Dolatian 2020: pre-inflectional vowel reduction and the Prosodic Stem

[Dol20]

Dolatian, H. (2020). Computational locality of cyclic phonology in Armenian. PhD dissertation, Stony Brook University.

Eastern Armenian Destressed High Vowel Reduction (DHR) overapplies before V-initial inflection but not before C-initial inflection: amusín 'husband' → amusn-óv (INST, V-initial: reduces) vs amusin-nér (PL, C-initial: no reduction). Dolatian argues the conditioning constituent is neither the foot (§2.5.3.1, fails) nor a (recursive) prosodic word (§2.5.3.2, argued against), but Downing's Prosodic Stem (PStem), an intermediate constituent mapped from the morphological stem. Before V-initial inflection the PStem is misaligned from syllable boundaries (onset maximization resyllabifies the stem-final consonant) and expands; expansion triggers the PStem-level cophonology, which in Eastern Armenian reduces, in Western Armenian only shifts stress (§2.5.4 (76), (78)). Before C-initial inflection the PStem stays isomorphic with the MStem, so nothing triggers.

This is not an OT analysis: Dolatian formalizes it as a serial/cyclic derivation (and computationally as MSO logical transductions), explicitly noting (fn. 20) that an OT/Match-theoretic formalization is an alternative he does not adopt. We therefore model the mechanism derivationally — onset-maximization syllabification → PStem misalignment → PStem-cophonology → DHR — rather than as constraint optimization. DHR is derived from the mechanism (see dhr_iff), not stipulated as a dialect × inflection table.

Dolatian also formalizes the phonology computationally, as MSO/quantifier-free logical transductions over word models (§4), whose locality (QF ⟹ Input Strictly Local, hence learnable) is his central computational claim. The final section realizes the Eastern Armenian cophonology in that framework (Core.Computability.Subregular.Logic): DHR is the local rewrite H → ∅ / _ C V, and the cyclic derivation is transduction composition. Reproducing the amusin contrast segmentally recovers the serial result by a different route (transduction_matches_trigger).

Main definitions

• Dolatian2020.pstemMisaligned — the MStem boundary no longer coincides with a syllable boundary (V-initial suffix resyllabified the stem-final consonant).
• Dolatian2020.dhrApplies — DHR derived from PStem expansion × dialect cophonology.
• Dolatian2020.dhrEast / dhrWest — the dialect cophonologies as quantifier-free logical transductions; dhrEast deletes the destressed high vowel before C V.

inductive Dolatian2020.Seg : Type

Coarse segment type — enough for onset-maximization syllabification.

• C : Seg
• V : Seg

@[implicit_reducible]

instance Dolatian2020.instDecidableEqSeg : DecidableEq Seg

Equations

• Dolatian2020.instDecidableEqSeg x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Dolatian2020.instReprSeg : Repr Seg

Equations

• Dolatian2020.instReprSeg = { reprPrec := Dolatian2020.instReprSeg.repr }

def Dolatian2020.instReprSeg.repr : Seg → ℕ → Std.Format

Equations

• Dolatian2020.instReprSeg.repr Dolatian2020.Seg.C prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Dolatian2020.Seg.C")).group prec✝
• Dolatian2020.instReprSeg.repr Dolatian2020.Seg.V prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Dolatian2020.Seg.V")).group prec✝

@[reducible, inline]

abbrev Dolatian2020.Suffix : Type

An inflectional suffix, as a segment string (only its initial segment matters for syllabification/misalignment).

Equations

• Dolatian2020.Suffix = List Dolatian2020.Seg

inductive Dolatian2020.Dialect : Type

Western vs Eastern Armenian. The dialects share the morphology and the PStem; they differ only in the PStem-level cophonology ([Dol20] §2.5.4 (76)).

• eArm : Dialect
• wArm : Dialect

@[implicit_reducible]

instance Dolatian2020.instDecidableEqDialect : DecidableEq Dialect

Equations

• Dolatian2020.instDecidableEqDialect x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Dolatian2020.instReprDialect.repr : Dialect → ℕ → Std.Format

Equations

• Dolatian2020.instReprDialect.repr Dolatian2020.Dialect.eArm prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Dolatian2020.Dialect.eArm")).group prec✝
• Dolatian2020.instReprDialect.repr Dolatian2020.Dialect.wArm prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Dolatian2020.Dialect.wArm")).group prec✝

@[implicit_reducible]

instance Dolatian2020.instReprDialect : Repr Dialect

Equations

• Dolatian2020.instReprDialect = { reprPrec := Dolatian2020.instReprDialect.repr }

def Dolatian2020.Dialect.pstemReduces : Dialect → Bool

The PStem-level cophonology: Eastern Armenian's PStem triggers stress and DHR; Western Armenian's triggers only stress ([Dol20] (76)).

