Narrog (2010, 2012) Deontic Necessity Typology

@cite{narrog-2012} @cite{narrog-2010}

Cross-linguistic survey data on deontic necessity from a genealogically diverse sample of 200 languages (@cite{narrog-2010} appendix; @cite{narrog-2012} Table 6.6).

Data sources

• Table 3 / Table 6.5: Area-level counts of whether each language has grammaticalized obligation (NEC) and/or ability/situational possibility (POT) markers, split by 6 geographic areas.

• Table 4 / Table 6.6: Aggregate counts of deontic necessity type (strong, weak, neutral, indeterminate). These are the finest-grained published data — per-language type assignments are not available.

• Appendix: The 200 languages in the sample, listed by phylum.

Notes

• The total of Table 4 (60 + 62 + 22 + 32 = 176) exceeds 131 (languages with any NEC marker) because 44 languages had markers of multiple types (@cite{narrog-2010} fn. 17).
• Per-language deontic necessity type assignments are not published; only aggregate counts are available.

inductive Core.Modality.DeonticNecessity.DeonticNecessityType : Type

How a language grammaticalizes deontic necessity. From @cite{narrog-2010} Table 4 / @cite{narrog-2012} Table 6.6.

• strong : DeonticNecessityType
• weak : DeonticNecessityType
• neutral : DeonticNecessityType
• indeterminate : DeonticNecessityType

instance Core.Modality.DeonticNecessity.instDecidableEqDeonticNecessityType : DecidableEq DeonticNecessityType

Equations

• Core.Modality.DeonticNecessity.instDecidableEqDeonticNecessityType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Core.Modality.DeonticNecessity.instReprDeonticNecessityType : Repr DeonticNecessityType

Equations

• Core.Modality.DeonticNecessity.instReprDeonticNecessityType = { reprPrec := Core.Modality.DeonticNecessity.instReprDeonticNecessityType.repr }

def Core.Modality.DeonticNecessity.instReprDeonticNecessityType.repr : DeonticNecessityType → Nat → Std.Format

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instance Core.Modality.DeonticNecessity.instBEqDeonticNecessityType : BEq DeonticNecessityType

Equations

• Core.Modality.DeonticNecessity.instBEqDeonticNecessityType = { beq := Core.Modality.DeonticNecessity.instBEqDeonticNecessityType.beq }

def Core.Modality.DeonticNecessity.instBEqDeonticNecessityType.beq : DeonticNecessityType → DeonticNecessityType → Bool

Equations

• Core.Modality.DeonticNecessity.instBEqDeonticNecessityType.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

def Core.Modality.DeonticNecessity.deonticNecessityCounts : List (DeonticNecessityType × Nat)

Language counts by deontic necessity type. Source: @cite{narrog-2010} Table 4, reproduced in @cite{narrog-2012} Table 6.6 (p. 251).

Total exceeds 200 because 44 languages have markers of multiple types (@cite{narrog-2010} fn. 17).

Equations

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def Core.Modality.DeonticNecessity.sampleSize : Nat

The sample size: 200 genealogically diverse languages.

Equations

• Core.Modality.DeonticNecessity.sampleSize = 200

inductive Core.Modality.DeonticNecessity.Area : Type

Geographic area classification used in the sample.

• africa : Area
• americas : Area
• australia : Area
• eurasia : Area
• pacific : Area
• southSoutheastAsia : Area

instance Core.Modality.DeonticNecessity.instDecidableEqArea : DecidableEq Area

Equations

• Core.Modality.DeonticNecessity.instDecidableEqArea x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Core.Modality.DeonticNecessity.instReprArea : Repr Area

Equations

• Core.Modality.DeonticNecessity.instReprArea = { reprPrec := Core.Modality.DeonticNecessity.instReprArea.repr }

def Core.Modality.DeonticNecessity.instReprArea.repr : Area → Nat → Std.Format

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instance Core.Modality.DeonticNecessity.instBEqArea : BEq Area

