McCarthy and Prince (1995): Faithfulness and Reduplicative Identity

This file formalizes three analyses from McCarthy and Prince's correspondence theory of reduplication. In the basic model a reduplicated form has an input stem, a base and a reduplicant, with faithfulness between input and base and identity between base and reduplicant, and a phonological constraint interacts with both. Javanese deletes intervocalic h, and in a suffixed reduplication the h is lost from both copies although only one is intervocalic, which is overapplication (§3.4). Balangao copies the first two syllables of the base without the final coda although the language allows codas, which is emergence of the unmarked (§4.2). Akan palatalizes a velar before a front vowel, but not in the reduplicant of kɪ–ka, which is underapplication (§5.1).

A candidate here is a correspondence between the input stem, the base and the reduplicant, and every constraint is computed from it: MAX and IDENT from the correspondence, and the phonological constraints from the surface string. The rankings are not fixed in advance. Each result says which rankings of the paper's constraints select which candidate.

Main definitions

• Javanese.Candidate, Balangao.Candidate, Akan.Candidate: the candidates of tableaux (39), (106) and (131), each with its correspondence and surface.
• Javanese.con, Balangao.con, Akan.con: the constraints of those tableaux.

Main results

• Javanese.optimal_eq: each candidate of (39) violates one constraint, and the winner is the candidate whose constraint is ranked last.
• Javanese.overapplication, Javanese.normalApplication, Javanese.underapplication_notMem: with *VhV above MAX-IO, MAX-BR above MAX-IO gives overapplication and the reverse gives normal application, and the underapplying candidate wins under no such ranking.
• Balangao.optimal_iff: the coda-sparing reduplicant wins exactly under MAX-IO ≫ NO-CODA ≫ MAX-BR.
• Akan.optimal_iff: with PAL above IDENT-IO(−cor), the unpalatalized kɪ–ka wins exactly when OCP(+cor) and IDENT-BR(−cor) both dominate PAL.

Implementation notes

Javanese is analysed with suffixing reduplication, the paper's tableau (39). Its prefixing alternative (38), where DEP-BR does the work of MAX-BR, is not formalized. A coda is counted as a consonant that no vowel follows, which suffices for the CV(C) syllables of the Balangao forms. The paper measures OCP(+cor) by featural duplication in dissimilar constituents and prints three marks for the overapplying candidate of (131) without spelling the count out. Here the constraint is violated once by a syllable with a palatal onset and a front vowel before a syllable with a coronal onset and a vowel that is not front, which agrees with the paper's verdicts on kita, tɕita, dʑidʑe and the three candidates. The Akan segments are those of the Akan fragment.

References

• [McCP95]

Phonological constraints on a surface string

def McCarthyPrince1995.codas {σ : Type u_1} (IsVowel : σ → Prop) [DecidablePred IsVowel] : List σ → ℕ

The number of codas of a string, a coda being a consonant that no vowel follows.

Equations

• McCarthyPrince1995.codas IsVowel [] = 0
• McCarthyPrince1995.codas IsVowel [x_1] = if IsVowel x_1 then 0 else 1
• McCarthyPrince1995.codas IsVowel (x_1 :: y :: rest) = (if ¬IsVowel x_1 ∧ ¬IsVowel y then 1 else 0) + McCarthyPrince1995.codas IsVowel (y :: rest)

def McCarthyPrince1995.intervocalic {σ : Type u_1} (IsVowel : σ → Prop) [DecidablePred IsVowel] [DecidableEq σ] (x : σ) : List σ → ℕ

The number of occurrences of x between two vowels.

Equations

• McCarthyPrince1995.intervocalic IsVowel x (a :: b :: c :: rest) = (if IsVowel a ∧ b = x ∧ IsVowel c then 1 else 0) + McCarthyPrince1995.intervocalic IsVowel x (b :: c :: rest)
• McCarthyPrince1995.intervocalic IsVowel x x✝ = 0

Javanese h-deletion: overapplication

inductive McCarthyPrince1995.Javanese.Seg : Type

The segments of bədah 'broken' and the demonstrative suffix -e.

