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Linglib.Phenomena.Classifiers.Studies.Downing1996

@cite{downing-1996} — Numeral Classifier Systems: The Case of Japanese #

@cite{downing-1996} @cite{aikhenvald-2000} @cite{chierchia-1998}

Formalizes core contributions from Downing's monograph on Japanese numeral classifiers (Studies in Discourse and Grammar, vol. 4).

Two Central Hypotheses (Ch. 5) #

Hypothesis 1 (Universal semantic trends): Classifier categories encode culturally significant categories defined by physical, functional, and social interaction. The choice of which features are exploited is culture-dependent.

Hypothesis 2 (Semantic supplementation): Classifiers systematically supplement the information carried by nouns — the classifier system provides categorization independent of and additional to the common noun system.

Individuation Function (Ch. 7) #

@cite{downing-1996} Ch. 7 treats classifier phrases and plural markers as individuators. @cite{chierchia-1998}'s later Nominal Mapping Parameter provides a formal framework for this insight: in [+arg, -pred] languages, bare nouns denote kinds, and classifiers supply individuation for enumeration. The bridge to @cite{chierchia-1998} is a linglib contribution, not one Downing herself makes (Chierchia 1998 postdates this monograph). The strict NMP correlation has been challenged (e.g., Turkish has bare arguments without classifiers; Li 2013 argues Chinese nouns are not uniformly mass), but the core insight — that classifiers relate to individuation — is preserved in current work, with the mechanism (atomization vs. unitization) still debated.

Anaphoric Use (Ch. 6) #

Classifier phrases (numeral + classifier without accompanying noun) serve as anaphoric devices in discourse, occupying a unique niche between zero anaphora (short range) and full lexical NPs (long range). Empirical findings:

87% of anaphoric classifier uses involve 人 nin (human classifier)
75% use numeral 2
Striking distance is intermediate: longer than pronouns, shorter than NPs

Shape Dimensionality (Ch. 5) #

Shape-based classifiers decompose along a 1D/2D/3D dimensionality axis, now formalized via ShapeDimension in ClassifierEntry.

Core Inventory (Table 1.1) #

All 27 classifiers from Table 1.1 are represented in the Japanese fragment, including the homophonous 軒 ken (buildings) / 件 ken' (incidents) pair, the maritime size split (隻 seki / 艘 soo), and the two building classifiers (軒 ken / 棟 mune).

Frequency Distribution (Ch. 3, Table 3.1) #

A 500-form corpus sample reveals extreme Zipfian skew: 人 nin (40%) and つ tsu (23%) together account for 63% of all classifier uses. The top five classifiers cover 82%. Quality classifiers (shape-based) are collectively more frequent than kind classifiers (function-based).

def Phenomena.Classifiers.Studies.Downing1996.shapeClassifiers :

List Core.NounCategorization.ClassifierEntry

Shape-based classifiers in the Japanese inventory decompose into three dimensionality classes (Ch. 5).

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theorem Phenomena.Classifiers.Studies.Downing1996.shape_classifier_count :

shapeClassifiers.length ≥ 5

At least 5 classifiers in the inventory encode shape.

All three shape dimensions (1D, 2D, 3D) are attested.

The animacy hierarchy in Japanese classifiers: human (nin/mei) > large animal (tou) > small animal (hiki) > inanimate (tsu). Each level is distinguished by a distinct classifier.

The human classifier has a formal register variant (名 mei) encoding social status, unlike other animacy classifiers.

structure Phenomena.Classifiers.Studies.Downing1996.AnaphoricDistribution :

Distribution of classifiers in anaphoric examples (Ch. 6, Table 6.1, n = 55).

classifier : Core.NounCategorization.ClassifierEntry
count : ℕ

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def Phenomena.Classifiers.Studies.Downing1996.instReprAnaphoricDistribution.repr :

AnaphoricDistribution → ℕ → Std.Format

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instance Phenomena.Classifiers.Studies.Downing1996.instReprAnaphoricDistribution :

Repr AnaphoricDistribution

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Phenomena.Classifiers.Studies.Downing1996.instReprAnaphoricDistribution = { reprPrec := Phenomena.Classifiers.Studies.Downing1996.instReprAnaphoricDistribution.repr }

def Phenomena.Classifiers.Studies.Downing1996.anaphoricClassifierData :

List AnaphoricDistribution

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theorem Phenomena.Classifiers.Studies.Downing1996.anaphoric_total :

List.foldl (fun (x1 x2 : ℕ) => x1 + x2) 0 (List.map (fun (x : AnaphoricDistribution) => x.count) anaphoricClassifierData) = 55

Total anaphoric classifier examples = 55.

