Itô & Mester 2009: the extended prosodic word

[IM09]

Itô, J. & Mester, A. (2009). The extended prosodic word. In J. Grijzenhout & B. Kabak (eds.), Phonological Domains: Universals and Deviations. Berlin: De Gruyter Mouton.

A function-word + lexical-word complex (English the dinosaurs, German ne Zigarette) has four conceivable prosodifications, arising from the factorial interaction of FtBin, Lex-to-ω, Parse-into-ω, and No-Recursion:

• full-ω [φ [ω fnc] [ω lex]] — the function word is its own ω (violates FtBin: a subminimal ω);
• amalgamated [ω fnc lex] — fused into one ω (violates Lex-to-ω: the lexical word has no ω of its own);
• ω-adjoined [ω fnc [ω lex]] — the function word adjoins, the lexical word keeps its ω (violates No-Recursion: ω over ω);
• φ-attached [φ fnc [ω lex]] — attached straight to φ (violates Parse-into-ω: the function word is in no ω).

With FtBin, Lex-to-ω ≫ Parse-into-ω ≫ No-Recursion, the ω-adjoined (recursive) structure is the optimum — Itô & Mester's central claim, that English and German function-word complexes use ω-adjunction, contra Selkirk's φ-attachment. This is a second OT consumer of prosodic-word recursion alongside Studies/Bennett2018.lean (Kaqchikel).

Candidates are Prosody.Trees; the constraints are Constraints.Constraint Tree values (No-Recursion is the carrier constraint Prosody.noRec, Parse-into-ω is Prosody.parseInto (·.isOm); FtBin-at-ω and Lex-to-ω are the function-word constraints below), and EVAL is the OT engine OptimalityTheory.Tableau.ofRanking … |>.optimal.

Function-word constraints

def ItoMester2009.subminimalOmega : Constraints.Constraint Prosody.Tree

FtBin-at-ω ([IM09]) as a Constraint Tree: ω-nodes whose mora count is below a foot (< 2) — a subminimal function word parsed as its own ω.

Equations

• ItoMester2009.subminimalOmega t = ItoMester2009.subminimalOmega.go t

def ItoMester2009.subminimalOmega.go : Prosody.Tree → ℕ

Equations

• ItoMester2009.subminimalOmega.go (RoseTree.node a cs) = (if (a.isOm && decide (Prosody.moraCount (RoseTree.node a cs) < 2)) = true then 1 else 0) + ItoMester2009.subminimalOmega.goList cs

def ItoMester2009.subminimalOmega.goList : List Prosody.Tree → ℕ

Equations

• ItoMester2009.subminimalOmega.goList [] = 0
• ItoMester2009.subminimalOmega.goList (t :: ts) = ItoMester2009.subminimalOmega.go t + ItoMester2009.subminimalOmega.goList ts

def ItoMester2009.lexHasOmega (lex : Prosody.Tree) : Prosody.Tree → Bool

Is the lexical word lex realised as its own ω-node somewhere in the tree?

Equations

• ItoMester2009.lexHasOmega lex t = ItoMester2009.lexHasOmega.go lex t

def ItoMester2009.lexHasOmega.go (lex : Prosody.Tree) : Prosody.Tree → Bool

Equations

• ItoMester2009.lexHasOmega.go lex (RoseTree.node a cs) = (a.isOm && decide (RoseTree.node a cs = lex) || ItoMester2009.lexHasOmega.goList lex cs)

def ItoMester2009.lexHasOmega.goList (lex : Prosody.Tree) : List Prosody.Tree → Bool

Equations

• ItoMester2009.lexHasOmega.goList lex [] = false
• ItoMester2009.lexHasOmega.goList lex (t :: ts) = (ItoMester2009.lexHasOmega.go lex t || ItoMester2009.lexHasOmega.goList lex ts)

The four candidate prosodifications of (fnc lex)

def ItoMester2009.fncσ : Prosody.Tree

The function word: one light syllable.

Equations

• ItoMester2009.fncσ = Prosody.Tree.σ Prosody.Syllable.Weight.light

def ItoMester2009.lexω : Prosody.Tree

The lexical word as a well-formed (bimoraic) ω.

Equations

• ItoMester2009.lexω = Prosody.Tree.om [Prosody.Tree.ft false [Prosody.Tree.σ Prosody.Syllable.Weight.heavy]]

def ItoMester2009.fullOmega : Prosody.Tree

(a) full-ω: [φ [ω fnc] [ω lex]].

Equations

• ItoMester2009.fullOmega = Prosody.Tree.ph [Prosody.Tree.om [ItoMester2009.fncσ], ItoMester2009.lexω]

def ItoMester2009.amalgamated : Prosody.Tree

(b) amalgamated: [ω fnc lex] (lexical word loses its own ω).

Equations

• ItoMester2009.amalgamated = Prosody.Tree.om [ItoMester2009.fncσ, Prosody.Tree.ft false [Prosody.Tree.σ Prosody.Syllable.Weight.heavy]]

def ItoMester2009.omegaAdjoined : Prosody.Tree

(c) ω-adjoined: [ω fnc [ω lex]] — recursive.

Equations

• ItoMester2009.omegaAdjoined = Prosody.Tree.om [ItoMester2009.fncσ, ItoMester2009.lexω]

def ItoMester2009.phiAttached : Prosody.Tree

(d) φ-attached: [φ fnc [ω lex]].

Equations

• ItoMester2009.phiAttached = Prosody.Tree.ph [ItoMester2009.fncσ, ItoMester2009.lexω]

def ItoMester2009.lexToOmega : Constraints.Constraint Prosody.Tree

Lex-to-ω ([IM09], after [McCP93]'s Align(Lex, ω)) as a Constraint Tree: 1 if the lexical word lexω is not aligned with an ω of its own.

Equations

• ItoMester2009.lexToOmega t = if ItoMester2009.lexHasOmega ItoMester2009.lexω t = true then 0 else 1

The ranking and the prediction

EVAL is the OT tableau engine; the ranking is FtBin, Lex-to-ω ≫ Parse-into-ω ≫ No-Recursion = [subminimalOmega, lexToOmega, parseInto (·.isOm), noRec].

def ItoMester2009.candidates : List Prosody.Tree

Equations

• ItoMester2009.candidates = [ItoMester2009.fullOmega, ItoMester2009.amalgamated, ItoMester2009.omegaAdjoined, ItoMester2009.phiAttached]

theorem ItoMester2009.omegaAdjunction_optimum : (OptimalityTheory.Tableau.ofRanking candidates [subminimalOmega, lexToOmega, Prosody.parseInto fun (x : Prosody.Constituent) => x.isOm, Prosody.noRec] ⋯).optimal = {omegaAdjoined}

The function-word complex is prosodified by ω-adjunction — the recursive [ω fnc [ω lex]] is the unique optimum, beating φ-attachment because Parse-into-ω ≫ No-Recursion ([IM09], contra Selkirk's φ-attached).

theorem ItoMester2009.winner_is_recursive : Prosody.noRec omegaAdjoined = 1

The winning structure is recursive: ω dominates ω.