Nichols & Bickel (2013): WALS chapters on possession (57A, 58A, 58B, 59A)

[NB13d] [DH13b]

The four WALS chapters by Nichols & Bickel (2013):

• Ch 57A: Position of Pronominal Possessive Affixes
• Ch 58A: Obligatory Possessive Inflection
• Ch 58B: Number of Possessive Nouns
• Ch 59A: Possessive Classification

This study file holds cross-linguistic generalisations that consume the per-language Fragment possession defs (projected into the study-local Lang row) with non-trivial semantic content (oceanic_have_classification, head_marking_mostly_complex, have_verb_implies_not_head_marking, etc.), plus corpus-level WALS distribution claims that depend on filtering by chapter value.

Per-language Fragment-vs-WALS data-equality theorems are deliberately absent — verifying that X.Possession.predicativeStrategy equals Data.WALS.lookup "iso" is "encoding conclusions as definitions": the two would have to silently diverge for the theorem to fail, and the typed Fragment value already encodes the WALS coding at definition site.

structure NicholsBickel2013.Lang : Type

Study-local row: the four typological dimensions Nichols & Bickel's WALS chapters cross-tabulate over the sample, projected from per-language Fragment defs (the bundle PossessionProfile was retired).

• predicativeStrategy : Possession.PredicativeStrategy
• adnominalStrategy : Possession.AdnominalMarking
• possessiveClassification : Possession.Classification
• obligatoryPossession : Possession.Obligatoriness

def NicholsBickel2013.instDecidableEqLang.decEq (x✝ x✝¹ : Lang) : Decidable (x✝ = x✝¹)

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@[implicit_reducible]

instance NicholsBickel2013.instDecidableEqLang : DecidableEq Lang

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• NicholsBickel2013.instDecidableEqLang = NicholsBickel2013.instDecidableEqLang.decEq

def NicholsBickel2013.instReprLang.repr : Lang → ℕ → Std.Format

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@[implicit_reducible]

instance NicholsBickel2013.instReprLang : Repr Lang

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• NicholsBickel2013.instReprLang = { reprPrec := NicholsBickel2013.instReprLang.repr }

def NicholsBickel2013.Lang.hasObligatoryPossession (p : Lang) : Bool

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• p.hasObligatoryPossession = (p.obligatoryPossession == Possession.Obligatoriness.exists_)

def NicholsBickel2013.Lang.hasClassification (p : Lang) : Bool

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• p.hasClassification = (p.possessiveClassification != Possession.Classification.noClassification)

def NicholsBickel2013.Lang.usesHaveVerb (p : Lang) : Bool

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• p.usesHaveVerb = (p.predicativeStrategy == Possession.PredicativeStrategy.haveVerb)

def NicholsBickel2013.Lang.usesLocational (p : Lang) : Bool

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• p.usesLocational = (p.predicativeStrategy == Possession.PredicativeStrategy.locational)

def NicholsBickel2013.Lang.isHeadMarking (p : Lang) : Bool

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• p.isHeadMarking = (p.adnominalStrategy == Possession.AdnominalMarking.headMarking)

def NicholsBickel2013.allLanguages : List Lang

The 19-language sample, each row projected from its Fragment defs.

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def NicholsBickel2013.countByPredicative (langs : List Lang) (s : Possession.PredicativeStrategy) : ℕ

Count of languages in the sample with a given predicative strategy.

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• NicholsBickel2013.countByPredicative langs s = (List.filter (fun (x : NicholsBickel2013.Lang) => x.predicativeStrategy == s) langs).length

def NicholsBickel2013.countByAdnominal (langs : List Lang) (s : Possession.AdnominalMarking) : ℕ

Count of languages in the sample with a given adnominal strategy.

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• NicholsBickel2013.countByAdnominal langs s = (List.filter (fun (x : NicholsBickel2013.Lang) => x.adnominalStrategy == s) langs).length

theorem NicholsBickel2013.no_classification_most_common : (List.filter (fun (x : Data.WALS.Datapoint Data.WALS.F59A.PossessiveClassification) => x.value == Data.WALS.F59A.PossessiveClassification.noPossessiveClassification) NicholsBickel2013.ch59✝).length > (List.filter (fun (x : Data.WALS.Datapoint Data.WALS.F59A.PossessiveClassification) => x.value == Data.WALS.F59A.PossessiveClassification.twoClasses) NicholsBickel2013.ch59✝).length ∧ (List.filter (fun (x : Data.WALS.Datapoint Data.WALS.F59A.PossessiveClassification) => x.value == Data.WALS.F59A.PossessiveClassification.twoClasses) NicholsBickel2013.ch59✝).length > (List.filter (fun (x : Data.WALS.Datapoint Data.WALS.F59A.PossessiveClassification) => x.value == Data.WALS.F59A.PossessiveClassification.threeToFiveClasses) NicholsBickel2013.ch59✝).length + (List.filter (fun (x : Data.WALS.Datapoint Data.WALS.F59A.PossessiveClassification) => x.value == Data.WALS.F59A.PossessiveClassification.moreThanFiveClasses) NicholsBickel2013.ch59✝).length

