Documentation

Linglib.Phenomena.Classifiers.Typology

Classifier Typology #

@cite{aikhenvald-2000} @cite{chierchia-1998} @cite{dixon-1982} @cite{greenberg-1972}

Cross-linguistic typology of noun categorization systems, following @cite{aikhenvald-2000} "Classifiers: A Typology of Noun Categorization Devices."

NounCategorizationSystem #

@cite{aikhenvald-2000}'s 7-property (A–G) per-language system description. The vocabulary types it depends on (ClassifierType, SemanticParameter, ClassifierEntry, etc.) live in Core.Lexical.NounCategorization as settled descriptive infrastructure; this file provides the framework for assembling them into per-language system descriptions.

Part I — Per-Language Data #

Four languages from three families:

French (Indo-European): Noun class / gender (2 classes). Agreement.
Italian (Indo-European): Noun class / gender (2 classes). Agreement.
Mandarin (Sino-Tibetan): Numeral classifiers (~100+). No agreement.
Japanese (Japonic): Numeral classifiers (josūshi). No agreement.

System descriptions are derived from Fragment data (single source of truth).

Part II — Universals #

@cite{aikhenvald-2000}'s empirical generalizations (Chapters 11, 15): agreement diagnostics, semantic parameter universals, inventory size constraints, @cite{greenberg-1972} classifier–number complementarity.

Thread map #

Core infrastructure: Core.NounCategorization — ClassifierType, SemanticParameter, ClassifierEntry
Classifier lexicons: Fragments.Mandarin.Classifiers, Fragments.Japanese.Classifiers
Noun entries: Fragments.{Mandarin,Japanese,French,Italian}.Nouns
WALS 55A: Core.WALS.F55A — 400-language numeral classifier survey (imported in Phenomena.Numerals.Typology)
Chierchia bridge: Theories.Semantics.Lexical.Noun.Kind.Chierchia1998

structure Phenomena.Classifiers.Typology.NounCategorizationSystem :

A noun categorization system in a language.

Captures @cite{aikhenvald-2000}'s 7 definitional properties (A–G from §1.5): (A) morphosyntactic locus → scopes (B) scope/domain → classifierType + scopes (C) assignment principles → assignment (D) surface realization → realizations (E) agreement → hasAgreement (F) markedness → hasUnmarkedDefault (G) grammaticalization → isObligatory

language : String
Language name
family : String
Language family
classifierType : Core.NounCategorization.ClassifierType
Aikhenvald classifier type
scopes : List Core.NounCategorization.CategorizationScope
Morphosyntactic scopes this system operates in (A, B)
assignment : Core.NounCategorization.AssignmentPrinciple
How nouns are assigned to classes/classifiers (C)
realizations : List Core.NounCategorization.SurfaceRealization
Morphological realization types used (D)
hasAgreement : Bool
Does the system involve agreement? (E) — definitional for noun classes
inventorySize : ℕ
Inventory size (number of classes or classifiers)
isObligatory : Bool
Is realization obligatory or optional? (G)
hasUnmarkedDefault : Bool
Is there a formally/functionally unmarked default? (F)
preferredSemantics : List Core.NounCategorization.SemanticParameter
Preferred semantic parameters (§11.2, Table 11.13)
source : String
Citation

Instances For

instance Phenomena.Classifiers.Typology.instReprNounCategorizationSystem :

Repr NounCategorizationSystem

Equations

Phenomena.Classifiers.Typology.instReprNounCategorizationSystem = { reprPrec := Phenomena.Classifiers.Typology.instReprNounCategorizationSystem.repr }

def Phenomena.Classifiers.Typology.instReprNounCategorizationSystem.repr :

NounCategorizationSystem → ℕ → Std.Format

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def Phenomena.Classifiers.Typology.isNounClassType (t : Core.NounCategorization.ClassifierType) :

@cite{dixon-1982}'s noun-class vs. classifier divide (Table 1.2). Noun classes: small, closed, grammaticalized, agreement. Classifiers: large, open, lexical, no agreement.

