Note: An affricate is a singlesegment rather than two segments.)

(5) Propose a rule that accounts for the Tibetan data.

(6) State the observation in (5) in terms of syllable constituents. Hint #1: Two consonants inword-medial clusters can be analyzed as belonging to different syllables. Hint #2: You mayuse the term ‘complex’, which refers to syllable constituents that consist of more than onesegment. For example, a ‘complex coda’ consists of two or more segments.

(7) Thus, there are two rather different ways of approaching the Tibetan data. According tothe rule-based analysis, the alternations are due to the rules of the language. According toan alternative approach, the alternations happen because some target must be met (i.e. nocomplex onsets are allowed).

1Using this example to point out the difference between rules and constraints is based on John McCarthy’s lecturenotes.

1

Tibetan numerals

• /ŋa/ → [ŋa] ‘5’

• /rgu/ → [gu] ‘9’

• /bdʒu/ → [dʒu] ‘10’

• /rgu-bdʒu/ → [gu-bdʒu] ‘90’

• /bdʒu-gdʒig/ → [dʒu-gdʒig] ‘11’

Tibetan generalizations

• /ŋa/ → [ŋa] ‘5’

• /bdʒu/ → [dʒu] ‘10’

• /rgu-bdʒu/ → [gub.dʒu] ‘90’

• /bdʒu-gdʒig/ → [dʒug.dʒig] ‘11’

• No complex onsets!

Tibetan generalizations

• /ŋa/ → [ŋa] ‘5’

• /bdʒu/ → [dʒu] ‘10’

• /rgu-bdʒu/ → [gub.dʒu] ‘90’

• /bdʒu-gdʒig/ → [dʒug.dʒig] ‘11’

• No complex onsets!

Page 14: What is Optimality Theory? Introduction to Optimality Theory

Tibetan generalizations

• In Tibetan, complex onsets violate some markedness constraint.

• How do we know?

• Tibetan avoids complex onsets.

• All languages that allow complex onsets also allow simple onsets.

No Complex Onset

• *COMPLEXONSET (or NOCOMPLEXONSET)

• No complex onsets.

• Note: Syllables with simple onsets do note violate this constraint.

Faithfulness

• The constraint *COMPLEXONSET outranks some faithfulness constraint. We will call this constraint simply Faith.

• FAITH

• No changes. (The input and the output must be identical.)

Tibetan ‘99’

Page 15: What is Optimality Theory? Introduction to Optimality Theory

(b) wins (b) wins

Evaluation of *COMPLEXONSET

• *COMPLEXONSET = No complex onsets.

Evaluation of FAITH

• FAITH = No changes.

Page 16: What is Optimality Theory? Introduction to Optimality Theory

Violation marks (*)

• Violations are marked with stars (*).

Violation marks (*)

• Violations are marked with stars (*).

Violation marks (*)

• Fatal violations are marked with an exclamation mark (!).

The ranking of constraints matters

• If the ranking of *COMPLEXONSET and FAITH were reversed, we would not get the right grammar.

Page 17: What is Optimality Theory? Introduction to Optimality Theory

Anti-Tibetan

• Anti-Tibetan preserves all segments rather than avoids complex onsets.

Rankings

• Higher constraints are more important than lower constraints.

• A violation of a higher constraint cannot be offset by not violating all other constraints.

Exercise: Winners

What’s next?

• Tuesday: Faithfulness, Intro to typologies

• Wednesday: Factorial Typology

• Thursday: More on rankings

• Friday: How to do an analysis?

Page 18: What is Optimality Theory? Introduction to Optimality Theory

Correspondence Theory

EGG 2011Peter Jurgec ~ [email protected]

Summary so far

• OT = A theory of constraint interaction

• Constraints = universal, violable, strictly ranked

• Tableaux = a tool to represent input–output mappings

Principles of OT (McCarthy & Prince 1993)

• Universality

• Violability

• Ranking

• Inclusiveness (large candidate set)

• Parallelism

Tibetan ‘99’

Page 19: What is Optimality Theory? Introduction to Optimality Theory

Some OT lingo

• Constraint = an element of Eval; a constraint can be satisfied or violated

• Strict Ranking of constraints = a violation of the highest ranked constraint cannot be offset by not violating all other constraints

• To outrank = A outranks B iff A is ranked above B (also: A ≫ B)

OT lingo

• Violation marks (*) = designate violations of a constraint

• Candidate = an input–output pair

• Optimal Candidate / Winner = the candidate tnjat incurs the least violation marks of the highest constraints compared to all other candidates (marked with ‘☞’)

OT lingo

• Loser = a candidate that is not optimal

• Fatal Violation (!) = a candidate fatally violates a constraint if (i) there is at least one other candidate that fares equally on all higher ranked constraints, and (ii) if another candidate does not violate the current constraint

Recall Tibetan

• Tibetan doesn’t allow complex onsets.

• In OT, this situation can be formalized using two constraints:

• a markedness constraint that penalizes complex onsets and is ranked above

• a faithfulness constraint that penalizes deletion

• markedness outranks faithfulness

Page 20: What is Optimality Theory? Introduction to Optimality Theory

Recall Tibetan

• Tibetan doesn’t allow complex onsets.

• In OT, this situation can be formalized using two constraints:

• a markedness constraint that penalizes complex onsets and is ranked above

• a faithfulness constraint that penalizes deletion

• markedness outranks faithfulness

Correspondence Theory (McCarthy & Prince 1995, 1999)

• Faithfulness constraints evaluate 2 different “forms”: the input and output.