Ch 59: No possessive classification (125) is the most common value, followed by two-way classification (94). Three-or-more-way classification (24) is the least common: 125 > 94 > 24.

theorem NicholsBickel2013.no_classification_plurality : (List.filter (fun (x : Data.WALS.Datapoint Data.WALS.F59A.PossessiveClassification) => x.value == Data.WALS.F59A.PossessiveClassification.noPossessiveClassification) NicholsBickel2013.ch59✝).length > NicholsBickel2013.ch59✝.length / 3

Most languages in the WALS sample lack possessive classification: 125 out of 243 (51.4%).

theorem NicholsBickel2013.no_obligatory_majority : (List.filter (fun (x : Data.WALS.Datapoint Data.WALS.F58A.ObligatoryPossessiveInflection) => x.value == Data.WALS.F58A.ObligatoryPossessiveInflection.absent) NicholsBickel2013.ch58✝).length > (List.filter (fun (x : Data.WALS.Datapoint Data.WALS.F58A.ObligatoryPossessiveInflection) => x.value == Data.WALS.F58A.ObligatoryPossessiveInflection.exists) NicholsBickel2013.ch58✝).length

Ch 58: Languages without obligatory possessive inflection (201) outnumber those with it (43) by a substantial margin.

theorem NicholsBickel2013.no_obligatory_over_half : (List.filter (fun (x : Data.WALS.Datapoint Data.WALS.F58A.ObligatoryPossessiveInflection) => x.value == Data.WALS.F58A.ObligatoryPossessiveInflection.absent) NicholsBickel2013.ch58✝).length > NicholsBickel2013.ch58✝.length / 2

Ch 58: Over half of sampled languages lack obligatory possession.

theorem NicholsBickel2013.classification_vs_no_classification : (List.filter (fun (x : Data.WALS.Datapoint Data.WALS.F59A.PossessiveClassification) => x.value == Data.WALS.F59A.PossessiveClassification.twoClasses) NicholsBickel2013.ch59✝).length + (List.filter (fun (x : Data.WALS.Datapoint Data.WALS.F59A.PossessiveClassification) => x.value == Data.WALS.F59A.PossessiveClassification.threeToFiveClasses) NicholsBickel2013.ch59✝).length + (List.filter (fun (x : Data.WALS.Datapoint Data.WALS.F59A.PossessiveClassification) => x.value == Data.WALS.F59A.PossessiveClassification.moreThanFiveClasses) NicholsBickel2013.ch59✝).length + (List.filter (fun (x : Data.WALS.Datapoint Data.WALS.F59A.PossessiveClassification) => x.value == Data.WALS.F59A.PossessiveClassification.noPossessiveClassification) NicholsBickel2013.ch59✝).length = NicholsBickel2013.ch59✝.length

Languages with possessive classification (2-way or 3+) come close to matching no-classification: 94 + 24 = 118 vs 125.

theorem NicholsBickel2013.two_way_dominates_three_plus : (List.filter (fun (x : Data.WALS.Datapoint Data.WALS.F59A.PossessiveClassification) => x.value == Data.WALS.F59A.PossessiveClassification.twoClasses) NicholsBickel2013.ch59✝).length > (List.filter (fun (x : Data.WALS.Datapoint Data.WALS.F59A.PossessiveClassification) => x.value == Data.WALS.F59A.PossessiveClassification.threeToFiveClasses) NicholsBickel2013.ch59✝).length + (List.filter (fun (x : Data.WALS.Datapoint Data.WALS.F59A.PossessiveClassification) => x.value == Data.WALS.F59A.PossessiveClassification.moreThanFiveClasses) NicholsBickel2013.ch59✝).length

Among languages with possessive classification, two-way systems are nearly four times as common as three-or-more-way systems.

theorem NicholsBickel2013.predicative_distribution : countByPredicative allLanguages Possession.PredicativeStrategy.locational = 12 ∧ countByPredicative allLanguages Possession.PredicativeStrategy.haveVerb = 4 ∧ countByPredicative allLanguages Possession.PredicativeStrategy.genitive = 1 ∧ countByPredicative allLanguages Possession.PredicativeStrategy.topic = 1 ∧ countByPredicative allLanguages Possession.PredicativeStrategy.comitative = 1