Equations

Phenomena.Classifiers.Typology.isNounClassType t = (t == Core.NounCategorization.ClassifierType.nounClass)

Instances For

def Phenomena.Classifiers.Typology.isClassifierType (t : Core.NounCategorization.ClassifierType) :

All non-noun-class types are "classifier" types in the broad sense.

Equations

Phenomena.Classifiers.Typology.isClassifierType t = !Phenomena.Classifiers.Typology.isNounClassType t

Instances For

def Phenomena.Classifiers.Typology.french :

NounCategorizationSystem

French noun categorization: 2-class gender system (masc/fem). Agreement on determiners, adjectives, and past participles. Aikhenvald type: noun class.

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def Phenomena.Classifiers.Typology.italian :

NounCategorizationSystem

Italian noun categorization: 2-class gender system (masc/fem). Like French, [-arg, +pred]. Agreement on determiners (il/la, un/una), adjectives (‑o/‑a), and past participles (‑o/‑a). Richer article allomorphy than French (il/lo/la, i/gli/le).

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def Phenomena.Classifiers.Typology.mandarin :

NounCategorizationSystem

Mandarin noun categorization: numeral classifier system. Large inventory, semantically motivated, no agreement. Aikhenvald type: numeral classifier.

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def Phenomena.Classifiers.Typology.japanese :

NounCategorizationSystem

Japanese noun categorization: numeral classifier system (josūshi). Similar to Mandarin but with native Japanese default counter (つ). Aikhenvald type: numeral classifier.

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theorem Phenomena.Classifiers.Typology.french_is_noun_class :

isNounClassType french.classifierType = true

French is a noun-class system.

theorem Phenomena.Classifiers.Typology.mandarin_is_classifier :

isClassifierType mandarin.classifierType = true

Mandarin is a classifier system (not noun class).

theorem Phenomena.Classifiers.Typology.japanese_is_classifier :

isClassifierType japanese.classifierType = true

Japanese is a classifier system (not noun class).

theorem Phenomena.Classifiers.Typology.agreement_divides_types :

french.hasAgreement = true ∧ mandarin.hasAgreement = false ∧ japanese.hasAgreement = false

French has agreement; Mandarin and Japanese do not (Table 15.1).

theorem Phenomena.Classifiers.Typology.mandarin_inventory_from_fragment :

mandarin.inventorySize = 15

Mandarin inventory is derived from the classifier lexicon.

theorem Phenomena.Classifiers.Typology.japanese_inventory_from_fragment :

japanese.inventorySize = 33

Japanese inventory is derived from the classifier lexicon.

theorem Phenomena.Classifiers.Typology.classifier_systems_have_default :

mandarin.hasUnmarkedDefault = true ∧ japanese.hasUnmarkedDefault = true

Both classifier systems have a default (Mandarin 个, Japanese つ).

def Phenomena.Classifiers.Typology.allSystems :

List NounCategorizationSystem

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theorem Phenomena.Classifiers.Typology.all_obligatory :

(allSystems.all fun (x : NounCategorizationSystem) => x.isObligatory) = true

All four systems are obligatory (not optional).

theorem Phenomena.Classifiers.Typology.all_have_default :

(allSystems.all fun (x : NounCategorizationSystem) => x.hasUnmarkedDefault) = true

All four systems have an unmarked default.

theorem Phenomena.Classifiers.Typology.classifier_no_agreement_nounclass_agreement :

((List.filter (fun (x : NounCategorizationSystem) => isClassifierType x.classifierType) allSystems).all fun (x : NounCategorizationSystem) => !x.hasAgreement) = true ∧ ((List.filter (fun (x : NounCategorizationSystem) => isNounClassType x.classifierType) allSystems).all fun (x : NounCategorizationSystem) => x.hasAgreement) = true