• b : Seg
• schwa : Seg
• d : Seg
• a : Seg
• h : Seg
• e : Seg

@[instance_reducible]

instance McCarthyPrince1995.Javanese.instDecidableEqSeg : DecidableEq Seg

Equations

• McCarthyPrince1995.Javanese.instDecidableEqSeg x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance McCarthyPrince1995.Javanese.instReprSeg : Repr Seg

Equations

• McCarthyPrince1995.Javanese.instReprSeg = { reprPrec := McCarthyPrince1995.Javanese.instReprSeg.repr }

def McCarthyPrince1995.Javanese.instReprSeg.repr : Seg → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def McCarthyPrince1995.Javanese.Seg.IsVowel : Seg → Prop

The vowels.

Equations

• McCarthyPrince1995.Javanese.Seg.schwa.IsVowel = True
• McCarthyPrince1995.Javanese.Seg.a.IsVowel = True
• McCarthyPrince1995.Javanese.Seg.e.IsVowel = True
• x✝.IsVowel = False

@[instance_reducible]

instance McCarthyPrince1995.Javanese.instDecidablePredSegIsVowel : DecidablePred Seg.IsVowel

Equations

• One or more equations did not get rendered due to their size.

def McCarthyPrince1995.Javanese.stem : List Seg

The stem bədah.

Equations

• One or more equations did not get rendered due to their size.

def McCarthyPrince1995.Javanese.stemNoH : List Seg

The stem without its h.

Equations

• McCarthyPrince1995.Javanese.stemNoH = [McCarthyPrince1995.Javanese.Seg.b, McCarthyPrince1995.Javanese.Seg.schwa, McCarthyPrince1995.Javanese.Seg.d, McCarthyPrince1995.Javanese.Seg.a]

inductive McCarthyPrince1995.Javanese.Candidate : Type

The candidates of tableau (39) for /bədah–RED–e/.

• overapplication : Candidate

  bəda–bəda–e, with h lost from base and reduplicant.

• underapplication : Candidate

  bədah–bədah–e, with h kept in both.

• normalApplication : Candidate

  bədah–bəda–e, with h lost where it is intervocalic.

@[instance_reducible]

instance McCarthyPrince1995.Javanese.instDecidableEqCandidate : DecidableEq Candidate

Equations

• McCarthyPrince1995.Javanese.instDecidableEqCandidate x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance McCarthyPrince1995.Javanese.instFintypeCandidate : Fintype Candidate

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance McCarthyPrince1995.Javanese.instReprCandidate : Repr Candidate

Equations

• McCarthyPrince1995.Javanese.instReprCandidate = { reprPrec := McCarthyPrince1995.Javanese.instReprCandidate.repr }

def McCarthyPrince1995.Javanese.instReprCandidate.repr : Candidate → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def McCarthyPrince1995.Javanese.Candidate.base : Candidate → List Seg

The base of a candidate.

Equations

• McCarthyPrince1995.Javanese.Candidate.overapplication.base = McCarthyPrince1995.Javanese.stemNoH
• McCarthyPrince1995.Javanese.Candidate.underapplication.base = McCarthyPrince1995.Javanese.stem
• McCarthyPrince1995.Javanese.Candidate.normalApplication.base = McCarthyPrince1995.Javanese.stem

def McCarthyPrince1995.Javanese.Candidate.reduplicant : Candidate → List Seg

The reduplicant of a candidate.

Equations

• McCarthyPrince1995.Javanese.Candidate.underapplication.reduplicant = McCarthyPrince1995.Javanese.stem
• McCarthyPrince1995.Javanese.Candidate.overapplication.reduplicant = McCarthyPrince1995.Javanese.stemNoH
• McCarthyPrince1995.Javanese.Candidate.normalApplication.reduplicant = McCarthyPrince1995.Javanese.stemNoH

def McCarthyPrince1995.Javanese.Candidate.correspondence (c : Candidate) : OptimalityTheory.Correspondence OptimalityTheory.ReduplicationRole Seg

The correspondence of a candidate between the stem, its base and its reduplicant.

Equations

• c.correspondence = OptimalityTheory.Correspondence.reduplication McCarthyPrince1995.Javanese.stem c.base c.reduplicant

def McCarthyPrince1995.Javanese.Candidate.surface (c : Candidate) : List Seg

The surface string, the base followed by the reduplicant and the suffix.

