Noun Categorization Typology

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

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

Defines the vocabulary types for describing noun categorization systems: classifier types, semantic parameters, structural properties, and a common ClassifierEntry type for individual classifier lexical entries.

Per-language system descriptions (NounCategorizationSystem) and the Dixon noun-class vs. classifier divide live in Theories.Typology.NounCategorization — they represent a specific typological framework, not framework-agnostic infrastructure.

Organization

• §1 Classifier types: The 9-type typology (Table 15.1)
• §2 Semantic parameters: What classifiers encode (§11.1.1)
• §3 Structural properties: Assignment, realization, scope
• §4 ClassifierEntry: Per-classifier lexical entry with semantic typing

inductive Core.NounCategorization.ClassifierType : Type

The 9 focal classifier types on the noun-categorization continuum.

Aikhenvald (2000 §1.5, Table 15.1) establishes these as "focal points" distinguished by morphosyntactic locus, scope, and grammatical function. Real systems are gradient — a language's system may sit between types.

• nounClass : ClassifierType

  Noun class / gender: closed agreement system, realized outside the noun on modifiers (head-modifier NP) or predicate (pred-arg agreement). Small inventory (2–20). Examples: Bantu, Indo-European gender. (Ch 2)

• nounClassifier : ClassifierType

  Noun classifier: independent of other NP elements, characterizes the noun itself. Free forms or affixes on the noun. (Ch 3)

• numeralClassifier : ClassifierType

  Numeral classifier: appears in numeral/quantifier NPs, required for enumeration. Free forms or affixes on the numeral. (Ch 4)

• relationalClassifier : ClassifierType

  Relational classifier: in possessive NPs, characterizes the possessive relation (how the noun can be possessed/handled). (Ch 5)

• possessedClassifier : ClassifierType

  Possessed classifier: in possessive NPs, characterizes the possessed noun in terms of its inherent properties. (Ch 5)

• possessorClassifier : ClassifierType

  Possessor classifier: in possessive NPs, characterizes the possessor. Very rare. (Ch 5)

• verbalClassifier : ClassifierType

  Verbal classifier: marks agreement on the verb with an S or O argument. Incorporated classifiers, affixes, or suppletive verb stems. (Ch 6)

• locativeClassifier : ClassifierType

  Locative classifier: in adpositional NPs, marks agreement with the head noun in locative expressions. (Ch 7)

• deicticClassifier : ClassifierType

  Deictic classifier: appears on deictics, articles, demonstratives. Marks spatial location and/or determination. (Ch 7)

instance Core.NounCategorization.instDecidableEqClassifierType : DecidableEq ClassifierType

Equations

• Core.NounCategorization.instDecidableEqClassifierType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Core.NounCategorization.instReprClassifierType : Repr ClassifierType

Equations

• Core.NounCategorization.instReprClassifierType = { reprPrec := Core.NounCategorization.instReprClassifierType.repr }

def Core.NounCategorization.instReprClassifierType.repr : ClassifierType → Nat → Std.Format

Equations

• One or more equations did not get rendered due to their size.

instance Core.NounCategorization.instBEqClassifierType : BEq ClassifierType

Equations

• Core.NounCategorization.instBEqClassifierType = { beq := Core.NounCategorization.instBEqClassifierType.beq }

def Core.NounCategorization.instBEqClassifierType.beq : ClassifierType → ClassifierType → Bool

Equations

• Core.NounCategorization.instBEqClassifierType.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

inductive Core.NounCategorization.SemanticParameter : Type

Universal semantic parameters employed in noun categorization.

Aikhenvald (2000 §11.1.1) identifies three large classes: animacy, physical properties, and function. These parameters are found across ALL types of noun categorization device, though different types show different preferences (Table 11.13).

• animacy : SemanticParameter
• humanness : SemanticParameter
• sex : SemanticParameter
• shape : SemanticParameter
• size : SemanticParameter
• consistency : SemanticParameter
• material : SemanticParameter
• boundedness : SemanticParameter
• function : SemanticParameter
• arrangement : SemanticParameter
• quanta : SemanticParameter
• socialStatus : SemanticParameter
• colour : SemanticParameter

instance Core.NounCategorization.instDecidableEqSemanticParameter : DecidableEq SemanticParameter

Equations

• Core.NounCategorization.instDecidableEqSemanticParameter x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Core.NounCategorization.instReprSemanticParameter.repr : SemanticParameter → Nat → Std.Format

Equations

• One or more equations did not get rendered due to their size.

instance Core.NounCategorization.instReprSemanticParameter : Repr SemanticParameter

Equations

• Core.NounCategorization.instReprSemanticParameter = { reprPrec := Core.NounCategorization.instReprSemanticParameter.repr }

def Core.NounCategorization.instBEqSemanticParameter.beq : SemanticParameter → SemanticParameter → Bool

Equations

• Core.NounCategorization.instBEqSemanticParameter.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Core.NounCategorization.instBEqSemanticParameter : BEq SemanticParameter

Equations

• Core.NounCategorization.instBEqSemanticParameter = { beq := Core.NounCategorization.instBEqSemanticParameter.beq }

inductive Core.NounCategorization.ShapeDimension : Type

Dimensionality sub-classification for shape-based classifiers.