• The main idea: Each segment, feature, constituent of the input is in correspondence with a segment, feature, constituent of the output.

• Input Output

Correspondence

• Each segment of the input has a corresponding segment in the output.

615:315 Phonology

Optimality Theory

Correspondence

Input / p1 a2 t3 a4 /

Output [ p1 a2 t3 a4 ]

Each segment of the input has a corresponding segment in the output.

Faithful candidates

• A candidate is faithful, if it doesn’t violate any faithfulness constraint. (This is slightly simplified.)

• Unfaithful candidates violate some faithfulness constraint.

Page 21: What is Optimality Theory? Introduction to Optimality Theory

Unfaithful candidate• Example:

• /a4/ doesn’t have an output correspondent. This violates some faithfulness constraint.

• Why are candidates not faithful?615:315 Phonology

Optimality Theory

Unfaithful outputs

•  What is the output is not faithful? •  Example:

Input / p1 a2 t3 a4 /

Output [ p1 a2 t3 ]

In this case, the /a4/ doesn’t have a correspondent. This violates some faithfulness constraint.

Two types of constraints

• There are two types of constraints:

• markedness constraints impose restrictions on outputs

• faithfulness constraints favor no changes between input and output

Two types of constraints

Faithfulness constraints

• Correspondence is evaluated by faithfulness constraints.

• There are many types of different faithfulness constraints.

Page 22: What is Optimality Theory? Introduction to Optimality Theory

Faithfulness constraints

• IDENT(ITY)An input segment and its output correspondent must be identical. (No changes.)

• MAX(IMALITY) Every input segment must have an output correspondent. (No deletion.)

• DEP(ENDENCE)Every output segment must have an input correspondent. (No epenthesis.)

Deletion

• /a4/ doesn’t have an output correspondent, violating MAX.

• MAX Every input segment must have an output correspondent. (No deletion.)

615:315 Phonology

Optimality Theory

Deletion

Input / p1 a2 t3 a4 /

Output [ p1 a2 t3 ]

•  /a4/ doesn’t have an output correspondent. This violates MAX. •  MAX

Every input segment must have an output correspondent. (No deletion.)

Epenthesis

• [a4] doesn’t have an input correspondent, violating DEP.

• DEP Every output segment must have an input correspondent. (No epenthesis.)

615:315 Phonology

Optimality Theory

Deletion

Input / p1 a2 t3 a4 /

Output [ p1 a2 t3 ]

•  /a4/ doesn’t have an output correspondent. This violates MAX. •  MAX

Every input segment must have an output correspondent. (No deletion.)

615:315 Phonology

Optimality Theory

Epenthesis

Input / p1 a2 t3 /

Output [ p1 a2 t3 a4 ]

•  [a4] doesn’t have an input correspondent. This violates DEP. •  DEP

Every output segment must have an input correspondent. (No epenthesis.)

Correspondence

• Each segment of the input has a corresponding segment in the output.

615:315 Phonology

Optimality Theory

Correspondence

Input / p1 a2 t3 a4 /

Output [ p1 a2 t3 a4 ]

Each segment of the input has a corresponding segment in the output.

Page 23: What is Optimality Theory? Introduction to Optimality Theory

Change

• /a4/ and [i4] are in correspondence, but they are not identical. This violates IDENT.

• IDENT An input segment and its output correspondent must be identical. (No changes.)

615:315 Phonology

Optimality Theory

Deletion

Input / p1 a2 t3 a4 /

Output [ p1 a2 t3 ]

•  /a4/ doesn’t have an output correspondent. This violates MAX. •  MAX

Every input segment must have an output correspondent. (No deletion.)

615:315 Phonology

Optimality Theory

Epenthesis

Input / p1 a2 t3 /

Output [ p1 a2 t3 a4 ]

•  [a4] doesn’t have an input correspondent. This violates DEP. •  DEP

Every output segment must have an input correspondent. (No epenthesis.)

615:315 Phonology

Optimality Theory

Change

Input / p1 a2 t3 a4 /

Output [ p1 a2 t3 i4 ]

•  /a4/ and [i4] are in correspondence, so neither DEP nor MAX are violated. IDENT is.

•  IDENT An input segment and its output correspondent must be identical. (No changes.)

Back to Tibetan

MAX

• The relevant constraint is MAX.

• MAX Every input segment must have an output correspondent. (No deletion.)

Are we done?

Page 24: What is Optimality Theory? Introduction to Optimality Theory

More candidates?

• Problem: Candidate (c) wins! ☹

• Solution: Candidate (c) violates another constraint that is not violated by (b).

What other constraints are there?

DEP

• DEP Every output segment must have an input correspondent. (No epenthesis.)

But where?

• This ranking makes wrong predictions. Candidate (c) is not the actual winner.

• Solution: Candidate (c), but not (c), violates DEP. To rule out (c), we need to rank DEP higher.

Page 25: What is Optimality Theory? Introduction to Optimality Theory

DEP ranked higher

• This ranking works! �

DEP ranked even higher

• This ranking works, too! The ranking between DEP and *COMPLEXONSET doesn’t matter.

• The data are ambiguous and can be explained but either ranking.

Multiple rankings

• Important: The constraints are still strictly ranked wrt to one another, it’s just that the ranking doesn’t matter.

Even more candidates

Page 26: What is Optimality Theory? Introduction to Optimality Theory

Even more candidates (with *s)

Can (d), (e) ever win?

(d), (e) are harmonically bounded

Harmonic bounding

• A candidate is harmonically bounded when it cannot win under any ranking.

