The class nodes of (3): Root over Laryngeal and Place, Place over Oral, Oral over VPlace, and VPlace over Height and Color.
Derives DecidableEq, Repr, Fintype.
Used by Node.pred, Node.instPartialOrder, Node.instDecidableLE, node
Docs / Studies / Studies.Padgett2002
Feature Classes in Phonology
Padgett, J. (2002). Language, 78(1), 81–110
Padgett argues that a constraint naming a feature class targets the features of the class directly and individually, not through a class node. Classes are sets of features, the unions (25), which carry over the classes of the geometry (3), and SPREAD(COLOR) (26) is violated once for each segment an autosegment of [back] or [round] fails to reach, so it can be satisfied in part. Turkish suffix harmony is then one Color harmony: under IDENT_Rt ≫ *[+rnd, −hi] ≫ SPREAD(COLOR) ≫ IDENT a nonhigh suffix vowel agrees with the root in [back] alone, while spreading a Color node carries both features or neither.
Main definitions
Node,node: the geometry (3);laryngeal,oral,vplace,height,color: (25).Tier,Tier.spread: the autosegments of one feature over a word, and SPREAD (26).tableau: the Turkish grammar of (17)–(22), over every fully specified candidate.
Implementation notes
Candidates are fully specified, as from (12) on. The segments are the vowels, as in (12)–(20), and in (21)–(22) the root's last vowel, the palatal lateral, which shares its [round] (footnote 6), and the suffix vowels, unspecified for color (§3.3): /I/ is the fragment's high archiphoneme and /A/ the meet of the four nonhigh vowels. [pharyngeal] has no counterpart in the inventory, so Place is left out of (25).
TODO
- The paper marks four IDENT violations on (22b) and (22c), where counting by segment and
feature, as in (17c) and (20d), gives three (
profile_22); the winner is unaffected. - HAVEPLACE, *PLACE and OCP(PLACE) ((27)–(29)), and the dissimilation of §5.
References
- Padgett 2002, Feature Classes in Phonology
- Padgett 2002, Feature Classes in Phonology
The geometry (3) and the classes (25)
The node immediately dominating each node, the root fixed.
- Node.root.pred = Node.root
- Node.laryngeal.pred = Node.root
- Node.place.pred = Node.root
- Node.oral.pred = Node.place
- Node.vplace.pred = Node.oral
- Node.height.pred = Node.vplace
- Node.color.pred = Node.vplace
Built from
Used by Node.instDecidableLE
a ≤ b when a lies on the walk from b up to the root.
The definition is too large to print here; read it in the source.
Built from
- a.instDecidableLE b = { decide := decide (List.elem a (List.iterate Node.pred b (Fintype.card Node)) = true), reflects_decide := ⋯ }
Built from ,
The node each feature of (3) hangs from, with [aspirated] and [glottalized] read as [spread glottis] and [constricted glottis].
Equations
- node Phonology.Feature.spreadGlottis = some Node.laryngeal
- node Phonology.Feature.voice = some Node.laryngeal
- node Phonology.Feature.constrGlottis = some Node.laryngeal
- node Phonology.Feature.nasal = some Node.root
- node Phonology.Feature.labial = some Node.oral
- node Phonology.Feature.coronal = some Node.oral
- node Phonology.Feature.dorsal = some Node.oral
- node Phonology.Feature.low = some Node.height
- node Phonology.Feature.high = some Node.height
- node Phonology.Feature.back = some Node.color
- node Phonology.Feature.round = some Node.color
- node x✝ = none
Built from
Used by classes_eq_featureClass, colorSpreading
Laryngeal, the union of Aspirated, Voiced and Glottalized (25).
- laryngeal = {Phonology.Feature.spreadGlottis} ∪ {Phonology.Feature.voice} ∪ {Phonology.Feature.constrGlottis}
Used by classes_eq_featureClass
Color, the union of Back and Round (25).
Used by vplace, classes_eq_featureClass, Candidate, back, round, identRoot, spreadColor, ident, eqOn_colorSpreading
Height, the union of Low and High (25).
Used by vplace, classes_eq_featureClass
Oral, the union of Labial, Coronal, Dorsal and VPlace (25).
- oral = {Phonology.Feature.labial} ∪ {Phonology.Feature.coronal} ∪ {Phonology.Feature.dorsal} ∪ vplace
Built from
Used by classes_eq_featureClass
The classes (25) are the feature classes of the nodes of (3), which they carry over.
Built from , , , , ,
SPREAD (26)
The autosegments of one feature over a word of n segments, each linked to a run of
segments and every segment to one of them: starts are the segments at which an autosegment
begins, and value j is the value of the autosegment segment j is linked to.
- starts : Finset (Fin n)
The segments at which an autosegment begins.
- value : Fin n → Bool
The value of each segment's autosegment.
- zero_mem (j : Fin n) : ↑j = 0 → j ∈ self.starts
An autosegment begins at the first segment.
