Marco and Rasin (2026): Optimal Paradigms #
This file formalizes the challenge to optimal paradigms of [MR26]. [McC05] derived the Moroccan Arabic noun–verb asymmetry in the position of schwa, verbs CCəC regardless of sonority and nouns CəCC when the second consonant is more sonorous than the third, from paradigm structure: most verbal suffixes are consonant-initial, so paradigm uniformity draws the unsuffixed verb to CCəC by majority rule, while the one-member noun paradigm is left to the sonority constraint. In Judeo-Tripolitanian Arabic verbs and nouns pattern as in Moroccan, but adjectives are CCəC regardless of sonority while inflecting, like nouns, with vowel-initial suffixes only, so under McCarthy's ranking optimal paradigms select the levelled CəCC paradigm for them; a category-specific template for verbs and adjectives derives the pattern, against category-neutral phonology ([Bob08]).
Implementation notes #
The paradigms, constraints, and ranking are those of the McCarthy 2005 study, run on the Judeo-Tripolitanian data; schwa is epenthetic, so the input is the bare root.
TODO #
The paper is not on file; example numbers are transcribed from an earlier version of this file and are UNVERIFIED.
References #
The CCəC realisation of the root /C₁C₂C₃/ in a cell, the schwa epenthetic.
Equations
- MarcoRasin2026.schwaMedial c₁ c₂ c₃ suffix = { cell := suffix, stem := [c₁, c₂, McCarthy2005.Arabic.Seg.schwa, c₃], io := [(0, 0), (1, 1), (2, 3)] }
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The CəCC realisation.
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- MarcoRasin2026.schwaInitial c₁ c₂ c₃ suffix = { cell := suffix, stem := [c₁, McCarthy2005.Arabic.Seg.schwa, c₂, c₃], io := [(0, 0), (1, 2), (2, 3)] }
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The candidate paradigms of a root over the bare cell, the C-initial and the V-initial suffixes (10): the bare stem CCəC or CəCC with the suffixed stems fixed by the phonotactics, or levelled to CCəC or to CəCC.
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- MarcoRasin2026.paradigms.root c₁ c₂ c₃ = [c₁, c₂, c₃]
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- MarcoRasin2026.paradigms.medial c₁ c₂ c₃ = MarcoRasin2026.schwaMedial c₁ c₂ c₃
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- MarcoRasin2026.paradigms.initial c₁ c₂ c₃ = MarcoRasin2026.schwaInitial c₁ c₂ c₃
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The constraints (8) in McCarthy's ranking: *ə]σ, *CCC >> OP-MAX-V >> SONCON.
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Moroccan Arabic (§2) #
The Moroccan perfective suffixes (6).
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(10): majority rules — the unsuffixed ʃrəb joins the C-suffixed CCəC stems, twenty OP-MAX-V marks against twenty-four.
(12): the one-member noun paradigm is left to SONCON, ʃərb.
Judeo-Tripolitanian Arabic verbs and nouns (§3.1) #
The JTA perfective suffixes (13): five C-initial, two V-initial.
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(13): the paradigms of ʃrəb 'drink', gdəm 'bite' and ktʃəb 'write' — CCəC in the bare form and before C-initial suffixes, CəCC before V-initial ones, whatever the sonority of the root — are OP's optima.
The roots of the nouns (14): CəCC with C₂ more sonorous than C₃ — kəlb, bəntʃ, wəld, səms, məlħ, tʃəlʒ — and CCəC otherwise — xʃəm, ħbəq, lħəm, sdər, bsəl, fħəm.
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(14): the one-member noun paradigms follow SONCON.
The challenge from adjectives (§3.2–3.3) #
Adjectives with C₂ more sonorous than C₃ — bjəd 'white', zrəq 'blue', trəʃ 'deaf', ħwəl 'cross-eyed' (15), the comparatives qrəb, zjən (16) — are CCəC like verbs, but inflect with the V-initial suffixes -a, -in alone (18).
The adjectival paradigm of a root (18): bare, feminine -a, plural -in.
Equations
- MarcoRasin2026.adjective c₁ c₂ c₃ = MarcoRasin2026.paradigms c₁ c₂ c₃ [] [[McCarthy2005.Arabic.Seg.a], [McCarthy2005.Arabic.Seg.i, McCarthy2005.Arabic.Seg.n]]
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The roots of the adjectives with C₂ more sonorous than C₃, (15a) and (16).
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(19): OP fails — the attested ⟨trəʃ, tərʃa, tərʃin⟩ draws four OP-MAX-V marks and one of SONCON, and the levelled ⟨tərʃ, tərʃa, tərʃin⟩ none.
(20): OP fails regardless of what constitutes a paradigm — as a paradigm of one, the adjective is left to SONCON, tərʃ.
Category-specific templates (§3.3) #
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- MarcoRasin2026.instDecidableEqCategory x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- MarcoRasin2026.instReprCategory = { reprPrec := MarcoRasin2026.instReprCategory.repr }
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{CCəC}_{Verb, Adj} (22): the stem of a verb or an adjective surfaces as CCəC.
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- MarcoRasin2026.template MarcoRasin2026.Category.noun x✝ = 0
- MarcoRasin2026.template x✝ [head, McCarthy2005.Arabic.Seg.schwa, head_1, head_2] = 1
- MarcoRasin2026.template x✝¹ x✝ = 0
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The ranking (23): *ə]σ, *CCC >> {CCəC}_{Verb, Adj} >> SONCON.
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(23): the template selects the attested adjectival paradigms against SONCON.
The template leaves the verbs (13) and the nouns (14) as they are.