Page 27: What is Optimality Theory? Introduction to Optimality Theory

(d), (e) are harmonically bounded

• On no constraint do (d), (e) fare better than all other candidates.

(a), (b), (c) can win under some ranking

• (a) wins when DEP, MAX ≫

*COMPLEXONSET

• (b) wins when DEP, *COMPLEXONSET ≫ MAX

• (c) wins when MAX, *COMPLEXONSET ≫ DEP

Exercise: Evaluation

Summary

• Faithfulness constrains are of different kinds.

• Constraints can have different rankings in different languages.

• There is no restriction on ranking. Cross-linguistic typologies come from possible rankings.

• Some candidates can never win in no language.

Page 28: What is Optimality Theory? Introduction to Optimality Theory

Factorial TypologyEGG 2011

Peter Jurgec ~ [email protected]

Summary so far

• OT grammar

• OT constraints

• Tableaux

• Correspondence Theory

Today’s Outline

• Nasalization typology

• Syllable typology

Factorial Typology

• Constraints are universal, but their ranking is language specific.

• The differences among languages are due to different constraint rankings.

Page 29: What is Optimality Theory? Introduction to Optimality Theory

Factorial Typology

• Suppose there are n universal constraints.

• These constraints produce n! different rankings.

Factorial Typology

• 10 constraints → 10! = 3,628,800 rankings

• At first, this seems to be a very large number of grammars, a portion of which are actually attested.

• However, it turns out that not all rankings produce different grammars.

Distribution of nasal vowels

• Four attested patterns

• Let’s look at them in more detail ...

Factorial Typology

Peter [email protected]

April 2011

(1) Constraints are a good ways to capture cross-linguistic generalizations. In particular, dif-ferent rankings produce different languages. Given a limited number of constraints, therewill be a limited number of possible languages.

(2) Example: The distribution of oral/nasal vowelsV + oral C V + nasal C

a. Highly Restricted Inventory pal panb. Complimentary Distribution pal panc. Positional Neutralization pal pal pand. Full Contrast pal pal pan pan

(3) Observation: There are seemingly no alternations. But that’s slightly misleading.(4) Richness of the Base (RotB)

No constraint holds at the level of the input. (Also, every possible input must map to someoutput.)

(5) Thus, we need to consider all possible inputs (and all possible mappings):a. palb. palc. pand. pan

(6) What constraints do we need?(7) Are all combinations of vowels (oral or nasal) and consonants (oral and nasal) attested?

Describe two theoretically possible, but unattested patterns. (Howmany patterns/languagesare unattested?)

a. Pattern/Language 1

b. Pattern/Language 2

(8) The unattested patterns/languages are indicative of the distributional restrictions on nasal-ity. Describe them. (You can state some of them as implicational generalizations. Forexample: If a language L has x, L will also have y.)

1

I. Highly restricted inventory

• Allows only oral vowels, but nasals (nasal sonorant stops) are possible.

• Attested: pal, pan

• Not attested: *pãl, *pa���n

Page 30: What is Optimality Theory? Introduction to Optimality Theory

II. Full contrast

• Nasal vowels are possible in all positions.

• Attested: pal, pan, pãl, pa���n

III. Complimentary Distribution

• Nasal vowels are possible only before nasals, and oral vowels are possible only before oral consonants.

• Attested: pal, pa���n

• Not attested: *pãl, *pan

1V. Positional Neutralization

• Only nasal vowels are possible before nasals.

• Attested: pal, pãl, pa���n

• Not attested: *pan

1. Highly restricted inventory

• Allows only oral vowels, but nasals (nasal sonorant stops) are possible.

• Attested: pal, pan

• Not attested: *pãl, *pa���n

Page 31: What is Optimality Theory? Introduction to Optimality Theory

Distribution of nasal vowels

• Four attested patterns

• Other patterns are not attested.

Factorial Typology

Peter [email protected]

April 2011

(1) Constraints are a good ways to capture cross-linguistic generalizations. In particular, dif-ferent rankings produce different languages. Given a limited number of constraints, therewill be a limited number of possible languages.

(2) Example: The distribution of oral/nasal vowelsV + oral C V + nasal C

a. Highly Restricted Inventory pal panb. Complimentary Distribution pal panc. Positional Neutralization pal pal pand. Full Contrast pal pal pan pan

(3) Observation: There are seemingly no alternations. But that’s slightly misleading.(4) Richness of the Base (RotB)

No constraint holds at the level of the input. (Also, every possible input must map to someoutput.)

(5) Thus, we need to consider all possible inputs (and all possible mappings):a. palb. palc. pand. pan

(6) What constraints do we need?(7) Are all combinations of vowels (oral or nasal) and consonants (oral and nasal) attested?

Describe two theoretically possible, but unattested patterns. (Howmany patterns/languagesare unattested?)

a. Pattern/Language 1

b. Pattern/Language 2

(8) The unattested patterns/languages are indicative of the distributional restrictions on nasal-ity. Describe them. (You can state some of them as implicational generalizations. Forexample: If a language L has x, L will also have y.)

1

OT analysis

• Let us think of what constraints are required to capture these patterns.

Constraints

• Three different types of constraints:

• general markedness constraints

• contextual markedness constraints

• faithfulness constraints

Two types of markedness constraints

• Why are they required?

• The general constraint penalizes one type of vowels regardless of their position.

• The context-specific constraint penalizes one type of vowels in a particular position.

Page 32: What is Optimality Theory? Introduction to Optimality Theory

General Markedness Constraints

• Similar sets of segments typically exhibit asymmetries in terms of markedness.