A segment at which no autosegment begins shares the previous segment's.
Used by Tier.equivSubtype, Tier.instDecidableEq, Tier.instFintype, Tier.Linked, Tier.instDecidableLinked, Tier.spread, Tier.spread_eq_zero_iff, Candidate, cand
A tier is its starts and values, the conditions being propositions.
{n : ℕ} :
Tier n ≃ { p : Finset (Fin n) × (Fin n → Bool) // (∀ (j : Fin n), ↑j = 0 → j ∈ p.1) ∧ ∀ (j k : Fin n), ↑k = ↑j + 1 → k ∉ p.1 → p.2 k = p.2 j }
The definition is too large to print here; read it in the source.
Built from
Used by Tier.instDecidableEq
The definition is too large to print here; read it in the source.
Built from
Segment j is linked to the autosegment beginning at a: j is at or after a and
before every later start.
Built from
Used by Tier.instDecidableLinked, Tier.spread
- t.instDecidableLinked a j = { decide := decide (a ≤ j) && decide (∀ b ∈ t.starts, a < b → j < b), reflects_decide := ⋯ }
Built from ,
The violations of SPREAD (26): each autosegment violates it once for every segment of the word it is not linked to.
Built from ,
Used by Tier.spread_eq_zero_iff, spreadColor
SPREAD holds of a tier iff it has at most one autosegment, every segment then sharing it.
Built from ,
Turkish
[back] as a feature of Color.
Built from
The output of a candidate: each input segment with the values of its color autosegments.
- surface x c j = ((x j).setFeature Phonology.Feature.back ((c back).value j)).setFeature Phonology.Feature.round ((c round).value j)
Built from , ,
IDENT_Rt (16), summed over Color: a segment of the root, the first r, keeps the input
value of each color feature.
Built from ,
Used by tableau, tableauTotal
*[+rnd, −hi]: a nonhigh segment is not round.
- noRoundNonhigh x c = {j : Fin n | (c round).value j = true ∧ (x j).HasValue Phonology.Feature.high false}.card
Built from ,
Used by tableau, tableauTotal
SPREAD(COLOR) (10, 26), summed over the features of Color.
- spreadColor c = ∑ f : ↥color, (c f).spread
Built from , ,
Used by tableau, tableauTotal
IDENT (11), summed over Color: a segment keeps the input value of each color feature, unspecified counting as a value.
Built from ,
Used by tableau, tableauTotal
IDENT_Rt ≫ *[+rnd, −hi] ≫ SPREAD(COLOR) ≫ IDENT, the ranking of (17)–(22), over every candidate.
- tableau x r = OptimalityTheory.Tableau.ofList Finset.univ [identRoot x r, noRoundNonhigh x, spreadColor, ident x]
Built from , , , ,
Used by profile_14, optimal_sonlAr, profile_20, profile_22, optimal_petrolI
The reverse ranking of SPREAD(COLOR) and *[+rnd, −hi], total class spreading as in Kirghiz (p. 93).
- tableauTotal x r = OptimalityTheory.Tableau.ofList Finset.univ [identRoot x r, spreadColor, noRoundNonhigh x, ident x]
Built from , , , ,
The outputs of the winners of the grammar for the segments w, the first r of the root.
The definition is too large to print here; read it in the source.
Used by predict_suffix_mem_reduced
The outputs of the winners under the reverse ranking.
The definition is too large to print here; read it in the source.
Used by predictTotal_son_lAr
Inputs and forms
/A/, the nonhigh suffix vowel unspecified for color: what the four nonhigh vowels share.
Used by suffixVowels, sonlAr, pullArIn, predict_suffix_mem_reduced, predictTotal_son_lAr, ne_colorSpreading
The segment a segment symbol of the paper's transcription contributes to harmony: a vowel,
with ɨ for ı, or the palatal lateral lʸ.
The definition is too large to print here; read it in the source.
Used by harmony
A root from its last vowel on, the segments after the vowel sharing its [round] (footnote 6).
- shareRound [] = []
- shareRound (v :: w) = v :: List.map (fun (x : Phonology.Feature → Flat Bool) => Function.update x Phonology.Feature.round (v Phonology.Feature.round)) w
Used by input
The suffix vowels of a cell, in the order of the suffixes: /A/ of the plural -lAr, then /I/ of the accusative -I or the genitive -In (§3.3).
- suffixVowels cell = (if cell.number = ↑UD.Number.Plur then [A'] else []) ++ if cell.case = ↑UD.Case.Nom then [] else [Turkish.Phonology.I]
Built from
Used by input
The tableaux (14), (20) and (22)
/son-lAr/ of (14) and (17).
- sonlAr = ![Turkish.Phonology.o, A']
Built from
Used by profile_14, optimal_sonlAr
(14a) {[son-lor]+B}+R, total Color harmony.
The definition is too large to print here; read it in the source.
Built from
Used by profile_14
(14b) [{son-}+R{lar}−R]+B, [back] harmony alone.