theorem Phenomena.Classifiers.Studies.Downing1996.nin_dominates_anaphoric :

Option.map (fun (x : AnaphoricDistribution) => x.count) (List.find? (fun (x : AnaphoricDistribution) => x.classifier == Fragments.Japanese.Classifiers.nin) anaphoricClassifierData) = some 48

人 nin dominates anaphoric classifier use (48/55 = 87%).

structure Phenomena.Classifiers.Studies.Downing1996.NumeralDistribution :

Distribution of numerals in anaphoric classifier examples (Ch. 6, Table 6.2, n = 55). Numeral 1 is absent — explained by competition with zero anaphora.

numeral : ℕ
count : ℕ

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def Phenomena.Classifiers.Studies.Downing1996.instReprNumeralDistribution.repr :

NumeralDistribution → ℕ → Std.Format

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instance Phenomena.Classifiers.Studies.Downing1996.instReprNumeralDistribution :

Repr NumeralDistribution

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Phenomena.Classifiers.Studies.Downing1996.instReprNumeralDistribution = { reprPrec := Phenomena.Classifiers.Studies.Downing1996.instReprNumeralDistribution.repr }

def Phenomena.Classifiers.Studies.Downing1996.anaphoricNumeralData :

List NumeralDistribution

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Phenomena.Classifiers.Studies.Downing1996.anaphoricNumeralData = [{ numeral := 2, count := 41 }, { numeral := 3, count := 12 }, { numeral := 4, count := 1 }, { numeral := 5, count := 1 }]

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theorem Phenomena.Classifiers.Studies.Downing1996.two_dominates_anaphoric :

Option.map (fun (x : NumeralDistribution) => x.count) (List.find? (fun (x : NumeralDistribution) => x.numeral == 2) anaphoricNumeralData) = some 41

Numeral 2 dominates anaphoric use (41/55 = 75%).

theorem Phenomena.Classifiers.Studies.Downing1996.one_absent_from_anaphoric :

(anaphoricNumeralData.all fun (x : NumeralDistribution) => decide (x.numeral ≠ 1)) = true

Numeral 1 is absent from anaphoric classifier constructions. explains: 'one' + CL has low contrastive information potential and competes with zero anaphora.

theorem Phenomena.Classifiers.Studies.Downing1996.argOnly_has_classifiers :

Fragments.Japanese.Nouns.japaneseMapping = Semantics.Lexical.Noun.Kind.Chierchia1998.NominalMapping.argOnly ∧ Typology.japanese.classifierType = Core.NounCategorization.ClassifierType.numeralClassifier

Ch. 7 discusses classifier phrases as individuators. @cite{chierchia-1998}'s later linking hypothesis formalizes this: [+arg, -pred] languages have kind-denoting bare nouns and need classifiers for individuation. The strict correlation is contested (see module docstring), but the co-occurrence is robustly attested.

Witnessed by: Japanese is [+arg, -pred] AND has numeral classifiers.

theorem Phenomena.Classifiers.Studies.Downing1996.no_blocking_needs_classifiers :

Fragments.Japanese.Nouns.japaneseBlocking.iotaBlocked = false ∧ Fragments.Japanese.Nouns.japaneseBlocking.existsBlocked = false ∧ Typology.japanese.classifierType = Core.NounCategorization.ClassifierType.numeralClassifier

In @cite{chierchia-1998}'s framework, [+arg, -pred] languages have no type-shift blocking (no articles), so bare nouns freely occur as arguments. Classifiers rather than articles provide individuation.

theorem Phenomena.Classifiers.Studies.Downing1996.classifiers_carry_individuation_info :

((List.filter (fun (c : Core.NounCategorization.ClassifierEntry) => !c.isDefault && !c.isMensural) Fragments.Japanese.Classifiers.allClassifiers).all fun (x : Core.NounCategorization.ClassifierEntry) => decide (x.semantics.length > 0)) = true

Non-default classifiers encode at least one semantic parameter, confirming they carry individuation-relevant information beyond mere enumeration. The default classifier つ is the only one that enumerates without individuating.

inductive Phenomena.Classifiers.Studies.Downing1996.MorphemeCategoryRelation :

Seven recurrent semantic relations between the independent sense of the classifier morpheme and the classifier category. Six are from Ch. 5, Table 5.2; the seventh (sharedQuality) is attested in non-Japanese languages and noted by Downing as recurring cross-linguistically but absent in Japanese.