Equations

• Dolatian2020.Dialect.eArm.pstemReduces = true
• Dolatian2020.Dialect.wArm.pstemReduces = false

def Dolatian2020.resyllabifiesAcrossStemBoundary (stem : List Seg) (suf : Suffix) : Bool

Onset maximization: a V-initial suffix pulls a single stem-final consonant into its onset, resyllabifying it across the MStem boundary. A C-initial suffix leaves the boundary at a syllable edge.

Equations

• Dolatian2020.resyllabifiesAcrossStemBoundary stem suf = (stem.getLast? == some Dolatian2020.Seg.C && List.head? suf == some Dolatian2020.Seg.V)

def Dolatian2020.pstemMisaligned (stem : List Seg) (suf : Suffix) : Bool

PStem misalignment ([Dol20] §2.5.3): the MStem boundary no longer coincides with a syllable boundary, because a V-initial suffix resyllabified the stem-final consonant.

Equations

• Dolatian2020.pstemMisaligned stem suf = Dolatian2020.resyllabifiesAcrossStemBoundary stem suf

def Dolatian2020.pstemCophonologyTriggered (stem : List Seg) (suf : Suffix) : Bool

The PStem-level cophonology is triggered exactly when the PStem is misaligned and so expands by incorporating the V-initial suffix ([Dol20]: the PStem cophonology applies only to misaligned PStems).

Equations

• Dolatian2020.pstemCophonologyTriggered stem suf = Dolatian2020.pstemMisaligned stem suf

def Dolatian2020.dhrApplies (d : Dialect) (stem : List Seg) (suf : Suffix) : Bool

Destressed High Vowel Reduction applies iff the expanded PStem-level cophonology is triggered and the dialect's PStem reduces. The pattern is derived from the cyclic mechanism, not a stipulated table (see dhr_iff).

Equations

• Dolatian2020.dhrApplies d stem suf = (Dolatian2020.pstemCophonologyTriggered stem suf && d.pstemReduces)

Worked forms: amusin 'husband' with V- and C-initial inflection

def Dolatian2020.amusin : List Seg

amusin = a.mu.sin, consonant-final.

Equations

• Dolatian2020.amusin = [Dolatian2020.Seg.V, Dolatian2020.Seg.C, Dolatian2020.Seg.V, Dolatian2020.Seg.C, Dolatian2020.Seg.V, Dolatian2020.Seg.C]

def Dolatian2020.sufOv : Suffix

-ov (INST): V-initial.

Equations

• Dolatian2020.sufOv = [Dolatian2020.Seg.V, Dolatian2020.Seg.C]

def Dolatian2020.sufNer : Suffix

-ner (PL): C-initial.

Equations

• Dolatian2020.sufNer = [Dolatian2020.Seg.C, Dolatian2020.Seg.V, Dolatian2020.Seg.C]

theorem Dolatian2020.ov_misaligns : pstemMisaligned amusin sufOv = true

theorem Dolatian2020.ner_aligned : pstemMisaligned amusin sufNer = false

theorem Dolatian2020.earm_ov_reduces : dhrApplies Dialect.eArm amusin sufOv = true

theorem Dolatian2020.earm_ner_blocks : dhrApplies Dialect.eArm amusin sufNer = false

theorem Dolatian2020.warm_ov_blocks : dhrApplies Dialect.wArm amusin sufOv = false

theorem Dolatian2020.warm_ner_blocks : dhrApplies Dialect.wArm amusin sufNer = false

theorem Dolatian2020.dhr_iff (d : Dialect) (stem : List Seg) (suf : Suffix) : dhrApplies d stem suf = true ↔ d = Dialect.eArm ∧ pstemMisaligned stem suf = true

Characterization: pre-inflectional DHR is exactly Eastern Armenian with a misaligned PStem. The V- vs C-initial split falls out of onset-maximization syllabification; the dialect split out of the PStem cophonology — neither is stipulated as a lookup table.