The definition is too large to print here; read it in the source.
Built from
Used by profile_14, optimal_sonlAr
(14c) {[son-]+B[lör]−B}+R, [round] harmony alone.
The definition is too large to print here; read it in the source.
Built from
Used by profile_14
(14d) [{son-}+R]+B[{lar}−R]+B, no harmony.
The definition is too large to print here; read it in the source.
Built from
Used by profile_14
Built from , , , , ,
Built from , ,
(20b) [{pul-}+R{lar-ɨn}−R]+B, the attested form.
The definition is too large to print here; read it in the source.
Built from
Used by profile_20
(20c) [{pul-}+R{lar-}−R{un}+R]+B, with the final vowel round on its own.
The definition is too large to print here; read it in the source.
Built from
Used by profile_20
Built from , , ,
/(petr)olʸ-I/ of (22), the lateral sharing the vowel's [+round].
- petrolI = ![Turkish.Phonology.o, Function.update Turkish.Phonology.l' Phonology.Feature.round (some true), Turkish.Phonology.I]
Used by profile_22, optimal_petrolI
(22a) {[o]+B[lʸ-ü]−B}+R, the attested form.
The definition is too large to print here; read it in the source.
Built from
Used by profile_22, optimal_petrolI
(22b) {[ölʸ-ü]−B}+R.
The definition is too large to print here; read it in the source.
Built from
Used by profile_22
(22c) {[ol-u]+B}+R.
The definition is too large to print here; read it in the source.
Built from
Used by profile_22
(22d) {[o]+B[lʸ]+R{-ɨ]−B}−R.
The definition is too large to print here; read it in the source.
Built from
Used by profile_22
Built from , , , , ,
Built from , ,
The forms
The segments a form contributes to harmony.
- harmony w = List.filterMap harmonySegment w.segments
Built from
Used by attestedVowels, predict_eq_attested, notMem_predict_marked
The position of the last vowel of a stem.
- lastVowel s = s.length - 1 - List.findIdx (fun (x : Phonology.Segment) => decide (x ∈ Turkish.Phonology.vowels)) s.reverse
Used by input, attestedVowels
The input of a form with stem s: the stem from its last vowel on, a following lateral
sharing the vowel's [round], and the suffix vowels of the form's cell.
- input s w = shareRound (List.drop (lastVowel s) s) ++ suffixVowels w.cell
Built from , ,
The vowels the grammar predicts for a form with stem s, the root being the stem from its
last vowel.
(s : List Phonology.Segment) (w : CLDF.Wordlist.Form Wordlist.Cell) :
Finset (List Phonology.Segment)
The definition is too large to print here; read it in the source.
Used by predict_eq_attested, notMem_predict_marked
The vowels of a form with stem s, from the stem's last vowel on.
- attestedVowels s w = List.filter (fun (x : Phonology.Segment) => decide (x ∈ Turkish.Phonology.vowels)) (List.drop (lastVowel s) (harmony w))
Built from ,
Used by predict_eq_attested, notMem_predict_marked
The grammar derives the vowels of every suffixed form of (6), p. 85 and (21) from its stem, the first form of its paradigm.
(p : CLDF.Wordlist.Paradigm Wordlist.Cell) :
p ∈ Wordlist.paradigms → ∀ s ∈ p.forms.head?, ∀ w ∈ p.forms.tail, predictedVowels (harmony s) w = {attestedVowels (harmony s) w}
Built from , ,
The grammar derives neither starred form of p. 85, *[pul-lar-un] or *[yüz-ler-ün].
(w : CLDF.Wordlist.Form Wordlist.Cell) :
w ∈ Wordlist.marked → ∀ p ∈ Wordlist.paradigms, p.lexeme.id = w.lexeme.id → ∀ s ∈ p.forms.head?, attestedVowels (harmony s) w ∉ predictedVowels (harmony s) w
Built from , ,
Harmony yields only the vowels of (13) in a suffix, whatever the root vowel.
(v : Phonology.Segment) :
v ∈ Turkish.Phonology.vowels → ∀ s ∈ [Turkish.Phonology.I, A'], ∀ w ∈ predict [v, s] 1, ∀ x ∈ List.drop 1 w, x ∈ {Turkish.Phonology.i, Turkish.Phonology.ü, Turkish.Phonology.ı, Turkish.Phonology.u, Turkish.Phonology.e, Turkish.Phonology.a}
Built from ,
Under the reverse ranking a nonhigh suffix vowel agrees in both features, [son-lor] and [yüz-lör].
Built from ,
Class nodes
Spreading the Color node of (3) from src onto tgt.
- colorSpreading src tgt = (Phonology.FeatureGeometry.featureClass node Node.color).piecewise src tgt
Built from
Used by eqOn_colorSpreading, ne_colorSpreading
Built from ,
No spreading or non-spreading of a Color node yields the suffix vowel of [son-lar] (9) or of [petrolʸ-ü] (23).
Built from ,