Aikhenvald (2000): Classifiers — A Typology of Noun Categorization Devices

[Aik00] [Gre72] [Dix82]

Aikhenvald, Alexandra Y. (2000). Classifiers: A Typology of Noun Categorization Devices. Oxford Studies in Typology and Linguistic Theory. Oxford University Press.

Cross-linguistic typology of noun categorization systems following Aikhenvald's 7-property schema (A–G, §1.5). The schema (System) lives in Typology/ClassifierSystem.lean; per-language data in Fragments/{Lang}/ClassifierSystem.lean.

This file aggregates the 7 currently-formalized systems (French/Italian/Mandarin/Japanese/Xhosa/Shona/Swahili) and verifies typological properties from [Aik00] (Tables 10.17, 15.1, 15.2) and [Gre72]'s classifier-number complementarity over that sample. None of the theorems below are universals over the abstract System type — they are sample-restricted empirical claims; adding a counterexample language to the sample is the right way to falsify them.

Western Armenian is intentionally excluded from the main allSystems sample: it is non-obligatory with no unmarked default, and the Aikhenvald-style sample-restricted findings (sample_all_obligatory, sample_all_have_default) are about the obligatory-classifier subspace. Armenian appears separately in optionalClassifierSystems.

Chierchia-anchored claims about Mandarin/Japanese type-shift blocking are in Studies/NMP.lean (chronologically older paper, separate study file). The Greenberg classifier-number complementarity claim appears here (Aikhenvald §15 cites Greenberg) and is refined in Studies/LittleMoroneyRoyer2022.lean (CLF-for-N vs CLF-for-NUM split).

@[reducible, inline]

abbrev Aikhenvald2000.french : NounCategorization.System

Equations

• Aikhenvald2000.french = French.classifierSystem

@[reducible, inline]

abbrev Aikhenvald2000.italian : NounCategorization.System

Equations

• Aikhenvald2000.italian = Italian.classifierSystem

@[reducible, inline]

abbrev Aikhenvald2000.mandarin : NounCategorization.System

Equations

• Aikhenvald2000.mandarin = Mandarin.classifierSystem

@[reducible, inline]

abbrev Aikhenvald2000.japanese : NounCategorization.System

Equations

• Aikhenvald2000.japanese = Japanese.classifierSystem

@[reducible, inline]

abbrev Aikhenvald2000.xhosa : NounCategorization.System

Equations

• Aikhenvald2000.xhosa = Xhosa.classifierSystem

@[reducible, inline]

abbrev Aikhenvald2000.shona : NounCategorization.System

Equations

• Aikhenvald2000.shona = Shona.classifierSystem

@[reducible, inline]

abbrev Aikhenvald2000.swahili : NounCategorization.System

Equations

• Aikhenvald2000.swahili = Swahili.classifierSystem

@[reducible, inline]

abbrev Aikhenvald2000.westernArmenian : NounCategorization.System

Equations

• Aikhenvald2000.westernArmenian = Armenian.classifierSystem

def Aikhenvald2000.allSystems : List NounCategorization.System

The seven obligatory-classifier systems formalized so far.

Equations

• Aikhenvald2000.allSystems = [Aikhenvald2000.french, Aikhenvald2000.italian, Aikhenvald2000.mandarin, Aikhenvald2000.japanese, Aikhenvald2000.xhosa, Aikhenvald2000.shona, Aikhenvald2000.swahili]

theorem Aikhenvald2000.sample_all_obligatory (s : NounCategorization.System) : s ∈ allSystems → s.IsObligatory

Languages whose Fragment is in allSystems are all obligatory.

theorem Aikhenvald2000.sample_all_have_default (s : NounCategorization.System) : s ∈ allSystems → s.HasUnmarkedDefault

Languages in the sample all have an unmarked default classifier/class.