Numeral classifier languages have no agreement; noun class languages have agreement (Aikhenvald Table 15.1).

theorem Phenomena.Classifiers.Typology.classifier_semantic_nounclass_mixed :

mandarin.assignment = Core.NounCategorization.AssignmentPrinciple.semantic ∧ japanese.assignment = Core.NounCategorization.AssignmentPrinciple.semantic ∧ french.assignment = Core.NounCategorization.AssignmentPrinciple.mixed

Numeral classifier systems have purely semantic assignment; noun class systems have mixed assignment (Aikhenvald Table 15.2).

theorem Phenomena.Classifiers.Typology.bare_np_tracks_arg :

Fragments.Mandarin.Nouns.bareNPLicensed = true ∧ Fragments.Japanese.Nouns.bareNPLicensed = true ∧ Fragments.French.Nouns.barePluralLicensed = false

Bare NPs are licensed in [+arg] languages, not in [-arg] languages. This connects Fragment-level bare NP facts to the typological parameter.

theorem Phenomena.Classifiers.Typology.blocking_tracks_mapping :

Fragments.Mandarin.Nouns.mandarinBlocking.iotaBlocked = false ∧ Fragments.Japanese.Nouns.japaneseBlocking.iotaBlocked = false ∧ Fragments.French.Nouns.frenchBlocking.iotaBlocked = true

Blocking principle: [+arg, -pred] languages have no articles to block covert type shifts. [-arg, +pred] languages block ι and ∃.

axiom Phenomena.Classifiers.Typology.noun_class_requires_agreement (sys : NounCategorizationSystem) :

isNounClassType sys.classifierType = true → sys.hasAgreement = true

U1 (Aikhenvald Table 15.1): Noun class / gender systems require agreement. This is definitional — agreement is what makes a noun class system a "class" rather than a "classifier" (@cite{dixon-1982}, Table 1.2).

axiom Phenomena.Classifiers.Typology.numeral_classifier_no_agreement (sys : NounCategorizationSystem) :

sys.classifierType = Core.NounCategorization.ClassifierType.numeralClassifier → sys.hasAgreement = false

U2 (Aikhenvald Table 15.1): Numeral classifier systems lack agreement. Classifiers are independent morphemes, not agreement markers. Witnessed by Mandarin and Japanese in our typology.

axiom Phenomena.Classifiers.Typology.classifier_assignment_semantic (sys : NounCategorizationSystem) :

isClassifierType sys.classifierType = true → sys.assignment = Core.NounCategorization.AssignmentPrinciple.semantic ∨ sys.assignment = Core.NounCategorization.AssignmentPrinciple.mixed

U3 (Aikhenvald §11.1.1): Classifier selection is always at least partly semantic. There are no purely phonological or purely morphological classifier systems (unlike noun class, which can be morphological).

theorem Phenomena.Classifiers.Typology.assignment_difference :

french.assignment = Core.NounCategorization.AssignmentPrinciple.mixed ∧ mandarin.assignment = Core.NounCategorization.AssignmentPrinciple.semantic ∧ japanese.assignment = Core.NounCategorization.AssignmentPrinciple.semantic

U4 (Aikhenvald Table 15.2): Noun class assignment may be mixed (semantic core + morphological overlay), while classifier systems are purely semantic. Witnessed by French (mixed) vs Mandarin (semantic).

axiom Phenomena.Classifiers.Typology.animacy_universal (sys : NounCategorizationSystem) :

(sys.preferredSemantics.any fun (x : Core.NounCategorization.SemanticParameter) => x == Core.NounCategorization.SemanticParameter.animacy) = true ∨ (sys.preferredSemantics.any fun (x : Core.NounCategorization.SemanticParameter) => x == Core.NounCategorization.SemanticParameter.humanness) = true

U5 (Aikhenvald §11.1.1): Animacy (animate vs. inanimate or human vs. non-human) is a semantic parameter found in EVERY type of noun categorization device. This is the universal semantic "core."

