Noun Categorization × @cite{chierchia-1998} Nominal Mapping Parameter @cite{chierchia-1998}

Connects the cross-linguistic noun categorization typology in Aikhenvald2000 to the Nominal Mapping Parameter from Theories.Semantics.Kinds.NMP.

Predictions verified

• argOnly_implies_numeral_classifier: [+arg, -pred] → numeral classifiers
• predOnly_implies_noun_class: [-arg, +pred] → noun class
• mandarin_chierchia_consistent, japanese_chierchia_consistent, french_chierchia_consistent, italian_chierchia_consistent: Actual classifier types match predictions

Classifier Strategy Connection (@cite{little-moroney-royer-2022})

@cite{chierchia-1998}'s theory is a CLF-for-N theory: the classifier atomizes the noun denotation (which denotes kinds in [+arg, -pred] languages). This predicts that classifiers in [+arg, -pred] languages should appear beyond numerals — with demonstratives, quantifiers, and relative clauses. Mandarin and Japanese confirm this (那本书 'that CLF book', Mandarin).

The NMP-to-classifier bridge is accurate at Aikhenvald's morphosyntactic level but does not distinguish between CLF-for-NUM and CLF-for-N within the numeral classifier type. Both Ch'ol (CLF-for-NUM) and Shan (CLF-for-N) are numeralClassifier in Aikhenvald's typology. The ClassifierStrategy field on NounCategorizationSystem captures this finer distinction.

Known gaps

• English [+arg, +pred] prediction (no system) not yet connected to data

def NMP.nominalMappingToClassifierType : Semantics.Kinds.NMP.NominalMapping → Option Typology.ClassifierType

Map NominalMapping to the expected classifier type. [+arg, -pred] languages have numeral classifiers. [-arg, +pred] languages have noun class/gender. [+arg, +pred] languages (English/Germanic) lack a productive system.

Equations

• NMP.nominalMappingToClassifierType Semantics.Kinds.NMP.NominalMapping.argOnly = some Typology.ClassifierType.numeralClassifier
• NMP.nominalMappingToClassifierType Semantics.Kinds.NMP.NominalMapping.predOnly = some Typology.ClassifierType.nounClass
• NMP.nominalMappingToClassifierType Semantics.Kinds.NMP.NominalMapping.argAndPred = none

theorem NMP.french_mapping : Fragments.French.Nouns.frenchMapping = Semantics.Kinds.NMP.NominalMapping.predOnly

French mapping is [-arg, +pred].

theorem NMP.mandarin_mapping : Fragments.Mandarin.Nouns.mandarinMapping = Semantics.Kinds.NMP.NominalMapping.argOnly

Mandarin mapping is [+arg, -pred].

theorem NMP.japanese_mapping : Fragments.Japanese.Nouns.japaneseMapping = Semantics.Kinds.NMP.NominalMapping.argOnly

Japanese mapping is [+arg, -pred].

theorem NMP.italian_mapping : Fragments.Italian.Nouns.italianMapping = Semantics.Kinds.NMP.NominalMapping.predOnly

Italian mapping is [-arg, +pred]. Italian is the star witness for predOnly: bare arguments are restricted and D must be projected for argumenthood.

theorem NMP.argOnly_implies_numeral_classifier : nominalMappingToClassifierType Semantics.Kinds.NMP.NominalMapping.argOnly = some Typology.ClassifierType.numeralClassifier

The Chierchia-Aikhenvald bridge: [+arg, -pred] languages are numeral classifier languages.

theorem NMP.predOnly_implies_noun_class : nominalMappingToClassifierType Semantics.Kinds.NMP.NominalMapping.predOnly = some Typology.ClassifierType.nounClass

[-arg, +pred] languages are noun class languages.

theorem NMP.argAndPred_no_system : nominalMappingToClassifierType Semantics.Kinds.NMP.NominalMapping.argAndPred = none

[+arg, +pred] languages (English/Germanic) lack a productive noun categorization system in Aikhenvald's sense.

theorem NMP.mandarin_chierchia_consistent : some Aikhenvald2000.mandarin.classifierType = nominalMappingToClassifierType Fragments.Mandarin.Nouns.mandarinMapping

Mandarin's actual classifier type matches the Chierchia prediction.

theorem NMP.japanese_chierchia_consistent : some Aikhenvald2000.japanese.classifierType = nominalMappingToClassifierType Fragments.Japanese.Nouns.japaneseMapping

Japanese's actual classifier type matches the Chierchia prediction.

theorem NMP.french_chierchia_consistent : some Aikhenvald2000.french.classifierType = nominalMappingToClassifierType Fragments.French.Nouns.frenchMapping

French's actual classifier type matches the Chierchia prediction.

theorem NMP.italian_chierchia_consistent : some Aikhenvald2000.italian.classifierType = nominalMappingToClassifierType Fragments.Italian.Nouns.italianMapping

Italian's actual classifier type matches the Chierchia prediction.

theorem NMP.french_italian_same_mapping : Fragments.French.Nouns.frenchMapping = Fragments.Italian.Nouns.italianMapping

French and Italian agree on Chierchia mapping: both are predOnly.

§2: @cite{chierchia-1998}'s per-language strategy assignments

@cite{chierchia-1998}'s theory is a CLF-for-N theory: the classifier atomizes the noun denotation. The NMP determines that nouns denote kinds (need individuation), so classifiers serve the noun (atomization), not the numeral. This commits Chierchia's framework to a .forNoun strategy for every [+arg, -pred] language with classifiers.

Per-language assignments live here (in this study file) rather than on NounCategorizationSystem, where they would silently endorse Chierchia's framework over alternatives like @cite{sudo-2016}'s .sudoBlocking.

def NMP.japaneseStrategy : Typology.ClassifierStrategy

Chierchia's strategy assignment for Japanese: CLF atomizes a kind-denoting noun.

Equations

• NMP.japaneseStrategy = Typology.ClassifierStrategy.forNoun

def NMP.mandarinStrategy : Typology.ClassifierStrategy

Chierchia's strategy assignment for Mandarin: CLF atomizes a kind-denoting noun.

Equations

• NMP.mandarinStrategy = Typology.ClassifierStrategy.forNoun

theorem NMP.chierchia_assignments_uniform : japaneseStrategy = Typology.ClassifierStrategy.forNoun ∧ mandarinStrategy = Typology.ClassifierStrategy.forNoun

Chierchia's framework assigns the CLF-for-N strategy to all [+arg, -pred] classifier languages.

Empirical predictions of @cite{chierchia-1998}'s Nominal Mapping Parameter, verified against Fragment data.

theorem NMP.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 (Chierchia's central typological prediction).

theorem NMP.blocking_tracks_mapping : Fragments.Mandarin.Nouns.mandarinBlocking.iotaBlocked = false ∧ Fragments.Japanese.Nouns.japaneseBlocking.iotaBlocked = false ∧ Fragments.French.Nouns.frenchBlocking.iotaBlocked = true

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

theorem NMP.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 ([+arg, -pred]: ι, ∃, ∩ all available).

theorem NMP.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.