Equations

• c.surface = c.base ++ c.reduplicant ++ [McCarthyPrince1995.Javanese.Seg.e]

def McCarthyPrince1995.Javanese.con : OptimalityTheory.ConstraintSet Candidate (Fin 3)

The constraints of (39) are MAX-BR, *VhV and MAX-IO.

Equations

• One or more equations did not get rendered due to their size.

def McCarthyPrince1995.Javanese.Candidate.violated : Candidate → Fin 3

The constraint a candidate violates.

Equations

• McCarthyPrince1995.Javanese.Candidate.normalApplication.violated = 0
• McCarthyPrince1995.Javanese.Candidate.underapplication.violated = 1
• McCarthyPrince1995.Javanese.Candidate.overapplication.violated = 2

def McCarthyPrince1995.Javanese.violator : Fin 3 → Candidate

The candidate that violates a given constraint.

Equations

• McCarthyPrince1995.Javanese.violator 0 = McCarthyPrince1995.Javanese.Candidate.normalApplication
• McCarthyPrince1995.Javanese.violator 1 = McCarthyPrince1995.Javanese.Candidate.underapplication
• McCarthyPrince1995.Javanese.violator 2 = McCarthyPrince1995.Javanese.Candidate.overapplication

@[simp]

theorem McCarthyPrince1995.Javanese.violated_violator (i : Fin 3) : (violator i).violated = i

theorem McCarthyPrince1995.Javanese.violated_injective : Function.Injective Candidate.violated

theorem McCarthyPrince1995.Javanese.con_apply (i : Fin 3) (c : Candidate) : con i c = if i = c.violated then 1 else 0

The cells of tableau (39), in which each candidate violates one constraint, once.

def McCarthyPrince1995.Javanese.tableau (r : OptimalityTheory.Ranking (Fin 3) 3) : OptimalityTheory.Tableau Candidate 3

Tableau (39) under a ranking of its constraints.

Equations

• One or more equations did not get rendered due to their size.

theorem McCarthyPrince1995.Javanese.optimal_eq (r : OptimalityTheory.Ranking (Fin 3) 3) : (tableau r).optimal = {violator (r 2)}

The winner of (39) is the candidate whose one violated constraint is ranked last.

theorem McCarthyPrince1995.Javanese.overapplication {r : OptimalityTheory.Ranking (Fin 3) 3} (h₁ : r.Dominates 0 2) (h₂ : r.Dominates 1 2) : (tableau r).optimal = {Candidate.overapplication}

With MAX-BR and *VhV above MAX-IO, the paper's skeletal ranking for overapplication, h is lost from both copies.

theorem McCarthyPrince1995.Javanese.normalApplication {r : OptimalityTheory.Ranking (Fin 3) 3} (h₁ : r.Dominates 1 2) (h₂ : r.Dominates 2 0) : (tableau r).optimal = {Candidate.normalApplication}

With *VhV above MAX-IO and MAX-IO above MAX-BR, application is normal.

theorem McCarthyPrince1995.Javanese.underapplication_notMem {r : OptimalityTheory.Ranking (Fin 3) 3} (h : r.Dominates 1 2) : Candidate.underapplication ∉ (tableau r).optimal

Underapplication is out of reach. While *VhV dominates MAX-IO, as h-deletion in unreduplicated words requires, no ranking selects the candidate that keeps both hs.

Balangao: emergence of the unmarked

inductive McCarthyPrince1995.Balangao.Seg : Type

The segments of tagtag.

• t : Seg
• a : Seg
• g : Seg

@[instance_reducible]

instance McCarthyPrince1995.Balangao.instDecidableEqSeg : DecidableEq Seg

Equations

• McCarthyPrince1995.Balangao.instDecidableEqSeg x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance McCarthyPrince1995.Balangao.instReprSeg : Repr Seg

Equations

• McCarthyPrince1995.Balangao.instReprSeg = { reprPrec := McCarthyPrince1995.Balangao.instReprSeg.repr }

def McCarthyPrince1995.Balangao.instReprSeg.repr : Seg → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def McCarthyPrince1995.Balangao.Seg.IsVowel : Seg → Prop

The vowel.