The cophonology as a quantifier-free logical transduction

[Dol20]'s computational formalization (§4): the cophonology as an MSO/quantifier-free logical transduction over a word model. Eastern Armenian DHR is the local rewrite H → ∅ / _ C V — the stem-final high vowel drops when a following consonant resyllabifies into a V-initial suffix's onset — realized with Core.Computability.Subregular.Logic. The rewrite reads a bounded right context, so it is quantifier-free, hence subregular and learnable (Dolatian's thesis).

inductive Dolatian2020.Phone : Type

Segments refined with the high-vowel target H of DHR.

• C : Phone
• V : Phone
• H : Phone

@[implicit_reducible]

instance Dolatian2020.instDecidableEqPhone : DecidableEq Phone

Equations

• Dolatian2020.instDecidableEqPhone x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Dolatian2020.instReprPhone.repr : Phone → ℕ → Std.Format

Equations

• Dolatian2020.instReprPhone.repr Dolatian2020.Phone.C prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Dolatian2020.Phone.C")).group prec✝
• Dolatian2020.instReprPhone.repr Dolatian2020.Phone.V prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Dolatian2020.Phone.V")).group prec✝
• Dolatian2020.instReprPhone.repr Dolatian2020.Phone.H prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Dolatian2020.Phone.H")).group prec✝

@[implicit_reducible]

instance Dolatian2020.instReprPhone : Repr Phone

Equations

• Dolatian2020.instReprPhone = { reprPrec := Dolatian2020.instReprPhone.repr }

def Dolatian2020.dhrEast : Subregular.Logic.Transduction Phone Phone

Eastern Armenian DHR as a logical transduction: delete a high vowel before C V (the resyllabification-and-expansion context); every other segment is faithful. A high vowel in that context matches no clause and is dropped.

Equations

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

def Dolatian2020.dhrWest : Subregular.Logic.Transduction Phone Phone

Western Armenian: the PStem cophonology shifts stress but does not reduce, so the high vowel is faithful in every context ([Dol20] (76)).

Equations

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

def Dolatian2020.amusinP : List Phone

amusin a-mu-si-n, segmentally V C V C H C (the stem-final high vowel is H).

Equations

• Dolatian2020.amusinP = [Dolatian2020.Phone.V, Dolatian2020.Phone.C, Dolatian2020.Phone.V, Dolatian2020.Phone.C, Dolatian2020.Phone.H, Dolatian2020.Phone.C]

def Dolatian2020.ovP : List Phone

-ov (INST), V-initial.

Equations

• Dolatian2020.ovP = [Dolatian2020.Phone.V, Dolatian2020.Phone.C]

def Dolatian2020.nerP : List Phone

-ner (PL), C-initial.

Equations

• Dolatian2020.nerP = [Dolatian2020.Phone.C, Dolatian2020.Phone.V, Dolatian2020.Phone.C]

theorem Dolatian2020.dhrEast_ov : dhrEast.apply (amusinP ++ ovP) = [Phone.V, Phone.C, Phone.V, Phone.C, Phone.C, Phone.V, Phone.C]

theorem Dolatian2020.dhrEast_ner : dhrEast.apply (amusinP ++ nerP) = amusinP ++ nerP

theorem Dolatian2020.dhrWest_ov : dhrWest.apply (amusinP ++ ovP) = amusinP ++ ovP

theorem Dolatian2020.transduction_matches_trigger : (dhrEast.apply (amusinP ++ ovP) ≠ amusinP ++ ovP ∧ dhrApplies Dialect.eArm amusin sufOv = true) ∧ dhrEast.apply (amusinP ++ nerP) = amusinP ++ nerP ∧ dhrApplies Dialect.eArm amusin sufNer = false

The transduction's segmental action agrees with the serial trigger dhrApplies: the form changes exactly when (Eastern, misaligned) DHR is predicted — the two formalizations coincide.

theorem Dolatian2020.dhr_cyclic_stable : dhrEast.applyComp dhrEast (amusinP ++ ovP) = dhrEast.apply (amusinP ++ ovP)

Cyclicity ([Dol20]: interactionist derivation = transduction composition): a further cophonology cycle composes with the first, and DHR is stable under re-application.