• More marked = less common cross-linguistically, subject to restrictions ...

• These phonological facts often have to do with their phonetic properties (harder to articulate, perceive etc.).

General Markedness Constraints

• Some examples:

• All languages have oral vowels, but some also have nasal vowels.

• All languages have front unrounded vowels, but not all languages have front rounded vowels.

• All languages have voiceless obstruents, but not all languages have voiced obstruents.

Nasal v. oral vowels

• Which are more marked?

• All languages have oral vowels, but some may also have nasal vowels.

• Oral vowels are more frequent than nasal vowels.

• No language have more nasal vowels than oral vowels.

Nasal vowels are marked

• ... compared to oral vowels

• This generalization can be captured using a markedness constraint.

• This constraint is context-free, and applies to all nasal vowels.

• *NASALVOWEL No nasal vowels.

Page 33: What is Optimality Theory? Introduction to Optimality Theory

Contextual markedness constraints

• Not all segments are equally marked in all positions.

• Examples:

• In the position before voiceless obstruents, voiced obstruents are more marked than voiceless obstruents.

• Voiced obstruents are more marked in word-final position than voiceless obstruents.

Contextual markedness constraints

• What about nasal and oral vowels?

• Recall: Nasal vowels are generally more marked than oral vowels.

• Is there a position in which the situation is reversed?

Contextual markedness constraints

• Oral vowels are more marked than nasal vowels in the position before a nasal consonant.

• [an] is more marked than [ãn]

Contextual markedness constraints

• Oral vowels are more marked than nasal vowels in the position before a nasal consonant. How do we know?

• Languages show neutralization before nasal consonants.

• Some languages only allow nasal vowels before nasal consonants.

Page 34: What is Optimality Theory? Introduction to Optimality Theory

Contextual markedness constraints

• Contextual markedness constraints penalize sequences of segments.

• *Vn No oral vowels followed by nasal consonants.

Two markedness constraints

• General markedness constraint:

• *NASALVOWEL No nasal vowels.

• Contextual markedness constraint:

• *Vn No oral vowels followed by nasal consonants.

Are these two constraints enough?

Faithfulness constraints

• If only markedness constraints existed, we would expect only two types of languages:

• no nasal vowels

• only nasal vowels before nasals, only oral vowels elsewhere

• Solution: A faithfulness constraint is also involved!

Page 35: What is Optimality Theory? Introduction to Optimality Theory

Let’s check that• Grammar 1: All vowels

map to oral vowels.

• 2 constr = 2 rankings

• Grammar II: Nasal vowels before nasal C,

• ...oral vowels elsewhere

Peter Jurgec 615:315 Phonology – Spring 2011

/a/ *a *an

a. [a] *!

b.☞ [a] (*)

4

Peter Jurgec 615:315 Phonology – Spring 2011

/al/ *an *a

a. [al] *!

b.☞ [al]

4

Peter Jurgec 615:315 Phonology – Spring 2011

/an/ *an *a

a. [an] *!

b.☞ [an] *

4

Faithfulness constraints

• If only markedness constraints existed, we would expect only two types of languages:

• no nasal vowels

• only nasal vowels before nasals, only oral vowels elsewhere

• Solution: A faithfulness constraint is also involved!

Richness of the Base• (Prince and Smolensky 1993:209)

• “All inputs are possible in all languages, [and] distributional and inventory regularities follow from the way the universal input set is mapped onto an output set by the grammar, a language-particular ranking of the constraints.”

• “No constraint holds at the level of the input.”

• Every possible input must map to some output.

Inputs wrt nasal vowels

• Four possible inputs must be considered:

• /pal/ = oral vowel + oral consonant

• /pan/ = oral vowel + nasal consonant

• /pãl/ = nasal vowel + oral consonant

• /pa���n/ = nasal vowel + nasal consonant

Page 36: What is Optimality Theory? Introduction to Optimality Theory

Why?

• Challenge: Some languages don’t even have nasal vowels.

• Question: Why do we need to consider inputs with nasal vowels?

• Answer: Richness of the Base = no constraint applies at the level of the input

Why?

• Challenge: Some languages don’t even have nasal vowels.

• Question: Why do we need to consider inputs with nasal vowels?

• Answer: Richness of the Base = no constraint applies at the level of the input.

Mappings in a language without nasal vowels• Inputs

• /pal/

• /pan/

• /pãl/

• /pa���n/

• ...

• Outputs

• [pal]

• [pan]

Mappings in a language without nasal vowels• Inputs

• /pal/

• /pan/

• /pãl/

• /pa���n/

• ...

• Outputs

• [pal]

• [pan]

Page 37: What is Optimality Theory? Introduction to Optimality Theory

Mappings in a language without nasal vowels• Inputs

• /pal/

• /pan/

• /pãl/

• /pa���n/

• ...

• Outputs

• [pal]

• [pan]

Lexicon Optimization

• How do we know what inputs map to what outputs?

• Lexicon Optimization (Prince and Smolensky 1993:209)

Lexicon OptimizationPeter Jurgec 16:615:521 Phonology – Spring 2011

by the grammar, a language-particular ranking of the constraints.No constraints hold at the level of the input.Every input must map to some output.

b. Lexicon Optimization (Prince & Smolensky 1993/2004:209)

Suppose that several different inputs I1, I1,. . . , In, when parsed bya grammar G lead to corresponding outputs O1, O1,. . . , On, all ofwhich are realized as the same phonetic form Φ—these inputs are allphonetically equivalent with respect to G. Now one of these outputsmust be the most harmonic, by virtue of incurring the least significantviolation marks: suppose this optimal one is labelled Ok. Then thelearner should choose, as the underlying form for M, the input Ik.

