Rich Phonological Representations for Vocabulary Insertion

@cite{alderete-1999} @cite{koehnlein-cameron-2024}

Standard Distributed Morphology assumes that Vocabulary Items specify only segmental exponents (strings). However, a growing body of work argues that exponents can carry lexical prespecification of suprasegmental properties: stress, metrical structure, tone, etc.

Motivation

@cite{aitha-2026} argues that Telugu singular -ni is prespecified for stress. This prespecification interacts with the phonological grammar (Stratal OT) to produce the weak alternation: stressed -ni cannot form a well-formed binary foot when PrWd-final, triggering its deletion. Without prespecification, the alternation would require a morpheme-specific phonological rule — exactly the kind of ad hoc device that modular DM aims to avoid.

Architecture

RichExponent extends the bare String exponent with an optional ProsodicPrespec field. RichVocabItem is a version of VocabItem that uses RichExponent instead of String.

The key insight: rich representations are not stipulations of surface behavior. They are underlying specifications that interact with general phonological constraints. The surface pattern is derived from the interaction, not encoded in the representation.

Precedents

• @cite{alderete-1999}: Lexical prespecification of stress (English stress-shifting suffixes like -ity, -ic)
• @cite{koehnlein-cameron-2024}: Foot structure as a lexical property (motivating syllable-internal prosodic oppositions)
• @cite{moren-zsiga-2006}: Lexical tone in Thai

structure Morphology.DM.RichRepresentation.ProsodicPrespec : Type

Prosodic prespecification for a morphological exponent.

An exponent may be lexically specified for suprasegmental properties that interact with the phonological grammar. These specifications are part of the underlying representation (List 2 in DM's architecture) and persist through phonological computation unless overridden by higher-ranked constraints.

Fields are optional: none means the property is unspecified (determined by the phonological grammar alone).

• inherentStress : Option Bool

  Inherent stress: some true = the exponent bears lexical stress; some false = the exponent is lexically unstressed; none = stress assignment is left to the phonological grammar.

  Example: Telugu singular -ni is some true — it enters the phonology with a prespecified stress that interacts with FT-BIN and IDENT-STRESS (@cite{aitha-2026} §5).

• preferredFoot : Option Theories.Phonology.Syllable.FootType

  Preferred foot type, if any. Relevant for exponents that impose metrical requirements (e.g., stress-shifting suffixes in English that require a specific foot structure).

  Example: English -ity requires a trochaic foot on the preceding syllable (@cite{alderete-1999}).

def Morphology.DM.RichRepresentation.instDecidableEqProsodicPrespec.decEq (x✝ x✝¹ : ProsodicPrespec) : Decidable (x✝ = x✝¹)

Equations

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instance Morphology.DM.RichRepresentation.instDecidableEqProsodicPrespec : DecidableEq ProsodicPrespec

Equations

• Morphology.DM.RichRepresentation.instDecidableEqProsodicPrespec = Morphology.DM.RichRepresentation.instDecidableEqProsodicPrespec.decEq

instance Morphology.DM.RichRepresentation.instBEqProsodicPrespec : BEq ProsodicPrespec

Equations

• Morphology.DM.RichRepresentation.instBEqProsodicPrespec = { beq := Morphology.DM.RichRepresentation.instBEqProsodicPrespec.beq }

def Morphology.DM.RichRepresentation.instBEqProsodicPrespec.beq : ProsodicPrespec → ProsodicPrespec → Bool

Equations

• Morphology.DM.RichRepresentation.instBEqProsodicPrespec.beq { inherentStress := a, preferredFoot := a_1 } { inherentStress := b, preferredFoot := b_1 } = (a == b && a_1 == b_1)
• Morphology.DM.RichRepresentation.instBEqProsodicPrespec.beq x✝¹ x✝ = false

instance Morphology.DM.RichRepresentation.instReprProsodicPrespec : Repr ProsodicPrespec

Equations

• Morphology.DM.RichRepresentation.instReprProsodicPrespec = { reprPrec := Morphology.DM.RichRepresentation.instReprProsodicPrespec.repr }

def Morphology.DM.RichRepresentation.instReprProsodicPrespec.repr : ProsodicPrespec → ℕ → Std.Format

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instance Morphology.DM.RichRepresentation.instInhabitedProsodicPrespec : Inhabited ProsodicPrespec

Equations

• Morphology.DM.RichRepresentation.instInhabitedProsodicPrespec = { default := { } }

def Morphology.DM.RichRepresentation.ProsodicPrespec.isInert (p : ProsodicPrespec) : Bool

Is this exponent prosodically inert (no prespecification)?

Equations

• p.isInert = (p.inherentStress.isNone && p.preferredFoot.isNone)

structure Morphology.DM.RichRepresentation.RichExponent : Type

A rich exponent: segmental content plus optional prosodic prespecification.

This replaces the bare String in VocabItem for analyses where morpheme-specific prosodic properties are needed. The segmental content and prosodic specification are independent: a morpheme can have rich prosody with simple segments, or complex segments with no prosodic specification.

• segments : String

  Segmental content (the traditional "exponent").