In the sample, locational strategies are the most common predicative possession type (12 languages), followed by have-verb (4), genitive (1), topic (1), and comitative (1).

theorem NicholsBickel2013.all_predicative_strategies_attested : (((((allLanguages.any fun (x : Lang) => x.predicativeStrategy == Possession.PredicativeStrategy.haveVerb) && allLanguages.any fun (x : Lang) => x.predicativeStrategy == Possession.PredicativeStrategy.locational) && allLanguages.any fun (x : Lang) => x.predicativeStrategy == Possession.PredicativeStrategy.genitive) && allLanguages.any fun (x : Lang) => x.predicativeStrategy == Possession.PredicativeStrategy.topic) && decide ((allLanguages.any fun (x : Lang) => x.predicativeStrategy == Possession.PredicativeStrategy.comitative) = true)) = true

All five predicative possession strategies are attested in the sample.

theorem NicholsBickel2013.adnominal_distribution : countByAdnominal allLanguages Possession.AdnominalMarking.dependentMarking = 9 ∧ countByAdnominal allLanguages Possession.AdnominalMarking.doubleMarking = 3 ∧ countByAdnominal allLanguages Possession.AdnominalMarking.headMarking = 5 ∧ countByAdnominal allLanguages Possession.AdnominalMarking.zeroMarking = 2

In the sample, dependent-marking is the most common adnominal possession strategy (9 languages), followed by head-marking (5), double-marking (3), and zero-marking (2).

theorem NicholsBickel2013.dependent_marking_dominant : countByAdnominal allLanguages Possession.AdnominalMarking.dependentMarking > countByAdnominal allLanguages Possession.AdnominalMarking.headMarking + countByAdnominal allLanguages Possession.AdnominalMarking.zeroMarking

Dependent-marking exceeds head-marking + zero-marking combined in the sample (with the European-bias caveat).

theorem NicholsBickel2013.have_verb_implies_not_head_marking : have haveLangs := List.filter (fun (x : Lang) => x.usesHaveVerb) allLanguages; (haveLangs.all fun (p : Lang) => p.adnominalStrategy != Possession.AdnominalMarking.headMarking) = true

In the sample, every language with a have-verb strategy for predicative possession uses dependent-marking or juxtaposition for adnominal possession; none use head-marking. This reflects a structural parallel: have-verb treats the possessor as subject (a dependent-marking strategy at the clause level).

theorem NicholsBickel2013.head_marking_mostly_complex_possession : have headLangs := List.filter (fun (x : Lang) => x.isHeadMarking) allLanguages; have complexHeadLangs := List.filter (fun (p : Lang) => p.hasObligatoryPossession || p.hasClassification) headLangs; headLangs.length = 5 ∧ complexHeadLangs.length = 4

In the sample, most head-marking languages have either obligatory possessive inflection or possessive classification. Four of five head-marking languages show complex possession systems, reflecting the structural affinity between head-marking and elaborate possessive morphology on the possessed noun. Swahili is the exception: head-marking via noun-class agreement but no obligatory possession or classification.

theorem NicholsBickel2013.locational_count : (List.filter (fun (x : Lang) => x.usesLocational) allLanguages).length = 12

In the sample, locational/existential predicative possession is the most widespread strategy (12 languages: Russian, Finnish, Hungarian, Korean, Georgian, Hawaiian, Fijian, Tsotsil, Tseltal, plus Hindi-Urdu, Irish, and Arabic, whose "at/near"-oblique possessives are Locational, not Genitive). The Eurasian "habeo-less" belt stretches from Finland through Korea, and locational strategies also appear in Oceanic and Mayan languages. (Turkish, with its genitive var-existential, is the sample's sole Genitive type.)

def NicholsBickel2013.oceanicLanguages : List Lang

In the sample, both Oceanic/Austronesian languages (Hawaiian, Fijian) have possessive classification (two-way or three-or-more). Possessive classification is an areal feature of the Pacific: the alienable/inalienable distinction is nearly universal in Oceanic.