identicalClass : MorphemeCategoryRelation
Morpheme denotes a class identical/superordinate to the category. e.g., 件 ken 'matter' → classifier for incidents.
partOfMembers : MorphemeCategoryRelation
Morpheme denotes a part possessed by category members. e.g., 頭 tou 'head' → classifier for large animals.
associatedAction : MorphemeCategoryRelation
Morpheme denotes an action associated with category members. e.g., 通 tsuu 'to pass' → classifier for letters/documents.
exemplar : MorphemeCategoryRelation
Morpheme denotes an exemplar possessing the defining traits. e.g., 筋 suji 'sinew' → classifier for long, slender objects.
creationAction : MorphemeCategoryRelation
Morpheme denotes the action creating category members. e.g., 巻 maki 'to roll up' → classifier for scrolls.
beneficiaryGoal : MorphemeCategoryRelation
Morpheme denotes the beneficiary/goal of category activity. e.g., 足 soku 'foot' → classifier for pairs of footwear.
sharedQuality : MorphemeCategoryRelation
Morpheme independently represents a quality shared by members. e.g., Indonesian bentuk 'curved' → classifier for rings, wheels.

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instance Phenomena.Classifiers.Studies.Downing1996.instDecidableEqMorphemeCategoryRelation :

DecidableEq MorphemeCategoryRelation

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Phenomena.Classifiers.Studies.Downing1996.instDecidableEqMorphemeCategoryRelation x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Classifiers.Studies.Downing1996.instReprMorphemeCategoryRelation :

Repr MorphemeCategoryRelation

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Phenomena.Classifiers.Studies.Downing1996.instReprMorphemeCategoryRelation = { reprPrec := Phenomena.Classifiers.Studies.Downing1996.instReprMorphemeCategoryRelation.repr }

def Phenomena.Classifiers.Studies.Downing1996.instReprMorphemeCategoryRelation.repr :

MorphemeCategoryRelation → ℕ → Std.Format

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def Phenomena.Classifiers.Studies.Downing1996.instBEqMorphemeCategoryRelation.beq :

MorphemeCategoryRelation → MorphemeCategoryRelation → Bool

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Phenomena.Classifiers.Studies.Downing1996.instBEqMorphemeCategoryRelation.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

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instance Phenomena.Classifiers.Studies.Downing1996.instBEqMorphemeCategoryRelation :

BEq MorphemeCategoryRelation

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Phenomena.Classifiers.Studies.Downing1996.instBEqMorphemeCategoryRelation = { beq := Phenomena.Classifiers.Studies.Downing1996.instBEqMorphemeCategoryRelation.beq }

structure Phenomena.Classifiers.Studies.Downing1996.MorphemeRelationWitness :

A witness pairing a classifier with its Table 5.2 morpheme-category relation and the independent meaning of the morpheme.

classifier : Core.NounCategorization.ClassifierEntry
relation : MorphemeCategoryRelation
independentMeaning : String

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def Phenomena.Classifiers.Studies.Downing1996.instReprMorphemeRelationWitness.repr :

MorphemeRelationWitness → ℕ → Std.Format

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instance Phenomena.Classifiers.Studies.Downing1996.instReprMorphemeRelationWitness :

Repr MorphemeRelationWitness

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Phenomena.Classifiers.Studies.Downing1996.instReprMorphemeRelationWitness = { reprPrec := Phenomena.Classifiers.Studies.Downing1996.instReprMorphemeRelationWitness.repr }

def Phenomena.Classifiers.Studies.Downing1996.table5_2_witnesses :

List MorphemeRelationWitness

Concrete Table 5.2 morpheme-category relation assignments for classifiers in our inventory. Each entry records the classifier, the relation type, and the independent lexical meaning of the morpheme that motivates the relation.

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theorem Phenomena.Classifiers.Studies.Downing1996.four_relation_types_attested :

(List.map (fun (x : MorphemeRelationWitness) => x.relation) table5_2_witnesses).eraseDups.length ≥ 4

At least four of the six Japanese-attested Table 5.2 relation types are witnessed in the inventory (Types 1, 2, 3, 6).

theorem Phenomena.Classifiers.Studies.Downing1996.witnesses_in_inventory :

(table5_2_witnesses.all fun (w : MorphemeRelationWitness) => Fragments.Japanese.Classifiers.allClassifiers.any fun (x : Core.NounCategorization.ClassifierEntry) => x == w.classifier) = true

All Table 5.2 witnesses reference classifiers in our inventory.

theorem Phenomena.Classifiers.Studies.Downing1996.sortal_dominance :

(List.filter (fun (x : Core.NounCategorization.ClassifierEntry) => !x.isMensural) Fragments.Japanese.Classifiers.allClassifiers).length > (List.filter (fun (x : Core.NounCategorization.ClassifierEntry) => x.isMensural) Fragments.Japanese.Classifiers.allClassifiers).length

The Japanese classifier inventory includes both sortal and mensural classifiers, with sortal classifiers dominating.