• prosody : ProsodicPrespec

  Prosodic prespecification (empty = prosodically inert).

def Morphology.DM.RichRepresentation.instDecidableEqRichExponent.decEq (x✝ x✝¹ : RichExponent) : Decidable (x✝ = x✝¹)

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instance Morphology.DM.RichRepresentation.instDecidableEqRichExponent : DecidableEq RichExponent

Equations

• Morphology.DM.RichRepresentation.instDecidableEqRichExponent = Morphology.DM.RichRepresentation.instDecidableEqRichExponent.decEq

instance Morphology.DM.RichRepresentation.instBEqRichExponent : BEq RichExponent

Equations

• Morphology.DM.RichRepresentation.instBEqRichExponent = { beq := Morphology.DM.RichRepresentation.instBEqRichExponent.beq }

def Morphology.DM.RichRepresentation.instBEqRichExponent.beq : RichExponent → RichExponent → Bool

Equations

• Morphology.DM.RichRepresentation.instBEqRichExponent.beq { segments := a, prosody := a_1 } { segments := b, prosody := b_1 } = (a == b && a_1 == b_1)
• Morphology.DM.RichRepresentation.instBEqRichExponent.beq x✝¹ x✝ = false

def Morphology.DM.RichRepresentation.instReprRichExponent.repr : RichExponent → ℕ → Std.Format

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instance Morphology.DM.RichRepresentation.instReprRichExponent : Repr RichExponent

Equations

• Morphology.DM.RichRepresentation.instReprRichExponent = { reprPrec := Morphology.DM.RichRepresentation.instReprRichExponent.repr }

def Morphology.DM.RichRepresentation.RichExponent.bare (s : String) : RichExponent

Create a prosodically inert exponent (equivalent to a bare string).

Equations

• Morphology.DM.RichRepresentation.RichExponent.bare s = { segments := s }

def Morphology.DM.RichRepresentation.RichExponent.stressed (s : String) : RichExponent

Create a stressed exponent.

Equations

• Morphology.DM.RichRepresentation.RichExponent.stressed s = { segments := s, prosody := { inherentStress := some true } }

def Morphology.DM.RichRepresentation.RichExponent.unstressed (s : String) : RichExponent

Create an unstressed exponent.

Equations

• Morphology.DM.RichRepresentation.RichExponent.unstressed s = { segments := s, prosody := { inherentStress := some false } }

structure Morphology.DM.RichRepresentation.RichVocabItem (Ctx Root : Type) : Type

A Vocabulary Item with rich phonological representation.

Identical to VocabItem except that exponent is a RichExponent rather than a bare String. The contextMatch, rootMatch, and specificity fields work exactly as in VocabItem.

• exponent : RichExponent

  The phonological exponent with optional prosodic prespecification.

• contextMatch : Ctx → Bool

  Context check: does the terminal's feature bundle match?

• rootMatch : Option (Root → Bool)

  Root restriction (optional).

• specificity : ℕ

  Specificity for Elsewhere Condition resolution.

def Morphology.DM.RichRepresentation.RichVocabItem.matches {Ctx Root : Type} (vi : RichVocabItem Ctx Root) (ctx : Ctx) (root : Root) : Bool

Does a Rich Vocabulary Item match at a given terminal node?

Equations

• vi.matches ctx root = (vi.contextMatch ctx && match vi.rootMatch with | none => true | some f => f root)

def Morphology.DM.RichRepresentation.richVocabularyInsert {Ctx Root : Type} (rules : List (RichVocabItem Ctx Root)) (ctx : Ctx) (root : Root) : Option RichExponent

Insert a Rich Vocabulary Item: same Elsewhere Condition logic as vocabularyInsert, but returns a RichExponent.

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def Morphology.DM.RichRepresentation.VocabItem.toRich {Ctx Root : Type} (vi : VI.VocabItem Ctx Root) : RichVocabItem Ctx Root

Convert a standard VocabItem to a RichVocabItem with inert prosody. All existing VI rules are automatically prosodically inert.

Equations

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theorem Morphology.DM.RichRepresentation.bare_is_inert (s : String) : (RichExponent.bare s).prosody.isInert = true

A bare exponent is prosodically inert.

theorem Morphology.DM.RichRepresentation.stressed_not_inert (s : String) : (RichExponent.stressed s).prosody.isInert = false

A stressed exponent is not prosodically inert.

def Morphology.DM.RichRepresentation.teluguSgNi : RichExponent

Telugu singular -ni: stressed exponent.

Equations

• Morphology.DM.RichRepresentation.teluguSgNi = Morphology.DM.RichRepresentation.RichExponent.stressed "ni"

theorem Morphology.DM.RichRepresentation.telugu_sg_ni_stressed : teluguSgNi.prosody.inherentStress = some true

def Morphology.DM.RichRepresentation.teluguNAm : RichExponent

Telugu n-exponent -am: prosodically inert (no prespecification).

Equations

• Morphology.DM.RichRepresentation.teluguNAm = Morphology.DM.RichRepresentation.RichExponent.bare "am"

theorem Morphology.DM.RichRepresentation.telugu_n_am_inert : teluguNAm.prosody.isInert = true