(6) Con

a. Strict ranking/dominationb. Types of constraints (in classic OT)

(i) Faithfulness constraintsA limited set of constraints evaluating the input and the output (Mc-Carthy & Prince 1995)Dep (“Don’t epenthesize”), Max (“No deletion”), Ident, Linear-ity (“No metathesis”), Integrity (“No breaking”), Contiguity

(“No skipping/No intrusion”), Uniformity (“No coalescence”), An-

chor

(ii) Markedness constraintsA large set of constraints that evaluate only the outputAny markedness constraint penalizes some output structuresTypologically and/or phonetically grounded

(7) Phonologist’s job (in OT)

a. Figure out the generalizationsb. Figure out possible and impossible segments/sequences (and alternations)c. Propose constraints (active constraints)

(i) Faithfulness constraints(ii) Markedness constraints

d. Figure out the ranking out these constraints(i) Method #1: Trial and error(ii) Method #2: Factorial Typology(iii) Method #3: Algorithms(iv) Method #4: Software (e.g. OTsoft)

2

Lexicon Optimization

• In a nutshell, if several phonetically equivalent inputs exist, we need to consider the one that that violates the lowest faithfulness constraints.

Page 38: What is Optimality Theory? Introduction to Optimality Theory

Faithfulness constraints

• We will consider changing of nasality from the input to output.

• IDENT(nasal)Corresponding segments must be identical in terms of nasality. (No changes in nasality.)

Faithfulness constraints

• We will consider changing of nasality from the input to output.

• IDENT(nasal)Corresponding segments must be identical in terms of nasality. (No changes in nasality.)

Constraints

• *NASALVOWEL No nasal vowels.

• *Vn No oral vowels followed by nasal consonants.

• IDENT(nasal)Corresponding segments must be identical in terms of nasality. (No changes in nasality.)

Highly restricted inventory

• No nasal vowels: *NASALVOWEL is top ranked

Peter Jurgec 615:315 Phonology – Spring 2011

(19) Highly Restricted Inventory (No nasal vowels)a. /pan/ *NASV *Vn IDENT(nas)

a.☞ [pan] *

b. [pan] *! *

b. /pan/ *NASV *Vn IDENT(nas)

a.☞ [pan] * *

b. [pan] *!

c. /pal/ *NASV *Vn IDENT(nas)

a.☞ [pal]

b. [pal] *! *

d. /pal/ *NASV *Vn IDENT(nas)

a.☞ [pal] *

b. [pal] *!

(20) Complimentary Distribution/AllophonicVariation (Nasal vowels before nasal consonants,oral vowels elsewhere)a. /pan/

a. [pan]

b. [pan]

b. /pan/

a. [pan]

b. [pan]

c. /pal/

a. [pal]

b. [pal]

d. /pal/

a. [pal]

b. [pal]

4

Page 39: What is Optimality Theory? Introduction to Optimality Theory

Highly restricted inventory

Peter Jurgec 615:315 Phonology – Spring 2011

(19) Highly Restricted Inventory (No nasal vowels)a. /pan/ *NASV *Vn IDENT(nas)

a.☞ [pan] *

b. [pan] *! *

b. /pan/ *NASV *Vn IDENT(nas)

a.☞ [pan] * *

b. [pan] *!

c. /pal/ *NASV *Vn IDENT(nas)

a.☞ [pal]

b. [pal] *! *

d. /pal/ *NASV *Vn IDENT(nas)

a.☞ [pal] *

b. [pal] *!

(20) Complimentary Distribution/AllophonicVariation (Nasal vowels before nasal consonants,oral vowels elsewhere)a. /pan/

a. [pan]

b. [pan]

b. /pan/

a. [pan]

b. [pan]

c. /pal/

a. [pal]

b. [pal]

d. /pal/

a. [pal]

b. [pal]

4

Full contrast

• No restrictions: *IDENT(nasal) is top ranked

Peter Jurgec 615:315 Phonology – Spring 2011

(21) Positional Neutralization (No oral vowels before nasal consonants)a. /pan/

a. [pan]

b. [pan]

b. /pan/

a. [pan]

b. [pan]

c. /pal/

a. [pal]

b. [pal]

d. /pal/

a. [pal]

b. [pal]

(22) Full Contrast (Oral and nasal vowels possible in all positions)a. /pan/ IDENT(nas) *NASV *Vn

a.☞ [pan] *

b. [pan] *! *

b. /pan/ IDENT(nas) *NASV *Vn

a. [pan] *! *

b.☞ [pan] *

c. /pal/ IDENT(nas) *NASV *Vn

a.☞ [pal]

b. [pal] *! *

d. /pal/ IDENT(nas) *NASV *Vn

a. [pal] *!

b.☞ [pal] *

5

Full contrast

Peter Jurgec 615:315 Phonology – Spring 2011

(21) Positional Neutralization (No oral vowels before nasal consonants)a. /pan/

a. [pan]

b. [pan]

b. /pan/

a. [pan]

b. [pan]

c. /pal/

a. [pal]

b. [pal]

d. /pal/

a. [pal]

b. [pal]

(22) Full Contrast (Oral and nasal vowels possible in all positions)a. /pan/ IDENT(nas) *NASV *Vn

a.☞ [pan] *

b. [pan] *! *

b. /pan/ IDENT(nas) *NASV *Vn

a. [pan] *! *

b.☞ [pan] *

c. /pal/ IDENT(nas) *NASV *Vn

a.☞ [pal]

b. [pal] *! *

d. /pal/ IDENT(nas) *NASV *Vn

a. [pal] *!

b.☞ [pal] *

5

*Vn is high ranked

• The ranking of the lower ranked constraints becomes relevant.