@cite{downing-1996} Ch. 5 and @cite{allan-1977} show that shape-based classifiers decompose along a dimensionality axis:

• 1D: long, slender, elongated (e.g., Japanese 本 hon, Mandarin 条 tiáo)
• 2D: flat, thin, planar (e.g., Japanese 枚 mai, Mandarin 张 zhāng)
• 3D: round, compact, globular (e.g., Japanese 個 ko)

• oneD : ShapeDimension
• twoD : ShapeDimension
• threeD : ShapeDimension

instance Core.NounCategorization.instDecidableEqShapeDimension : DecidableEq ShapeDimension

Equations

• Core.NounCategorization.instDecidableEqShapeDimension x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Core.NounCategorization.instReprShapeDimension.repr : ShapeDimension → Nat → Std.Format

Equations

• One or more equations did not get rendered due to their size.

instance Core.NounCategorization.instReprShapeDimension : Repr ShapeDimension

Equations

• Core.NounCategorization.instReprShapeDimension = { reprPrec := Core.NounCategorization.instReprShapeDimension.repr }

def Core.NounCategorization.instBEqShapeDimension.beq : ShapeDimension → ShapeDimension → Bool

Equations

• Core.NounCategorization.instBEqShapeDimension.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Core.NounCategorization.instBEqShapeDimension : BEq ShapeDimension

Equations

• Core.NounCategorization.instBEqShapeDimension = { beq := Core.NounCategorization.instBEqShapeDimension.beq }

inductive Core.NounCategorization.CategorizationScope : Type

Morphosyntactic scope of a classifier type (Table 15.1, column 2).

• headModifierNP : CategorizationScope
• predicateArgument : CategorizationScope
• noun : CategorizationScope
• numeralNP : CategorizationScope
• possessiveNP : CategorizationScope
• clause : CategorizationScope
• adpositionalNP : CategorizationScope
• attributiveNP : CategorizationScope

instance Core.NounCategorization.instDecidableEqCategorizationScope : DecidableEq CategorizationScope

Equations

• Core.NounCategorization.instDecidableEqCategorizationScope x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Core.NounCategorization.instReprCategorizationScope : Repr CategorizationScope

Equations

• Core.NounCategorization.instReprCategorizationScope = { reprPrec := Core.NounCategorization.instReprCategorizationScope.repr }

def Core.NounCategorization.instReprCategorizationScope.repr : CategorizationScope → Nat → Std.Format

Equations

• One or more equations did not get rendered due to their size.

instance Core.NounCategorization.instBEqCategorizationScope : BEq CategorizationScope

Equations

• Core.NounCategorization.instBEqCategorizationScope = { beq := Core.NounCategorization.instBEqCategorizationScope.beq }

def Core.NounCategorization.instBEqCategorizationScope.beq : CategorizationScope → CategorizationScope → Bool

Equations

• Core.NounCategorization.instBEqCategorizationScope.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

inductive Core.NounCategorization.AssignmentPrinciple : Type

Principles governing noun-to-class/classifier assignment (§2.3).

• semantic : AssignmentPrinciple

  Purely semantic: class determined by referent meaning

• morphological : AssignmentPrinciple

  Morphological: class determined by derivational affix, declension, etc.

• phonological : AssignmentPrinciple

  Phonological: class determined by initial segment, final vowel, etc.

• mixed : AssignmentPrinciple

  Mixed: semantic core + morphological/phonological overlay

instance Core.NounCategorization.instDecidableEqAssignmentPrinciple : DecidableEq AssignmentPrinciple

Equations

• Core.NounCategorization.instDecidableEqAssignmentPrinciple x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Core.NounCategorization.instReprAssignmentPrinciple.repr : AssignmentPrinciple → Nat → Std.Format

Equations

• One or more equations did not get rendered due to their size.

instance Core.NounCategorization.instReprAssignmentPrinciple : Repr AssignmentPrinciple

Equations

• Core.NounCategorization.instReprAssignmentPrinciple = { reprPrec := Core.NounCategorization.instReprAssignmentPrinciple.repr }

instance Core.NounCategorization.instBEqAssignmentPrinciple : BEq AssignmentPrinciple

Equations

• Core.NounCategorization.instBEqAssignmentPrinciple = { beq := Core.NounCategorization.instBEqAssignmentPrinciple.beq }

def Core.NounCategorization.instBEqAssignmentPrinciple.beq : AssignmentPrinciple → AssignmentPrinciple → Bool

Equations

• Core.NounCategorization.instBEqAssignmentPrinciple.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

inductive Core.NounCategorization.SurfaceRealization : Type

Surface realization of a classifier morpheme (Table 15.3).

