Cophonology Theory

@cite{inkelas-zoll-2007} @cite{sande-jenks-2017} @cite{rolle-2018}

Cophonology Theory (CPT) proposes that individual morphemes can trigger morpheme-specific constraint rankings — cophonologies — that override parts of the default phonological grammar. The resulting surface form is the optimal candidate under the morpheme's cophonology rather than the default ranking.

Triggers: VIs, not constructions

In classic CPT (@cite{inkelas-zoll-2007}), cophonologies are properties of constructions (e.g., compounding, reduplication). @cite{sande-jenks-2017} and @cite{rolle-2018} argue that the trigger should instead be the individual Vocabulary Item inserted at a terminal node: the R component of a VI specifies a constraint subranking that applies when that VI wins insertion.

This gives DM's Vocabulary Item a four-part structure:

1. M — morphosyntactic features (= contextMatch in VocabItem)
2. F — phonological content (= exponent)
3. P — prosodic subcategorization (not formalized here; see RichExponent)
4. R — constraint subranking (= subranking below)

Connection to linglib

CophVocabItem extends VocabItem with an R component. The cophonologicalEval function merges the winning VI's subranking with the default ranking and runs Tableau.optimal, connecting DM vocabulary insertion (Morphology.DM.VI) to OT constraint evaluation (Core.Constraint.OT / Core.Constraint.Evaluation).

Phasal extension: see CophonologyByPhrase.lean

@cite{sande-jenks-inkelas-2020} extend the trigger from individual Vocabulary Items to spell-out phases — the cophonology can be associated with a vP, CP, or DP phase head, activating over the entire phase complement at spell-out. The substrate for that extension lives in the sibling file CophonologyByPhrase.lean. Consumers handling long-distance morphologically conditioned phonological effects (cross- word) — e.g. Phenomena/Phonology/Studies/SandeClemDabkowski2026.lean — should reach for the phrasal version. Per-VI cophonology (this file) remains the right substrate for morpheme-internal effects.

structure Phonology.CophonologyTheory.CophVocabItem (Ctx Root C : Type) extends Morphology.DM.VI.VocabItem Ctx Root : Type

A Vocabulary Item enriched with a morpheme-specific constraint subranking (the R component of @cite{rolle-2018} Ch 4).

Extends VocabItem with all its fields (exponent, contextMatch, rootMatch, specificity) plus:

• C: the candidate type for phonological evaluation
• subranking: constraints promoted above the default ranking

When this VI wins insertion, its subranking overrides the default constraint ranking: constraints named in subranking are promoted to the top of the ranking (in the order listed), and the remaining default constraints follow.

• exponent : String
• contextMatch : Ctx → Bool
• rootMatch : Option (Root → Bool)
• specificity : ℕ
• subranking : List (Core.Constraint.OT.NamedConstraint C)

  Morpheme-specific constraint subranking (R component). Constraints listed here are promoted to the top of the effective ranking, overriding their default position. An empty subranking means this VI imposes no morpheme-specific phonology.

def Phonology.CophonologyTheory.mergeRanking {C : Type} (default sub : List (Core.Constraint.OT.NamedConstraint C)) : List (Core.Constraint.OT.NamedConstraint C)

Merge a morpheme-specific subranking with the default ranking.

The effective ranking places the subranking constraints first (in the order given), then appends default constraints whose names do not appear in the subranking. This implements the intuition that the morpheme "promotes" certain constraints above the default ranking without disturbing the relative order of other constraints.

When sub is empty, the result is exactly default.

Equations

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

theorem Phonology.CophonologyTheory.mergeRanking_empty_sub {C : Type} (default : List (Core.Constraint.OT.NamedConstraint C)) : mergeRanking default [] = default

An empty subranking produces the default ranking unchanged.

theorem Phonology.CophonologyTheory.mergeRanking_sub_prefix {C : Type} (default sub : List (Core.Constraint.OT.NamedConstraint C)) : List.take sub.length (mergeRanking default sub) = sub

Subranking constraints appear first in the merged ranking.

theorem Phonology.CophonologyTheory.mergeRanking_sub_subset {C : Type} (default sub : List (Core.Constraint.OT.NamedConstraint C)) (c : Core.Constraint.OT.NamedConstraint C) (h : c ∈ sub) : c ∈ mergeRanking default sub

Every subranking constraint is in the merged ranking.

theorem Phonology.CophonologyTheory.mergeRanking_preserves_default {C : Type} (default sub : List (Core.Constraint.OT.NamedConstraint C)) (c : Core.Constraint.OT.NamedConstraint C) (hMem : c ∈ default) (hName : ¬(List.map (fun (x : Core.Constraint.OT.NamedConstraint C) => x.name) sub).contains c.name = true) : c ∈ mergeRanking default sub

Every default constraint whose name is not in the subranking is preserved in the merged ranking.

def Phonology.CophonologyTheory.cophonologicalEval {C : Type} [DecidableEq C] (defaultRanking subranking : List (Core.Constraint.OT.NamedConstraint C)) (candidates : List C) (h : candidates ≠ [] := by decide) : Finset C

Evaluate a candidate set under a cophonology: merge the winning VI's subranking with the default ranking, then return optimal candidates.

This is the core of CPT: the same candidate set can yield different winners depending on which VI's subranking is active. A dominant GT trigger, for instance, has a subranking that promotes a faithfulness constraint (basemap correspondence) above default markedness constraints, forcing the output to match the basemap rather than preserving the target's underlying tones (@cite{rolle-2018} Ch 5).

Equations

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

theorem Phonology.CophonologyTheory.cophonologicalEval_empty_sub {C : Type} [DecidableEq C] (defaultRanking : List (Core.Constraint.OT.NamedConstraint C)) (candidates : List C) (h : candidates ≠ []) : cophonologicalEval defaultRanking [] candidates h = (Core.Constraint.OT.mkTableau candidates defaultRanking h).optimal

When the subranking is empty, cophonological evaluation reduces to standard OT evaluation. CPT is a proper generalization of OT.

def Phonology.CophonologyTheory.CophVocabItem.isDominantCoph {Ctx Root C : Type} (cvi : CophVocabItem Ctx Root C) : Bool

A dominant cophonology is one whose subranking is non-empty: the VI imposes morpheme-specific constraint effects on the phonological evaluation.

In @cite{rolle-2018}'s analysis of grammatical tone, dominant GT triggers have a subranking that promotes basemap faithfulness, while non-dominant triggers have an empty subranking (relying on the default ranking).

Equations

• cvi.isDominantCoph = !cvi.subranking.isEmpty

def Phonology.CophonologyTheory.CophVocabItem.isNonDominantCoph {Ctx Root C : Type} (cvi : CophVocabItem Ctx Root C) : Bool

A non-dominant cophonology imposes no morpheme-specific constraints: the phonological evaluation proceeds under the default ranking.

Equations

• cvi.isNonDominantCoph = cvi.subranking.isEmpty

theorem Phonology.CophonologyTheory.coph_dominant_complement {Ctx Root C : Type} (cvi : CophVocabItem Ctx Root C) : cvi.isDominantCoph = !cvi.isNonDominantCoph

Dominant and non-dominant are complementary.