Uchihara & Mendoza Ruiz 2021: minimality, maximality, and the perfect word in Mixtec

[UMR21]

Uchihara, H. & Mendoza Ruiz, J. (2021). Minimality, maximality and perfect prosodic word in Alcozauca Mixtec. Natural Language & Linguistic Theory 40, 599–649.

In Alcozauca Mixtec the prosodic word is ideally both minimally and maximally bimoraic: monosyllabic stems lengthen to bimoraic (CVV), and over-long words truncate to fit the bimoraic template. The paper's reductionist claim is that one constraint set — FtBin, Parse(μ), AllFeetRight — derives both bounds, so the ideal word is the perfect prosodic word: ω coextensive with a single well-formed (bimoraic) foot. The typological prediction is that maximality always entails minimality, not conversely.

We exercise the unified prosodic machinery: candidates are Prosody.Trees, the constraints are Constraints.Constraint Tree values (FtBin is the local ftBin, Parse(μ) is the carrier constraint Prosody.parseInto (·.isFt)), the word-size notions are Prosody.PerfectWord / MinimalWord / MaximalWord, and EVAL is the OT engine OptimalityTheory.Tableau.ofRanking … |>.optimal. The same ranking FtBin ≫ Parse selects the bimoraic foot for both a too-small input (lengthening) and a too-big one (truncation); the winner is a PerfectWord.

Constraint ranking

def Uchihara2021.ftBin : Constraints.Constraint Prosody.Tree

FtBin ([UMR21]) as a Constraint Tree: feet whose mora count is not 2. (Parse(μ) is the carrier constraint parseInto (·.isFt) — unfooted syllables.)

Equations

• Uchihara2021.ftBin t = (List.filter (fun (f : List Prosody.Syllable.Weight) => Prosody.footMorae f != 2) (Prosody.feet t)).length

Minimality: a monomoraic input lengthens to a bimoraic foot

def Uchihara2021.bimoraic : Prosody.Tree

(taa) — one heavy syllable footed: the bimoraic perfect word.

Equations

• Uchihara2021.bimoraic = Prosody.Tree.om [Prosody.Tree.ft false [Prosody.Tree.σ Prosody.Syllable.Weight.heavy]]

def Uchihara2021.degenerate : Prosody.Tree

(ta) — a degenerate monomoraic foot (FtBin violation).

Equations

• Uchihara2021.degenerate = Prosody.Tree.om [Prosody.Tree.ft false [Prosody.Tree.σ Prosody.Syllable.Weight.light]]

def Uchihara2021.unfooted : Prosody.Tree

[ta] — an unfooted light syllable (Parse violation).

Equations

• Uchihara2021.unfooted = Prosody.Tree.om [Prosody.Tree.σ Prosody.Syllable.Weight.light]

def Uchihara2021.minCandidates : List Prosody.Tree

Equations

• Uchihara2021.minCandidates = [Uchihara2021.bimoraic, Uchihara2021.degenerate, Uchihara2021.unfooted]

theorem Uchihara2021.minimality_optimum : (OptimalityTheory.Tableau.ofRanking minCandidates [ftBin, Prosody.parseInto fun (x : Prosody.Constituent) => x.isFt] ⋯).optimal = {bimoraic}

Minimality: from a monomoraic input the bimoraic foot is the unique optimum (lengthening beats both the degenerate foot and the unfooted syllable).

Maximality: a trimoraic input truncates to a bimoraic foot

def Uchihara2021.trimoraicFoot : Prosody.Tree

(taa.ta) — a trimoraic foot (FtBin violation).

Equations

• Uchihara2021.trimoraicFoot = Prosody.Tree.om [Prosody.Tree.ft false [Prosody.Tree.σ Prosody.Syllable.Weight.heavy, Prosody.Tree.σ Prosody.Syllable.Weight.light]]

def Uchihara2021.footPlusStray : Prosody.Tree

(taa).ta — a bimoraic foot plus an unfooted syllable (Parse violation).

Equations

• Uchihara2021.footPlusStray = Prosody.Tree.om [Prosody.Tree.ft false [Prosody.Tree.σ Prosody.Syllable.Weight.heavy], Prosody.Tree.σ Prosody.Syllable.Weight.light]

def Uchihara2021.maxCandidates : List Prosody.Tree

Equations

• Uchihara2021.maxCandidates = [Uchihara2021.bimoraic, Uchihara2021.trimoraicFoot, Uchihara2021.footPlusStray]

theorem Uchihara2021.maximality_optimum : (OptimalityTheory.Tableau.ofRanking maxCandidates [ftBin, Prosody.parseInto fun (x : Prosody.Constituent) => x.isFt] ⋯).optimal = {bimoraic}

Maximality: from a trimoraic input the bimoraic foot is again the unique optimum (truncation beats the trimoraic foot and the foot-plus-stray) — the same FtBin ≫ Parse ranking, hence "maximality from the minimality constraints" ([UMR21]).

The winner is the perfect prosodic word

theorem Uchihara2021.winner_perfect : Prosody.PerfectWord Prosody.footMorae bimoraic

The shared optimum is the perfect prosodic word: ω coextensive with one well-formed (moraic-trochee) foot.

theorem Uchihara2021.winner_minimal_and_maximal : Prosody.MinimalWord Prosody.footMorae bimoraic ∧ Prosody.MaximalWord Prosody.footMorae bimoraic

Hence the optimum is both minimal and maximal (Itô & Mester's perfect word = minimal ∧ maximal).