Equations

• McCarthyPrince1995.Balangao.Seg.a.IsVowel = True
• x✝.IsVowel = False

@[instance_reducible]

instance McCarthyPrince1995.Balangao.instDecidablePredSegIsVowel : DecidablePred Seg.IsVowel

Equations

• One or more equations did not get rendered due to their size.

def McCarthyPrince1995.Balangao.stem : List Seg

The stem tagtag.

Equations

• One or more equations did not get rendered due to their size.

def McCarthyPrince1995.Balangao.stemNoCoda : List Seg

The stem without its final coda.

Equations

• One or more equations did not get rendered due to their size.

inductive McCarthyPrince1995.Balangao.Candidate : Type

The candidates of tableau (106) for /RED–tagtag/.

• unfaithfulBase : Candidate

  tagta–tagta, with the final coda lost from the base too.

• exactCopy : Candidate

  tagtag–tagtag, an exact copy.

• codalessReduplicant : Candidate

  tagta–tagtag, with a reduplicant that lacks the final coda.

@[instance_reducible]

instance McCarthyPrince1995.Balangao.instDecidableEqCandidate : DecidableEq Candidate

Equations

• McCarthyPrince1995.Balangao.instDecidableEqCandidate x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance McCarthyPrince1995.Balangao.instFintypeCandidate : Fintype Candidate

Equations

• One or more equations did not get rendered due to their size.

def McCarthyPrince1995.Balangao.instReprCandidate.repr : Candidate → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance McCarthyPrince1995.Balangao.instReprCandidate : Repr Candidate

Equations

• McCarthyPrince1995.Balangao.instReprCandidate = { reprPrec := McCarthyPrince1995.Balangao.instReprCandidate.repr }

def McCarthyPrince1995.Balangao.Candidate.base : Candidate → List Seg

The base of a candidate.

Equations

• McCarthyPrince1995.Balangao.Candidate.unfaithfulBase.base = McCarthyPrince1995.Balangao.stemNoCoda
• McCarthyPrince1995.Balangao.Candidate.exactCopy.base = McCarthyPrince1995.Balangao.stem
• McCarthyPrince1995.Balangao.Candidate.codalessReduplicant.base = McCarthyPrince1995.Balangao.stem

def McCarthyPrince1995.Balangao.Candidate.reduplicant : Candidate → List Seg

The reduplicant of a candidate.

Equations

• McCarthyPrince1995.Balangao.Candidate.exactCopy.reduplicant = McCarthyPrince1995.Balangao.stem
• McCarthyPrince1995.Balangao.Candidate.unfaithfulBase.reduplicant = McCarthyPrince1995.Balangao.stemNoCoda
• McCarthyPrince1995.Balangao.Candidate.codalessReduplicant.reduplicant = McCarthyPrince1995.Balangao.stemNoCoda

def McCarthyPrince1995.Balangao.Candidate.correspondence (c : Candidate) : OptimalityTheory.Correspondence OptimalityTheory.ReduplicationRole Seg

The correspondence of a candidate between the stem, its base and its reduplicant.

Equations

• c.correspondence = OptimalityTheory.Correspondence.reduplication McCarthyPrince1995.Balangao.stem c.base c.reduplicant

def McCarthyPrince1995.Balangao.Candidate.surface (c : Candidate) : List Seg

The surface string, the reduplicant followed by the base.

Equations

• c.surface = c.reduplicant ++ c.base

def McCarthyPrince1995.Balangao.con : OptimalityTheory.ConstraintSet Candidate (Fin 3)

The constraints of (106) are MAX-IO, NO-CODA and MAX-BR.

Equations

• One or more equations did not get rendered due to their size.

theorem McCarthyPrince1995.Balangao.con_apply : (fun (x : Fin 3) => con x Candidate.unfaithfulBase) = ![1, 2, 0] ∧ (fun (x : Fin 3) => con x Candidate.exactCopy) = ![0, 4, 0] ∧ (fun (x : Fin 3) => con x Candidate.codalessReduplicant) = ![0, 3, 1]

The cells of tableau (106).

def McCarthyPrince1995.Balangao.tableau (r : OptimalityTheory.Ranking (Fin 3) 3) : OptimalityTheory.Tableau Candidate 3

Tableau (106) under a ranking of its constraints.