theorem Phenomena.Classifiers.Studies.Downing1996.function_classifiers_numerous :

(List.filter (fun (x : Core.NounCategorization.ClassifierEntry) => x.encodes Core.NounCategorization.SemanticParameter.function) Fragments.Japanese.Classifiers.allClassifiers).length ≥ 8

Function-based classifiers are the largest semantic group, confirming observation that the system concentrates on interactionally significant categories.

theorem Phenomena.Classifiers.Studies.Downing1996.core_inventory_complete :

Fragments.Japanese.Classifiers.coreClassifiers.length = 27

The core inventory from Table 1.1 has exactly 27 classifiers, all of which are represented in the Japanese fragment.

theorem Phenomena.Classifiers.Studies.Downing1996.full_inventory_includes_core :

(Fragments.Japanese.Classifiers.coreClassifiers.all fun (c : Core.NounCategorization.ClassifierEntry) => Fragments.Japanese.Classifiers.allClassifiers.any fun (x : Core.NounCategorization.ClassifierEntry) => x == c) = true

The full inventory includes the 27 core classifiers plus 6 extended classifiers (sao, wa, furi, zen, kyaku, hai).

The core inventory distinguishes two homophonous ken classifiers: 軒 ken (buildings) and 件 ken' (incidents) — different kanji, different semantic domains.

theorem Phenomena.Classifiers.Studies.Downing1996.two_building_classifiers :

Fragments.Japanese.Classifiers.ken.gloss = "building" ∧ Fragments.Japanese.Classifiers.mune.gloss = "building.roof"

Two building classifiers exist: 軒 ken (functional capacity — home/shop) and 棟 mune (roofed structure).

theorem Phenomena.Classifiers.Studies.Downing1996.maritime_size_split :

Fragments.Japanese.Classifiers.seki.gloss = "large.boat" ∧ Fragments.Japanese.Classifiers.soo.gloss = "small.boat"

Two maritime classifiers exist: 隻 seki (large boats) and 艘 soo (small boats), paralleling the animacy size split (頭 tou / 匹 hiki).

structure Phenomena.Classifiers.Studies.Downing1996.FrequencyEntry :

Frequency data from Ch. 3, Table 3.1: raw counts of classifiers in a 500-form corpus sample (first 50 uses from each of five works of fiction + 250 forms from transcribed conversations and oral narrative).

classifier : Core.NounCategorization.ClassifierEntry
count : ℕ

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def Phenomena.Classifiers.Studies.Downing1996.instReprFrequencyEntry.repr :

FrequencyEntry → ℕ → Std.Format

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instance Phenomena.Classifiers.Studies.Downing1996.instReprFrequencyEntry :

Repr FrequencyEntry

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Phenomena.Classifiers.Studies.Downing1996.instReprFrequencyEntry = { reprPrec := Phenomena.Classifiers.Studies.Downing1996.instReprFrequencyEntry.repr }

def Phenomena.Classifiers.Studies.Downing1996.frequencyData :

List FrequencyEntry

Frequency distribution of classifiers from our inventory that appear in Table 3.1 (n = 500). Classifiers with 0 occurrences in the sample are omitted.

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theorem Phenomena.Classifiers.Studies.Downing1996.nin_most_frequent :

Option.map (fun (x : FrequencyEntry) => x.count) (List.find? (fun (x : FrequencyEntry) => x.classifier == Fragments.Japanese.Classifiers.nin) frequencyData) = some 201

人 nin is the single most frequent classifier (201/500 = 40%).

theorem Phenomena.Classifiers.Studies.Downing1996.nin_tsu_dominate :

have ninCount := 201; have tsuCount := 115; ninCount + tsuCount = 316 ∧ 316 * 100 / 500 = 63

人 nin and つ tsu together account for 316/500 = 63% of all classifier uses, a striking concentration that highlights as the major frequency finding (Ch. 3).

theorem Phenomena.Classifiers.Studies.Downing1996.top_five_dominate :

have top5 := [201, 115, 32, 31, 31]; List.foldl (fun (x1 x2 : ℕ) => x1 + x2) 0 top5 = 410 ∧ 410 * 100 / 500 = 82

The top five classifiers (nin, tsu, hiki, hon, mai) account for 410/500 = 82% of uses, confirming the Zipfian skew.

theorem Phenomena.Classifiers.Studies.Downing1996.quality_over_kind_classifiers :

have qualityTotal := 31 + 31 + 11; have kindMax := 11; qualityTotal > kindMax

Quality classifiers (shape-based: hon, mai, ko) are collectively more frequent than any individual kind classifier (function-based like ken, dai). Ch. 3 observes that "classifiers denoting categories united by a common shape ... are used relatively more often than most of the 'kind-based' classifiers."