Page 40: What is Optimality Theory? Introduction to Optimality Theory

Exercise: Factorial Typology

Two other grammars

• Complimentary distribution: *Vn ≫ *NASALVOWEL ≫ IDENT(nasal)

• Nasal vowels only before nasal consonants, oral vowels in all other positions.

• Positional neutralization: *Vn ≫ IDENT(nasal) ≫ *NASALVOWEL

• Only nasal vowels before nasal consonants, full contrast in all other positions.

Four possible grammars

• Highly restrictive inventory: *NASALVOWEL ≫ IDENT(nasal), *Vn

• Full contrast: IDENT(nasal) ≫ *NASALVOWEL, *Vn

• Complimentary distribution: *Vn ≫ *NASALVOWEL ≫ IDENT(nasal)

• Positional neutralization: *Vn ≫ IDENT(nasal) ≫ *NASALVOWEL

Rankings vs. grammars

• 3 constraints → 3! = 6 rankings

• ... but only 4 different grammars!

• Not all rankings will result in a distinct grammar. Some rankings produce the same grammar.

• Hence, 10 constraints won’t produce 10! = 3,628,800 different grammars.

Page 41: What is Optimality Theory? Introduction to Optimality Theory

Interim summary

• Constraints are universal.

• Cross-linguistic differences stem from rankings.

• Not every ranking produces a unique grammar. Some rankings don’t matters.

• Factorial typology produces the full range of attested grammars.

Another example: Syllable typology

The Syllable

615:315 Phonology

Prosody

Nuclear

Onsets

• All languages have onsets.

• Some languages may also have syllables without onsets.

Page 42: What is Optimality Theory? Introduction to Optimality Theory

Codas

• Not all languages allow codas.

• If a language has syllables with codas, it will also have syllables without codas.

Constraints

• ONSET Syllables must have onsets. *[σV

• *CODA No codas. *C]σ

Syllable types

Syllable type ONSET *CODA

CV � �

CVC � *

V * �

VC * *

Some universals

• Universal syllabification CV.CV ⧽ CVC.V (⧽ ‘more harmonic than’)

Page 43: What is Optimality Theory? Introduction to Optimality Theory

No language has [tat.a]

Factorial Typology

Fill in the violation marks and determine the winners.

(1) *Vn! *NASV ! IDENT(nas)a. /tata/ ONSET *CODA

a.☞ [ta.ta]

b. [tat.a] *! *!

b. /pan/ *Vn *NASV IDENT(nas)

a. [pan]

b. [pan]

c. /pal/ *Vn *NASV IDENT(nas)

a. [pal]

b. [pal]

d. /pal/ *Vn *NASV IDENT(nas)

a. [pal]

b. [pal]

(2) *Vn! IDENT(nas)! *NASVa. /pan/ *Vn IDENT(nas) *NASV

a. [pan]

b. [pan]

b. /pan/ *Vn IDENT(nas) *NASV

a. [pan]

b. [pan]

c. /pal/ *Vn IDENT(nas) *NASV

a. [pal]

b. [pal]

d. /pal/ *Vn IDENT(nas) *NASV

a. [pal]

b. [pal]

How do we get syllables?

• They can be in the input or not.

• Richness of the Base allows for any kind of syllabification in the input.

How do we get syllables?

• Usually, we assume that only the output is syllabified (prosodified):

• Freedom of Analysis = Any amount of structure may be posited.

• Syllabification is governed by markedness constraints.

Summary

• Factorial typology predicts the range of attested languages.

• Some rankings produce the same grammar.

Page 44: What is Optimality Theory? Introduction to Optimality Theory

More on constraint ranking

EGG 2011Peter Jurgec ~ [email protected]

Summary so far

• OT grammar

• OT constraints

• Factorial Typology

Today’s Outline

• The Emergence of the Unmarked (TETU)

• Homogeneity of Target/Heterogeneity of Process (HoTHoP)

• Generalized Alignment

How does constraint ranking work?

• Dominant constraints are much more likely to be active compared to low-ranked constraints.

• ‘Active’ = have fatal violations, exclude one or more candidates.

• Violations of lower ranked constraints many times do not matter.

Page 45: What is Optimality Theory? Introduction to Optimality Theory

The Emergence of the Unmarked

• aka TETU

• A phenomenon in which a lower-ranked constraint becomes active.

Recall last time ...

• Constraints on syllable structure:

• ONSET Syllables must have onsets. *[σV

• *CODA No codas. *C]σ

A toy language

• Allows onsetless syllables

• Never prefers deletion or epenthesis

• DEP and MAX outrank ONSET

Mappings

• /pata/ → [pata]

• /pae/ → [pae]

• /ata/ → [ata]

Page 46: What is Optimality Theory? Introduction to Optimality Theory

Assign *s

Peter Jurgec 16:615:521 Phonology – Spring 2011

(13) Rank the two constraints in tableau (14). If the ranking does not work, use tableau(15).

(14) /azadeg/ → [azade] ‘freeborn-nom’

/azadeg/

a. azadeg

b. azade

(15) /ata/ → [ata]

/ata/ Dep Max Onset

a. ☞ a.ta

b. Pa.ta

(16) Now, rank the constraint *g with respect to the other two constraints by consideringthe genitive forms, as in (17). Feel free to use the other two tableaux if the originalranking does not work.