Equations

• One or more equations did not get rendered due to their size.

theorem McCarthyPrince1995.Balangao.optimal_iff (r : OptimalityTheory.Ranking (Fin 3) 3) : (tableau r).optimal = {Candidate.codalessReduplicant} ↔ r.Dominates 0 1 ∧ r.Dominates 1 2

The coda-sparing reduplicant wins exactly under MAX-IO ≫ NO-CODA ≫ MAX-BR, the paper's instance of the ranking for emergence of the unmarked.

Akan palatalization: underapplication

def McCarthyPrince1995.Akan.IsCoronal (s : Phonology.Segment) : Prop

A coronal consonant.

Equations

• McCarthyPrince1995.Akan.IsCoronal s = (s.HasValue Phonology.Feature.syllabic false ∧ s.HasValue Phonology.Feature.coronal true)

def McCarthyPrince1995.Akan.IsVelar (s : Phonology.Segment) : Prop

A plain velar, which PAL requires to palatalize before a front vowel.

Equations

• McCarthyPrince1995.Akan.IsVelar s = (s.HasValue Phonology.Feature.syllabic false ∧ s.HasValue Phonology.Feature.dorsal true ∧ s.HasValue Phonology.Feature.coronal false)

def McCarthyPrince1995.Akan.IsFrontVowel (s : Phonology.Segment) : Prop

A front vowel.

Equations

• McCarthyPrince1995.Akan.IsFrontVowel s = (s.HasValue Phonology.Feature.syllabic true ∧ s.HasValue Phonology.Feature.front true)

@[instance_reducible]

instance McCarthyPrince1995.Akan.instDecidablePredSegmentIsCoronal : DecidablePred IsCoronal

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance McCarthyPrince1995.Akan.instDecidablePredSegmentIsVelar : DecidablePred IsVelar

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance McCarthyPrince1995.Akan.instDecidablePredSegmentIsFrontVowel : DecidablePred IsFrontVowel

Equations

• One or more equations did not get rendered due to their size.

def McCarthyPrince1995.Akan.pal : List Phonology.Segment → ℕ

PAL counts the plain velars that stand before a front vowel.

Equations

• McCarthyPrince1995.Akan.pal (c :: v :: rest) = (if McCarthyPrince1995.Akan.IsVelar c ∧ McCarthyPrince1995.Akan.IsFrontVowel v then 1 else 0) + McCarthyPrince1995.Akan.pal (v :: rest)
• McCarthyPrince1995.Akan.pal x✝ = 0

def McCarthyPrince1995.Akan.ocpCoronal : List Phonology.Segment → ℕ

OCP(+cor) counts the syllables of palatal onset and front vowel that stand before a syllable of coronal onset and a vowel that is not front, the clash of syllabic and segmental palatality.

Equations

• One or more equations did not get rendered due to their size.
• McCarthyPrince1995.Akan.ocpCoronal x✝ = 0

theorem McCarthyPrince1995.Akan.ocpCoronal_kita : ocpCoronal [Akan.k, Akan.i, Data.PHOIBLE.FeatureMatrix.t.toSegment, Akan.a] = 0 ∧ ocpCoronal [Akan.tcCurl, Akan.i, Data.PHOIBLE.FeatureMatrix.t.toSegment, Akan.a] = 1 ∧ ocpCoronal [Akan.tcCurl, Akan.i, Akan.tcCurl, Akan.e] = 0

By the paper's verdicts on OCP(+cor) in (127), kita obeys it and tɕita violates it, while a word whose two syllables are both palatal obeys it.

def McCarthyPrince1995.Akan.stem : List Phonology.Segment

The stem ka 'bite'.

Equations

• McCarthyPrince1995.Akan.stem = [Akan.k, Akan.a]

inductive McCarthyPrince1995.Akan.Candidate : Type

The candidates of tableau (131) for /RED–ka/.

• overapplication : Candidate

  tɕɪ–tɕa, palatalized in reduplicant and base.