theorem Phenomena.Classifiers.Typology.classifiers_prefer_physical :

(mandarin.preferredSemantics.any fun (x : Core.NounCategorization.SemanticParameter) => x == Core.NounCategorization.SemanticParameter.shape) = true ∧ (japanese.preferredSemantics.any fun (x : Core.NounCategorization.SemanticParameter) => x == Core.NounCategorization.SemanticParameter.shape) = true

U6 (Aikhenvald §11.1.1): Physical properties (shape, size) are the preferred semantic parameters for numeral classifiers, while animacy is the core for noun classes.

axiom Phenomena.Classifiers.Typology.classifier_semantic_hierarchy (sys : NounCategorizationSystem) :

isClassifierType sys.classifierType = true → ((sys.preferredSemantics.any fun (x : Core.NounCategorization.SemanticParameter) => x == Core.NounCategorization.SemanticParameter.shape) = true → (sys.preferredSemantics.any fun (x : Core.NounCategorization.SemanticParameter) => x == Core.NounCategorization.SemanticParameter.animacy) = true) ∧ ((sys.preferredSemantics.any fun (x : Core.NounCategorization.SemanticParameter) => x == Core.NounCategorization.SemanticParameter.function) = true → (sys.preferredSemantics.any fun (x : Core.NounCategorization.SemanticParameter) => x == Core.NounCategorization.SemanticParameter.shape) = true)

U7 (Aikhenvald §11.2.3): In numeral classifier systems, animacy outranks shape, which outranks function. Formalized as an implicational universal: if a system uses shape, it also uses animacy; if function, also shape. TODO: prove from attested systems once typology is extended.

theorem Phenomena.Classifiers.Typology.animacy_in_both_classifier_systems :

(mandarin.preferredSemantics.any fun (x : Core.NounCategorization.SemanticParameter) => x == Core.NounCategorization.SemanticParameter.animacy) = true ∧ (japanese.preferredSemantics.any fun (x : Core.NounCategorization.SemanticParameter) => x == Core.NounCategorization.SemanticParameter.animacy) = true

Animacy is attested in both Mandarin and Japanese classifiers. Derived from the classifier lexicons (witnessed by 只 zhī and 匹 hiki).

axiom Phenomena.Classifiers.Typology.noun_class_small_inventory (sys : NounCategorizationSystem) :

isNounClassType sys.classifierType = true → sys.inventorySize ≤ 20

U8 (Aikhenvald Table 15.1): Noun class systems have small inventories (2–20 classes), while classifier systems have large inventories (typically 20–200+).

theorem Phenomena.Classifiers.Typology.french_smaller_than_classifiers :

french.inventorySize < mandarin.inventorySize ∧ french.inventorySize < japanese.inventorySize

U9 (Aikhenvald §1.5): Classifier systems have larger inventories than noun class systems. Open (extendable) vs. closed.

theorem Phenomena.Classifiers.Typology.numeral_classifiers_scope_numeralNP :

(mandarin.scopes.any fun (x : Core.NounCategorization.CategorizationScope) => x == Core.NounCategorization.CategorizationScope.numeralNP) = true ∧ (japanese.scopes.any fun (x : Core.NounCategorization.CategorizationScope) => x == Core.NounCategorization.CategorizationScope.numeralNP) = true

U10 (Aikhenvald Table 15.1): Numeral classifiers operate inside numeral/quantifier NPs.

theorem Phenomena.Classifiers.Typology.noun_class_scope_agreement :

(french.scopes.any fun (x : Core.NounCategorization.CategorizationScope) => x == Core.NounCategorization.CategorizationScope.headModifierNP) = true ∧ (french.scopes.any fun (x : Core.NounCategorization.CategorizationScope) => x == Core.NounCategorization.CategorizationScope.predicateArgument) = true

U11 (Aikhenvald Table 15.1): Noun classes operate inside head-modifier NPs and predicate-argument structures (agreement).

inductive Phenomena.Classifiers.Typology.GrammaticalCategory :

Table 10.17 interaction matrix (simplified): Which grammatical categories interact with which classifier types.

