Itô and Mester (2009): The Extended Prosodic Word

This file formalizes the prosodification of function-word complexes in [IM09]. A function word followed by its lexical host, English the dinosaurs or German 'ne Zigarette, has the four prosodic sites of (25): a prosodic word of its own, fusion into the host's word, adjunction to the host's word, and attachment to the phonological phrase, (20a)–(20d). Each site violates exactly one of the constraints FtBin, Lex-to-ω, No-Recursion and Parse-into-ω, so the factorial typology of the four constraints yields the four sites (fullOmega_optimum and its three siblings). With FtBin and Lex-to-ω undominated, the tableaux (33) and (34) leave adjunction and phrase attachment tied, and the ranking of Parse-into-ω above No-Recursion, which the evidence of Section 3 supports for English and German, selects the recursive word [ω fnc [ω lex]] (omegaAdjunction_optimum), against [Sel96]'s phrase attachment.

Implementation notes

• Candidates are Prosody.Trees and constraints Constraint Tree values: No-Recursion is the substrate's Prosody.noRec and Parse-into-ω its Prosody.parseInto; FtBin at the word level and Lex-to-ω are defined here, the latter for the fixed lexical word lexω.
• The tableau engine is OptimalityTheory.Tableau.ofRanking; the winning recursive structure is a legal prosodic word of the substrate, No-Recursion being violable.

References

• [IM09]
• [Sel96]
• [McCP93]

Function-word constraints

def ItoMester2009.subminimalOmega : OptimalityTheory.Constraint Prosody.Tree

FtBin at the word level assigns a violation to each ω-node whose mora count is below a foot, such as 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.level = Prosody.Level.om ∧ Prosody.moraCount (RoseTree.node a cs) < 2 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

Whether the lexical word lex is 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) = (decide (a.level = Prosody.Level.om) && 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 sites of (25)

def ItoMester2009.fncσ : Prosody.Tree

The function word is 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

[φ [ω fnc] [ω lex]] is the full-ω site, (25a) and (20a).

Equations

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

def ItoMester2009.amalgamated : Prosody.Tree

[ω fnc lex] is the amalgamated site, (25b) and (20b).

Equations

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

def ItoMester2009.omegaAdjoined : Prosody.Tree

[ω fnc [ω lex]] is the ω-adjoined site, (25c) and (20c).

Equations

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

def ItoMester2009.phiAttached : Prosody.Tree

[φ fnc [ω lex]] is the φ-attached site, (25d) and (20d).

Equations

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

def ItoMester2009.lexToOmega : OptimalityTheory.Constraint Prosody.Tree

Lex-to-ω, (12), after the alignment constraint of [McCP93], assigns a violation when the lexical word is not a ω of its own.

Equations

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

def ItoMester2009.candidates : List Prosody.Tree

The candidate set.

Equations

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

theorem ItoMester2009.one_violation_each : subminimalOmega fullOmega = 1 ∧ lexToOmega amalgamated = 1 ∧ Prosody.noRec omegaAdjoined = 1 ∧ Prosody.parseInto Prosody.Level.om phiAttached = 1

Each site violates exactly one of the four constraints, (20).

The factorial typology and the ranking for English and German

theorem ItoMester2009.fullOmega_optimum : (OptimalityTheory.Tableau.ofRanking candidates [lexToOmega, Prosody.parseInto Prosody.Level.om, Prosody.noRec, subminimalOmega] fullOmega_optimum._proof_1).optimal = {fullOmega}

Demoting FtBin makes the function word its own prosodic word.

theorem ItoMester2009.amalgamated_optimum : (OptimalityTheory.Tableau.ofRanking candidates [subminimalOmega, Prosody.parseInto Prosody.Level.om, Prosody.noRec, lexToOmega] fullOmega_optimum._proof_1).optimal = {amalgamated}

Demoting Lex-to-ω fuses the function word into the host.

theorem ItoMester2009.phiAttached_optimum : (OptimalityTheory.Tableau.ofRanking candidates [subminimalOmega, lexToOmega, Prosody.noRec, Prosody.parseInto Prosody.Level.om] fullOmega_optimum._proof_1).optimal = {phiAttached}

Demoting Parse-into-ω attaches the function word to the phrase, [Sel96]'s site.

theorem ItoMester2009.adjoined_attached_tie : (OptimalityTheory.Tableau.ofRanking candidates [subminimalOmega, lexToOmega] fullOmega_optimum._proof_1).optimal = {omegaAdjoined, phiAttached}

With FtBin and Lex-to-ω alone ranked, the ω-adjoined and φ-attached sites tie, each fulfilling both, (33) and (34).

theorem ItoMester2009.omegaAdjunction_optimum : (OptimalityTheory.Tableau.ofRanking candidates [subminimalOmega, lexToOmega, Prosody.parseInto Prosody.Level.om, Prosody.noRec] fullOmega_optimum._proof_1).optimal = {omegaAdjoined}

The function-word complex of English and German is prosodified by ω-adjunction, since under FtBin, Lex-to-ω ≫ Parse-into-ω ≫ No-Recursion the recursive [ω fnc [ω lex]] is the unique optimum.

theorem ItoMester2009.winner_recursive_isWord : Prosody.noRec omegaAdjoined = 1 ∧ Prosody.IsWord omegaAdjoined

The winning structure is recursive, ω dominating ω, and a legal prosodic word of the substrate, so No-Recursion is violable, not part of well-formedness.