(17) /azadeg-an/ → [azadegan] ‘freeborn-gen’

/azadeg-an/

a. azadegan

b. azadean

(18) /azadeg-an/ → [azadegan] ‘freeborn-gen’

/azadeg-an/

a. azadegan

b. azadean

(19) /azadeg-an/ → [azadegan] ‘freeborn-gen’

/azadeg-an/

a. azadegan

b. azadean

(20) How did you figure out the correct ranking?

4

ONSET is not active

Peter Jurgec 16:615:521 Phonology – Spring 2011

(13) Rank the two constraints in tableau (14). If the ranking does not work, use tableau(15).

(14) /azadeg/ → [azade] ‘freeborn-nom’

/azadeg/

a. azadeg

b. azade

(15) /ata/ → [ata]

/ata/ Dep Max Onset

a. ☞ a.ta *

b. Pa.ta *!

(16) Now, rank the constraint *g with respect to the other two constraints by consideringthe genitive forms, as in (17). Feel free to use the other two tableaux if the originalranking does not work.

(17) /azadeg-an/ → [azadegan] ‘freeborn-gen’

/azadeg-an/

a. azadegan

b. azadean

(18) /azadeg-an/ → [azadegan] ‘freeborn-gen’

/azadeg-an/

a. azadegan

b. azadean

(19) /azadeg-an/ → [azadegan] ‘freeborn-gen’

/azadeg-an/

a. azadegan

b. azadean

(20) How did you figure out the correct ranking?

4

Constraint ranking

• Lower ranked constraints typically don’t matter!

More candidates

Peter Jurgec 16:615:521 Phonology – Spring 2011

(13) Rank the two constraints in tableau (14). If the ranking does not work, use tableau(15).

(14) /azadeg/ → [azade] ‘freeborn-nom’

/azadeg/

a. azadeg

b. azade

(15) /ata/ → [ata]

/ata/ Dep Max Onset

a. ☞ a.ta *

b. at.a **!

c. Pa.ta *!

(16) Now, rank the constraint *g with respect to the other two constraints by consideringthe genitive forms, as in (17). Feel free to use the other two tableaux if the originalranking does not work.

(17) /azadeg-an/ → [azadegan] ‘freeborn-gen’

/azadeg-an/

a. azadegan

b. azadean

(18) /azadeg-an/ → [azadegan] ‘freeborn-gen’

/azadeg-an/

a. azadegan

b. azadean

(19) /azadeg-an/ → [azadegan] ‘freeborn-gen’

/azadeg-an/

a. azadegan

b. azadean

(20) How did you figure out the correct ranking?

4

Page 47: What is Optimality Theory? Introduction to Optimality Theory

TETU

• Even though ONSET is frequently violated in this language (and thus ranked low), it is nevertheless still active, crucially deciding among some candidates.

• ONSET prefers outputs with onsets rather than codas.

Homogeneity of Target/Heterogeneity of

Process (HoTHoP)

HoTHoP

• OT is a target-oriented theory.

• Targets are enforced by markedness constraints.

HoTHoP

• There are several ways of satisfying a markedness constraint.

• The way a markedness constraint is satisfied is determined by other constraints.

• Pre-OT term: “conspiracy” (Kisseberth 1970)

Page 48: What is Optimality Theory? Introduction to Optimality Theory

Example: *NC

• (Pater 1999)

• *NC No nasal + voiceless consonant sequences.

• Is *NC a good constraint?

Example: *NC

• (Pater 1999)

• *NC No nasal + voiceless consonant sequences.

• Is *NC a good constraint?

*NC

• *NC is formally not an ideal markedness constraint.

• The featural connection between a nasal and a voiceless consonant is unclear.

*NC

• Phonetically grounded: nasalization correlates with voicing, and it is difficult to produce a sequence of consonants that differ in voicing.

• Typologically grounded: languages that allow NC clusters also allow NC clusters, but not vice versa.

Page 49: What is Optimality Theory? Introduction to Optimality Theory

Let’s look at some data NC resolution

• Toba Batak: nasals become oral

• Kelantan Malay: nasals delete

• Japanese: voiceless C becomes voiced

Ranking of other constraints matters!

• These grammars are predicted by different rankings of *NC and other constraints:

• IDENT(nasal)

• IDENT(voice)

• MAX

Rankings

Peter Jurgec 16:615:521 Phonology – Spring 2011

(6) These grammars are predicted by different rankings of *NC˚

and other constraints:Ident(nasal)Ident(voice)Max

(7) Rankings

a. Toba Batak*NC

˚, Ident(voice), Max ! Ident(nasal)

b. Kelantan Malay*NC

˚, Ident(voice), Ident(nasal) ! Max

c. Japanese*NC

˚, Ident(nasal), Max ! Ident(voice)

d. EnglishIdent(voice), Ident(nasal), Max ! *NC

˚(8) Conspiracies = HoTHoP patterns within a single language

(9) Example: Slovenian (Becker & Jurgec 2008)

(10) In Slovenian, combinations of H(igh tone) and [−ATR] (mid) vowels are avoided.

a. Native words lower the tone./pRomEt-a/ → [pRomEt-a] ‘traffic-gen.sg’

b. Loanwords change vowel quality./mEtS/ → [metS] ‘match’

(11) *H/[−ATR]No segments that have High tone and [−ATR].