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theorem NicholsBickel2013.oceanic_have_classification : (oceanicLanguages.all fun (x : Lang) => x.hasClassification) = true

theorem NicholsBickel2013.double_marking_count : countByAdnominal allLanguages Possession.AdnominalMarking.doubleMarking = 3

Double-marking (both possessor and possessum overtly marked) appears in Turkish, Quechua, and Georgian in the sample. This is the most "redundant" strategy — both participants in the possessive relation carry morphological marking.

theorem NicholsBickel2013.double_marking_languages : have doubleLangs := List.filter (fun (x : Lang) => x.adnominalStrategy == Possession.AdnominalMarking.doubleMarking) allLanguages; doubleLangs.length = 3

All double-marking languages in the sample are agglutinative or have rich morphology (Turkish, Quechua, Georgian). This is expected: double-marking requires the morphological resources to place markers on both nouns in the possessive construction.

theorem NicholsBickel2013.have_verb_mostly_no_obligatory : have haveLangs := List.filter (fun (x : Lang) => x.usesHaveVerb) allLanguages; have haveNoOblig := List.filter (fun (p : Lang) => !p.hasObligatoryPossession) haveLangs; haveLangs.length = 4 ∧ haveNoOblig.length = 3

Most have-verb languages in the sample lack obligatory possessive inflection (English, Mandarin, Yoruba). Quechua is the exception: it has both a have-verb-like construction and obligatory possessive suffixes on kinship/body-part nouns. Three of four have-verb languages lack obligatory possession.

theorem NicholsBickel2013.classification_and_obligatory_independent : have classified := List.filter (fun (x : Lang) => x.hasClassification) allLanguages; have classifiedAndObligatory := List.filter (fun (x : Lang) => x.hasObligatoryPossession) classified; classified.length = 5 ∧ classifiedAndObligatory.length = 3

The two phenomena (classification and obligatory possession) are logically independent: a language could require possession AND classify it. In the sample, three of five classifying languages (Quechua, Tsotsil, Tseltal) also have obligatory possession; the other two (Hawaiian, Fijian) do not.

theorem NicholsBickel2013.sample_size : allLanguages.length = 19

Number of languages in the sample.

theorem NicholsBickel2013.sample_obligatory_count : (List.filter (fun (x : Lang) => x.hasObligatoryPossession) allLanguages).length = 5

Distribution of obligatory possession in the sample.

theorem NicholsBickel2013.sample_classification_count : (List.filter (fun (x : Lang) => x.hasClassification) allLanguages).length = 5

Distribution of possessive classification in the sample.

theorem NicholsBickel2013.all_adnominal_strategies_attested : ((((allLanguages.any fun (x : Lang) => x.adnominalStrategy == Possession.AdnominalMarking.headMarking) && allLanguages.any fun (x : Lang) => x.adnominalStrategy == Possession.AdnominalMarking.dependentMarking) && allLanguages.any fun (x : Lang) => x.adnominalStrategy == Possession.AdnominalMarking.doubleMarking) && decide ((allLanguages.any fun (x : Lang) => x.adnominalStrategy == Possession.AdnominalMarking.zeroMarking) = true)) = true

All four adnominal strategies are attested in the sample.

theorem NicholsBickel2013.inalienability_ordering : Possession.InalienabilityRank.bodyPart.toNat > Possession.InalienabilityRank.kinship.toNat ∧ Possession.InalienabilityRank.kinship.toNat > Possession.InalienabilityRank.spatialRelation.toNat ∧ Possession.InalienabilityRank.spatialRelation.toNat > Possession.InalienabilityRank.partWhole.toNat ∧ Possession.InalienabilityRank.partWhole.toNat > Possession.InalienabilityRank.culturalItem.toNat ∧ Possession.InalienabilityRank.culturalItem.toNat > Possession.InalienabilityRank.generalProperty.toNat

The inalienability hierarchy ordering from the substrate is consistent: body parts > kinship > spatial relations > part-whole > cultural items

general property.

theorem NicholsBickel2013.location_source_dominates : have locationCount := (List.filter (fun (p : Lang) => Possession.predicativeSource p.predicativeStrategy == Possession.Source.location) allLanguages).length; have actionCount := (List.filter (fun (p : Lang) => Possession.predicativeSource p.predicativeStrategy == Possession.Source.action) allLanguages).length; locationCount > actionCount

In the sample, the two most common grammaticalization sources for predicative possession are location and action.

theorem NicholsBickel2013.attested_sources : (((((allLanguages.any fun (p : Lang) => Possession.predicativeSource p.predicativeStrategy == Possession.Source.action) && allLanguages.any fun (p : Lang) => Possession.predicativeSource p.predicativeStrategy == Possession.Source.location) && allLanguages.any fun (p : Lang) => Possession.predicativeSource p.predicativeStrategy == Possession.Source.genitive) && allLanguages.any fun (p : Lang) => Possession.predicativeSource p.predicativeStrategy == Possession.Source.companion) && decide ((allLanguages.any fun (p : Lang) => Possession.predicativeSource p.predicativeStrategy == Possession.Source.topic) = true)) = true

Five of the eight Heine schemas are attested in the sample via predicativeSource.