theorem Aikhenvald2000.french_is_noun_class : NounCategorization.System.isNounClassType French.classifierSystem.classifierType = true

theorem Aikhenvald2000.mandarin_is_classifier : NounCategorization.System.isClassifierType Mandarin.classifierSystem.classifierType = true

theorem Aikhenvald2000.japanese_is_classifier : NounCategorization.System.isClassifierType Japanese.classifierSystem.classifierType = true

theorem Aikhenvald2000.mandarin_inventory_from_fragment : Mandarin.classifierSystem.inventorySize = 15

theorem Aikhenvald2000.japanese_inventory_from_fragment : Japanese.classifierSystem.inventorySize = 36

theorem Aikhenvald2000.classifier_systems_have_default : Mandarin.classifierSystem.HasUnmarkedDefault ∧ Japanese.classifierSystem.HasUnmarkedDefault

theorem Aikhenvald2000.sample_classifier_no_agreement_nounclass_agreement : (∀ s ∈ allSystems, NounCategorization.System.isClassifierType s.classifierType = true → ¬s.HasAgreement) ∧ ∀ s ∈ allSystems, NounCategorization.System.isNounClassType s.classifierType = true → s.HasAgreement

[Aik00] Table 15.1, sample-restricted: classifier-type systems lack agreement; noun-class systems have agreement.

theorem Aikhenvald2000.fr_mandarin_jp_agreement_split : French.classifierSystem.HasAgreement ∧ ¬Mandarin.classifierSystem.HasAgreement ∧ ¬Japanese.classifierSystem.HasAgreement

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

theorem Aikhenvald2000.fr_mandarin_jp_assignment_split : Mandarin.classifierSystem.assignment = NounCategorization.AssignmentPrinciple.semantic ∧ Japanese.classifierSystem.assignment = NounCategorization.AssignmentPrinciple.semantic ∧ French.classifierSystem.assignment = NounCategorization.AssignmentPrinciple.mixed

Numeral classifier systems have purely semantic assignment; the noun-class system has mixed assignment ([Aik00] Table 15.2).

theorem Aikhenvald2000.mandarin_japanese_prefer_shape : (Mandarin.classifierSystem.preferredSemantics.any fun (x : NounCategorization.SemanticParameter) => x == NounCategorization.SemanticParameter.shape) = true ∧ (Japanese.classifierSystem.preferredSemantics.any fun (x : NounCategorization.SemanticParameter) => x == NounCategorization.SemanticParameter.shape) = true

East Asian classifier systems prefer physical properties (shape) — partial witness for Aikhenvald's cross-linguistic generalization.

theorem Aikhenvald2000.mandarin_japanese_have_animacy : (Mandarin.classifierSystem.preferredSemantics.any fun (x : NounCategorization.SemanticParameter) => x == NounCategorization.SemanticParameter.animacy) = true ∧ (Japanese.classifierSystem.preferredSemantics.any fun (x : NounCategorization.SemanticParameter) => x == NounCategorization.SemanticParameter.animacy) = true

Animacy is attested in both Mandarin and Japanese classifiers.

theorem Aikhenvald2000.fr_inventory_smaller_than_clf_inventories : French.classifierSystem.inventorySize < Mandarin.classifierSystem.inventorySize ∧ French.classifierSystem.inventorySize < Japanese.classifierSystem.inventorySize

Mandarin/Japanese classifier inventories exceed French's noun-class inventory. [Aik00] Table 15.1 generalization.

theorem Aikhenvald2000.mandarin_japanese_scope_numeralNP : (Mandarin.classifierSystem.scopes.any fun (x : NounCategorization.CategorizationScope) => x == NounCategorization.CategorizationScope.numeralNP) = true ∧ (Japanese.classifierSystem.scopes.any fun (x : NounCategorization.CategorizationScope) => x == NounCategorization.CategorizationScope.numeralNP) = true

Numeral classifiers operate inside numeral/quantifier NPs.

theorem Aikhenvald2000.french_scope_agreement : (French.classifierSystem.scopes.any fun (x : NounCategorization.CategorizationScope) => x == NounCategorization.CategorizationScope.headModifierNP) = true ∧ (French.classifierSystem.scopes.any fun (x : NounCategorization.CategorizationScope) => x == NounCategorization.CategorizationScope.predicateArgument) = true

French (the noun-class member of the sample) operates in head-modifier and predicate-argument scopes.