• prefix : SurfaceRealization
• suffix : SurfaceRealization
• clitic : SurfaceRealization
• freeForm : SurfaceRealization
• suppletion : SurfaceRealization
• stress : SurfaceRealization
• reduplication : SurfaceRealization
• nounIncorporation : SurfaceRealization
• repeater : SurfaceRealization

instance Core.NounCategorization.instDecidableEqSurfaceRealization : DecidableEq SurfaceRealization

Equations

• Core.NounCategorization.instDecidableEqSurfaceRealization x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Core.NounCategorization.instReprSurfaceRealization : Repr SurfaceRealization

Equations

• Core.NounCategorization.instReprSurfaceRealization = { reprPrec := Core.NounCategorization.instReprSurfaceRealization.repr }

def Core.NounCategorization.instReprSurfaceRealization.repr : SurfaceRealization → Nat → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def Core.NounCategorization.instBEqSurfaceRealization.beq : SurfaceRealization → SurfaceRealization → Bool

Equations

• Core.NounCategorization.instBEqSurfaceRealization.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Core.NounCategorization.instBEqSurfaceRealization : BEq SurfaceRealization

Equations

• Core.NounCategorization.instBEqSurfaceRealization = { beq := Core.NounCategorization.instBEqSurfaceRealization.beq }

structure Core.NounCategorization.ClassifierEntry : Type

A classifier lexical entry with semantic typing.

Replaces the unstructured Option String representation. Each classifier carries its form, a gloss, and the semantic parameters that motivate its selection — making it possible to verify Aikhenvald's claims about which parameters different classifier types encode.

• form : String

  Surface form (e.g. "只", "匹", "本")

• gloss : String

  Gloss (e.g. "small.animal", "flat.bound.object")

• semantics : List SemanticParameter

  Semantic parameters motivating selection of this classifier

• isDefault : Bool

  Is this the "general" or "default" classifier? (个 in Mandarin, つ in Japanese)

• isMensural : Bool

  Sortal (inherent properties) vs. mensural (configuration/measure)

• shapeDimension : Option ShapeDimension

  Shape dimensionality sub-classification (@cite{downing-1996} Ch. 5). Only meaningful when semantics includes .shape.

instance Core.NounCategorization.instReprClassifierEntry : Repr ClassifierEntry

Equations

• Core.NounCategorization.instReprClassifierEntry = { reprPrec := Core.NounCategorization.instReprClassifierEntry.repr }

def Core.NounCategorization.instReprClassifierEntry.repr : ClassifierEntry → Nat → Std.Format

Equations

• One or more equations did not get rendered due to their size.

instance Core.NounCategorization.instBEqClassifierEntry : BEq ClassifierEntry

Equations

• Core.NounCategorization.instBEqClassifierEntry = { beq := Core.NounCategorization.instBEqClassifierEntry.beq }

def Core.NounCategorization.instBEqClassifierEntry.beq : ClassifierEntry → ClassifierEntry → Bool

Equations

• One or more equations did not get rendered due to their size.
• Core.NounCategorization.instBEqClassifierEntry.beq x✝¹ x✝ = false

def Core.NounCategorization.ClassifierEntry.encodes (c : ClassifierEntry) (p : SemanticParameter) : Bool

Whether this classifier encodes a given semantic parameter.

Equations

• c.encodes p = c.semantics.any fun (x : Core.NounCategorization.SemanticParameter) => x == p

def Core.NounCategorization.ClassifierEntry.toString (c : ClassifierEntry) : String

The form string of a classifier entry (for backward compatibility).

Equations

• c.toString = c.form

instance Core.NounCategorization.instToStringClassifierEntry : ToString ClassifierEntry

Equations

• Core.NounCategorization.instToStringClassifierEntry = { toString := Core.NounCategorization.ClassifierEntry.toString }

def Core.NounCategorization.collectSemantics (cls : List ClassifierEntry) : List SemanticParameter

Collect all distinct semantic parameters attested across a classifier inventory. Used to derive preferredSemantics from fragment data rather than hand-listing.

Equations

• One or more equations did not get rendered due to their size.