• normalApplication : Candidate

  tɕɪ–ka, palatalized before the front vowel only.

• underapplication : Candidate

  kɪ–ka, not palatalized.

@[instance_reducible]

instance McCarthyPrince1995.Akan.instDecidableEqCandidate : DecidableEq Candidate

Equations

• McCarthyPrince1995.Akan.instDecidableEqCandidate x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance McCarthyPrince1995.Akan.instFintypeCandidate : Fintype Candidate

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance McCarthyPrince1995.Akan.instReprCandidate : Repr Candidate

Equations

• McCarthyPrince1995.Akan.instReprCandidate = { reprPrec := McCarthyPrince1995.Akan.instReprCandidate.repr }

def McCarthyPrince1995.Akan.instReprCandidate.repr : Candidate → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def McCarthyPrince1995.Akan.Candidate.base : Candidate → List Phonology.Segment

The base of a candidate.

Equations

• McCarthyPrince1995.Akan.Candidate.overapplication.base = [Akan.tcCurl, Akan.a]
• McCarthyPrince1995.Akan.Candidate.normalApplication.base = McCarthyPrince1995.Akan.stem
• McCarthyPrince1995.Akan.Candidate.underapplication.base = McCarthyPrince1995.Akan.stem

def McCarthyPrince1995.Akan.Candidate.reduplicant : Candidate → List Phonology.Segment

The reduplicant of a candidate, a consonant and a high vowel.

Equations

• McCarthyPrince1995.Akan.Candidate.underapplication.reduplicant = [Akan.k, Akan.smallCapitalI]
• McCarthyPrince1995.Akan.Candidate.overapplication.reduplicant = [Akan.tcCurl, Akan.smallCapitalI]
• McCarthyPrince1995.Akan.Candidate.normalApplication.reduplicant = [Akan.tcCurl, Akan.smallCapitalI]

def McCarthyPrince1995.Akan.Candidate.correspondence (c : Candidate) : OptimalityTheory.Correspondence OptimalityTheory.ReduplicationRole Phonology.Segment

The correspondence of a candidate between the stem, its base and its reduplicant.

Equations

• c.correspondence = OptimalityTheory.Correspondence.reduplication McCarthyPrince1995.Akan.stem c.base c.reduplicant

def McCarthyPrince1995.Akan.Candidate.surface (c : Candidate) : List Phonology.Segment

The surface string, the reduplicant followed by the base.

Equations

• c.surface = c.reduplicant ++ c.base

def McCarthyPrince1995.Akan.con : OptimalityTheory.ConstraintSet Candidate (Fin 4)

The constraints of (131) are OCP(+cor), IDENT-BR(−cor), PAL and IDENT-IO(−cor). An IDENT(−cor) constraint is violated by a [−coronal] segment whose correspondent is not [−coronal].

Equations

• One or more equations did not get rendered due to their size.

theorem McCarthyPrince1995.Akan.con_apply : (fun (x : Fin 4) => con x Candidate.overapplication) = ![1, 0, 0, 1] ∧ (fun (x : Fin 4) => con x Candidate.normalApplication) = ![0, 1, 0, 0] ∧ (fun (x : Fin 4) => con x Candidate.underapplication) = ![0, 0, 1, 0]

The cells of tableau (131), with one mark where the paper prints three for OCP(+cor).

def McCarthyPrince1995.Akan.tableau (r : OptimalityTheory.Ranking (Fin 4) 4) : OptimalityTheory.Tableau Candidate 4

Tableau (131) under a ranking of its constraints.

Equations

• One or more equations did not get rendered due to their size.

theorem McCarthyPrince1995.Akan.optimal_iff {r : OptimalityTheory.Ranking (Fin 4) 4} (h : r.Dominates 2 3) : (tableau r).optimal = {Candidate.underapplication} ↔ r.Dominates 0 2 ∧ r.Dominates 1 2

While PAL dominates IDENT-IO(−cor), as palatalization in unreduplicated words requires, the unpalatalized kɪ–ka wins exactly when OCP(+cor) and IDENT-BR(−cor) both dominate PAL. The blocking constraint rules out overapplication and identity rules out normal application.