theorem Aikhenvald2000.noun_class_more_interactions : have cats := [NounCategorization.GrammaticalCategory.definiteness, NounCategorization.GrammaticalCategory.number, NounCategorization.GrammaticalCategory.case_, NounCategorization.GrammaticalCategory.tenseAspect, NounCategorization.GrammaticalCategory.possession]; have ncInteractions := List.filter (NounCategorization.interacts NounCategorization.ClassifierType.nounClass) cats; have clInteractions := List.filter (NounCategorization.interacts NounCategorization.ClassifierType.numeralClassifier) cats; ncInteractions.length > clInteractions.length

[Aik00] Table 10.17: noun classes interact with more grammatical categories than numeral classifiers. Verified against the framework-agnostic interacts table in NounCategorization.NounCategorization.

theorem Aikhenvald2000.sample_greenberg_complementarity : (∀ s ∈ allSystems, NounCategorization.System.isClassifierType s.classifierType = true → ¬s.HasObligatoryNumber) ∧ ∀ s ∈ allSystems, NounCategorization.System.isNounClassType s.classifierType = true → s.HasObligatoryNumber

[Gre72]: numeral classifiers and obligatory number marking are in complementary distribution. Holds in the sample. Aikhenvald §15 endorses Greenberg's generalization; [LMR22] §3.4 refines it (CLF-for-N languages obey it, CLF-for-NUM languages — Ch'ol, Mi'gmaq — falsify it).

theorem Aikhenvald2000.mandarin_japanese_have_default_clf : Mandarin.Classifiers.defaultClassifier.isDefault = true ∧ Japanese.Classifier.defaultClassifier? = some Japanese.Classifier.tsu

Mandarin and Japanese both have a semantically bleached default classifier (Mandarin 个 ge, Japanese つ tsu).

theorem Aikhenvald2000.specific_classifiers_motivated : ((List.filter (fun (x : NounCategorization.ClassifierEntry) => !x.isDefault) Mandarin.Classifiers.allClassifiers).all fun (x : NounCategorization.ClassifierEntry) => decide (x.semantics.length > 0)) = true ∧ ∀ (c : Japanese.Classifier), ¬c.IsDefault → ¬c.IsMensural → c.encodes ≠ []

Non-default classifiers always carry at least one semantic parameter.

theorem Aikhenvald2000.xhosa_is_noun_class : NounCategorization.System.isNounClassType Xhosa.classifierSystem.classifierType = true

theorem Aikhenvald2000.shona_is_noun_class : NounCategorization.System.isNounClassType Shona.classifierSystem.classifierType = true

theorem Aikhenvald2000.swahili_is_noun_class : NounCategorization.System.isNounClassType Swahili.classifierSystem.classifierType = true

theorem Aikhenvald2000.xhosa_has_agreement : Xhosa.classifierSystem.HasAgreement

theorem Aikhenvald2000.sample_bantu_inventory_within_aikhenvald_range : Xhosa.classifierSystem.inventorySize ≤ 20 ∧ Shona.classifierSystem.inventorySize ≤ 20 ∧ Swahili.classifierSystem.inventorySize ≤ 20

The three sampled Bantu languages have inventories in the [Aik00] Table 15.1 noun-class range (≤ 20).

theorem Aikhenvald2000.bantu_have_prefix_realization : (Xhosa.classifierSystem.realizations.any fun (x : NounCategorization.SurfaceRealization) => x == NounCategorization.SurfaceRealization.prefix) = true ∧ (Shona.classifierSystem.realizations.any fun (x : NounCategorization.SurfaceRealization) => x == NounCategorization.SurfaceRealization.prefix) = true ∧ (Swahili.classifierSystem.realizations.any fun (x : NounCategorization.SurfaceRealization) => x == NounCategorization.SurfaceRealization.prefix) = true

def Aikhenvald2000.optionalClassifierSystems : List NounCategorization.System

Languages with non-obligatory classifier systems (per WALS Ch 55 optional). Western Armenian is the worked example ([BK14]). Kept separate from allSystems because the sample-restricted findings above are over obligatory systems — Armenian is precisely the kind of language those generalizations don't cover.

Equations

• Aikhenvald2000.optionalClassifierSystems = [Armenian.classifierSystem]

theorem Aikhenvald2000.westernArmenian_not_obligatory : ¬Armenian.classifierSystem.IsObligatory ∧ ¬Armenian.classifierSystem.HasUnmarkedDefault