Key patterns:

Noun classes interact with definiteness, number, case, tense/aspect
Numeral classifiers interact with number, definiteness
Verbal classifiers interact with tense/aspect

Instances For

instance Phenomena.Classifiers.Typology.instDecidableEqGrammaticalCategory :

DecidableEq GrammaticalCategory

Equations

Phenomena.Classifiers.Typology.instDecidableEqGrammaticalCategory x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Classifiers.Typology.instReprGrammaticalCategory :

Repr GrammaticalCategory

Equations

Phenomena.Classifiers.Typology.instReprGrammaticalCategory = { reprPrec := Phenomena.Classifiers.Typology.instReprGrammaticalCategory.repr }

def Phenomena.Classifiers.Typology.instReprGrammaticalCategory.repr :

GrammaticalCategory → ℕ → Std.Format

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instance Phenomena.Classifiers.Typology.instBEqGrammaticalCategory :

BEq GrammaticalCategory

Equations

Phenomena.Classifiers.Typology.instBEqGrammaticalCategory = { beq := Phenomena.Classifiers.Typology.instBEqGrammaticalCategory.beq }

def Phenomena.Classifiers.Typology.instBEqGrammaticalCategory.beq :

GrammaticalCategory → GrammaticalCategory → Bool

Equations

Phenomena.Classifiers.Typology.instBEqGrammaticalCategory.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

Instances For

def Phenomena.Classifiers.Typology.interacts :

Core.NounCategorization.ClassifierType → GrammaticalCategory → Bool

Whether a classifier type typically interacts with a grammatical category (Aikhenvald Table 10.17).

Equations

Instances For

theorem Phenomena.Classifiers.Typology.noun_class_more_interactions :

have cats := [GrammaticalCategory.definiteness , GrammaticalCategory.number , GrammaticalCategory.case_, GrammaticalCategory.tenseAspect , GrammaticalCategory.possession ]; have ncInteractions := List.filter (interacts Core.NounCategorization.ClassifierType.nounClass) cats; have clInteractions := List.filter (interacts Core.NounCategorization.ClassifierType.numeralClassifier) cats; ncInteractions.length > clInteractions.length

Noun classes interact with more grammatical categories than numeral classifiers (Table 10.17). This reflects their deeper grammaticalization.

theorem Phenomena.Classifiers.Typology.mandarin_no_blocking :

Fragments.Mandarin.Nouns.mandarinBlocking.iotaBlocked = false ∧ Fragments.Mandarin.Nouns.mandarinBlocking.existsBlocked = false ∧ Fragments.Mandarin.Nouns.mandarinBlocking.downBlocked = false

No type-shift blocking in Mandarin.

theorem Phenomena.Classifiers.Typology.japanese_no_blocking :

Fragments.Japanese.Nouns.japaneseBlocking.iotaBlocked = false ∧ Fragments.Japanese.Nouns.japaneseBlocking.existsBlocked = false ∧ Fragments.Japanese.Nouns.japaneseBlocking.downBlocked = false

No type-shift blocking in Japanese.

theorem Phenomena.Classifiers.Typology.default_classifiers_exist :

Fragments.Mandarin.Classifiers.defaultClassifier.isDefault = true ∧ Fragments.Japanese.Classifiers.defaultClassifier.isDefault = true

U12: Every numeral classifier system has a semantically bleached default classifier that can substitute for any specific classifier (Aikhenvald §4.2). The default is the "elsewhere" case.