(12) These grammars are predicted by different rankings of *H/[−ATR] and other con-straints: Ident(ATR)Ident(tone)

(13) Rankings

a. Native Slovenian*H/[−ATR], Ident(ATR) ! Ident(tone)

b. Loanword Slovenian*H/[−ATR], Ident(tone) ! Ident(ATR)

2 Typologies and universals

(14) OT is inherently typologically oriented:

a. accounting for the attested patternsb. excluding the unattested patterns

(15) Example: Nasal harmony (Schourup 1973; Cohn 1990, 1993a; Walker 1998/2000,2003; Piggott & van der Hulst 1997; Piggott 2000, 2003, inter alia)

2

Page 50: What is Optimality Theory? Introduction to Optimality Theory

Interim summary

• Constraints can be satisfied by different repairs.

• This is an advantage of the theory!

• The repair is determined by other constraints.

OT is typological

• OT constraints and rankings predict attested patterns.

• OT constraints and rankings exclude unattested patterns.

What’s our task?

• Figure out the data & generalizations

• Figure out constraints

• Figure out the factorial typology

What’s next?

• Recall *NC • ✔ phonetically & typologically grounded

• ✘ formally somewhat problematic

• We will now look at a constraint (family) that satisfies both criteria.

Page 51: What is Optimality Theory? Introduction to Optimality Theory

Generalized Alignment(McCarthy & Prince 1993)

Generalized Alignment

• The idea is that morphological and prosodic domains tend to be aligned with one another.

• Alignment constraints are a way to formalize this tendency.

Evidence for alignment

• Prosody:

• many languages have initial or final stress

• no language has stress on the syllable that is further from both edges

• feet are often alignment with one or another edge

Evidence for alignment

• Assimilation:

• directional, targets an edge of a domain

• often fails to apply across a domain boundary

Page 52: What is Optimality Theory? Introduction to Optimality Theory

The template

• (McCarthy & Prince 1993:2)

• ALIGN(Cat1, Edge1, Cat2, Edge2) ∀Cat1 ∃ Cat2 such that Edge1 of Cat1 and Edge2 of Cat2 coincide. Where Cat1, Cat2 ∈ PCat ∪ GCat Edge1, Edge2 ∈ {Right, Left}

Some observations

• One violation mark per locus of violation ≡ One violation mark per {Cat1, Edge1, Cat2, Edge2}.

• If there is no Cat1, the constraint is vacuously satisfied.

Some examples

• ALIGN(stress, R, word, R) For every stress(ed syllable), there should be a word, such that the right edge of the stress(ed syllable) and the right edge of the word coincide.

Some examples

• ALIGN(stress, R, word, R)

• ALIGN(word, R, stress, R)

Page 53: What is Optimality Theory? Introduction to Optimality Theory

Order matters!

• ALIGN(stress, R, word, R) For every stress(ed syllable), there should be a word, such that the right edge of the stress(ed syllable) and the right edge of the word coincide.

• ALIGN(word, R, stress, R) For word, there should be a every stress(ed syllable), such that the right edge of the word and the right edge of the every stress(ed syllable) coincide.

More examples

• ALIGN(foot, R, word, R) and ALIGN(word, R, foot, R)

• ALIGN(foot, R, word, L) and ALIGN(word, R, foot, L) ...

• ALIGN(word, L, phrase, L) and ALIGN(phrase, R, word, L) ...

Beyond stress

• morpheme position

• assimilation

Exercise: Nasal harmony

Page 54: What is Optimality Theory? Introduction to Optimality Theory

Conclusions

• We have seen several predictions of OT.

• Lower ranked constraints matter (in some cases, for some candidates).

• OT constraints can be satisfied in different ways.

• Formalizing and grounding OT constraints is a challenging task.

How to do OT?EGG 2011

Peter Jurgec ~ [email protected]

Summary so far ...

• Gen, Con

• ROTB, Input, Output, Tableaux

• Correspondence Theory

• TETU

• HoPHoP

• Generalized Alignment

Today’s question:How to do OT?

Page 55: What is Optimality Theory? Introduction to Optimality Theory

How to analyze data using OT?

• Figure out the generalizations

• Figure out possible and impossible segments/sequences

• Propose constraints

• Faithfulness constraints

• Markedness constraints

How to analyze data using OT?

• Figure out the ranking out these constraints

• Method #1: Trial and error

• Method #2: Factorial Typology

• Method #3: Algorithms

• Method #4: Software (e.g. OTsoft)

How do we know what constraints are needed?• Markedness constraints (MCs)

• M penalizes structures/segments/sequences

• If an MC is high ranked, the relevant structure will not be attested in a language

• Sometimes, several different MCs interact

• Keep in mind that MCs are usually phonetically grounded

How do we know what constraints are needed?

• Markedness constraints are of two types:

• context-free

• context-specific

Page 56: What is Optimality Theory? Introduction to Optimality Theory

How do we know what constraints are needed?• Faithfulness constraints

• a small set of constraints

• Correspondence Theory

• (all constraints are either markedness or faithfulness constraints)

How do constraints work?

How do constraints work?

• The idea: constraints are needed to exclude unattested candidates.

• Constraints are evidence why some candidates are attested, but others are not.

If your analysis doesn’t work ...

• Check *, constraints, rankings ...

• Consider other constraints

• Try to figure out where’s the problem

Page 57: What is Optimality Theory? Introduction to Optimality Theory

Exercise: Farsi, Greek

The Predictive Power of OT

• OT makes strong predictions about cross-linguistic typologies.

• Constraint interaction is a simple and straightforward tool to achieve this.

Thank youContact me:

[email protected]://www.jurgec.net

www.facebook.com/phonology