Witnessed by: Mandarin 个 gè, Japanese つ tsu.

theorem Phenomena.Classifiers.Typology.specific_classifiers_motivated :

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

Non-default classifiers always carry at least one semantic parameter. The default is the only semantically empty classifier.

inductive Phenomena.Classifiers.Typology.ClassifierStatus :

Whether a language uses numeral classifiers (WALS Ch 55).

Numeral classifiers are morphemes that co-occur with a numeral when it modifies a noun (e.g., Mandarin san ge ren 'three CL person'). The key distinction is between obligatory classifiers (required whenever a numeral modifies a noun) and optional classifiers (available but not required).

absent : ClassifierStatus
optional : ClassifierStatus
obligatory : ClassifierStatus

Instances For

instance Phenomena.Classifiers.Typology.instDecidableEqClassifierStatus :

DecidableEq ClassifierStatus

Equations

Phenomena.Classifiers.Typology.instDecidableEqClassifierStatus x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Classifiers.Typology.instBEqClassifierStatus.beq :

ClassifierStatus → ClassifierStatus → Bool

Equations

Phenomena.Classifiers.Typology.instBEqClassifierStatus.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

Instances For

instance Phenomena.Classifiers.Typology.instBEqClassifierStatus :

BEq ClassifierStatus

Equations

Phenomena.Classifiers.Typology.instBEqClassifierStatus = { beq := Phenomena.Classifiers.Typology.instBEqClassifierStatus.beq }

def Phenomena.Classifiers.Typology.instReprClassifierStatus.repr :

ClassifierStatus → ℕ → Std.Format

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Instances For

instance Phenomena.Classifiers.Typology.instReprClassifierStatus :

Repr ClassifierStatus

Equations

Phenomena.Classifiers.Typology.instReprClassifierStatus = { reprPrec := Phenomena.Classifiers.Typology.instReprClassifierStatus.repr }

structure Phenomena.Classifiers.Typology.ClassifierDistribution :

WALS Chapter 55 distribution: language counts per classifier status. Total: 400 languages.

absent : ℕ
optional : ℕ
obligatory : ℕ

Instances For

def Phenomena.Classifiers.Typology.instReprClassifierDistribution.repr :

ClassifierDistribution → ℕ → Std.Format

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instance Phenomena.Classifiers.Typology.instReprClassifierDistribution :

Repr ClassifierDistribution

Equations

Phenomena.Classifiers.Typology.instReprClassifierDistribution = { reprPrec := Phenomena.Classifiers.Typology.instReprClassifierDistribution.repr }

def Phenomena.Classifiers.Typology.ClassifierDistribution.total (d : ClassifierDistribution) :

Equations

d.total = d.absent + d.optional + d.obligatory

Instances For

def Phenomena.Classifiers.Typology.ch55Distribution :

ClassifierDistribution

Actual WALS Ch 55 counts.

Equations

Phenomena.Classifiers.Typology.ch55Distribution = { absent := 260, optional := 62, obligatory := 78 }

Instances For

def Phenomena.Classifiers.Typology.fromWALS55A :

Core.WALS.F55A.NumeralClassifiers → ClassifierStatus

Convert WALS 55A numeral classifier values to our ClassifierStatus type. The mapping is one-to-one: absent, optional, obligatory.

Equations

Instances For

theorem Phenomena.Classifiers.Typology.no_classifiers_is_majority :

ch55Distribution.absent > ch55Distribution.optional + ch55Distribution.obligatory

Languages without numeral classifiers are the global majority (WALS Ch 55). 260 out of 400 sampled languages lack classifiers entirely.

theorem Phenomena.Classifiers.Typology.no_classifiers_over_half :

ch55Distribution.absent * 2 > ch55Distribution.total

Languages without classifiers constitute over half the sample.

theorem Phenomena.Classifiers.Typology.obligatory_more_common_than_optional :

ch55Distribution.obligatory > ch55Distribution.optional

Obligatory classifiers are more common than optional ones globally. This is somewhat counterintuitive — it suggests that once a language develops classifiers, they tend to become grammaticalized as obligatory.