Equations

• Core.Modality.DeonticNecessity.instBEqArea = { beq := Core.Modality.DeonticNecessity.instBEqArea.beq }

def Core.Modality.DeonticNecessity.instBEqArea.beq : Area → Area → Bool

Equations

• Core.Modality.DeonticNecessity.instBEqArea.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

structure Core.Modality.DeonticNecessity.AreaModalPresence : Type

Per-area counts of obligation (NEC) and ability/possibility (POT) marking. Source: @cite{narrog-2010} Table 3 / @cite{narrog-2012} Table 6.5 (p. 250).

• area : Area
• bothNecPot : Nat
• onlyNec : Nat
• onlyPot : Nat
• neither : Nat

instance Core.Modality.DeonticNecessity.instReprAreaModalPresence : Repr AreaModalPresence

Equations

• Core.Modality.DeonticNecessity.instReprAreaModalPresence = { reprPrec := Core.Modality.DeonticNecessity.instReprAreaModalPresence.repr }

def Core.Modality.DeonticNecessity.instReprAreaModalPresence.repr : AreaModalPresence → Nat → Std.Format

Equations

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

instance Core.Modality.DeonticNecessity.instBEqAreaModalPresence : BEq AreaModalPresence

Equations

• Core.Modality.DeonticNecessity.instBEqAreaModalPresence = { beq := Core.Modality.DeonticNecessity.instBEqAreaModalPresence.beq }

def Core.Modality.DeonticNecessity.instBEqAreaModalPresence.beq : AreaModalPresence → AreaModalPresence → Bool

Equations

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• Core.Modality.DeonticNecessity.instBEqAreaModalPresence.beq x✝¹ x✝ = false

def Core.Modality.DeonticNecessity.AreaModalPresence.total (a : AreaModalPresence) : Nat

Equations

• a.total = a.bothNecPot + a.onlyNec + a.onlyPot + a.neither

def Core.Modality.DeonticNecessity.areaData : List AreaModalPresence

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def Core.Modality.DeonticNecessity.countOf (t : DeonticNecessityType) : Nat

Count of a specific deontic necessity type.

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def Core.Modality.DeonticNecessity.areaSampleTotal : Nat

Total languages across all areas.

Equations

• Core.Modality.DeonticNecessity.areaSampleTotal = List.foldl (fun (x1 : Nat) (x2 : Core.Modality.DeonticNecessity.AreaModalPresence) => x1 + x2.total) 0 Core.Modality.DeonticNecessity.areaData

def Core.Modality.DeonticNecessity.languagesWithNec : Nat

Total languages with any NEC marker (both + onlyNec).

Equations

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

def Core.Modality.DeonticNecessity.languagesWithPot : Nat

Total languages with any POT marker (both + onlyPot).

Equations

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theorem Core.Modality.DeonticNecessity.area_totals_sum_to_200 : areaSampleTotal = sampleSize

Area totals sum to the sample size.

theorem Core.Modality.DeonticNecessity.nec_count : languagesWithNec = 131

Languages with any NEC marker: 121 + 10 = 131.

theorem Core.Modality.DeonticNecessity.pot_count : languagesWithPot = 156

Languages with any POT marker: 121 + 35 = 156. (Paper says 157 = 121 + 35 + 1; the discrepancy is in the original.)

theorem Core.Modality.DeonticNecessity.strong_count : countOf DeonticNecessityType.strong = 60

Strong deontic necessity: 60 languages.

theorem Core.Modality.DeonticNecessity.weak_count : countOf DeonticNecessityType.weak = 62

Weak deontic necessity: 62 languages.

theorem Core.Modality.DeonticNecessity.neutral_count : countOf DeonticNecessityType.neutral = 22

Neutral: 22 languages.

theorem Core.Modality.DeonticNecessity.indeterminate_count : countOf DeonticNecessityType.indeterminate = 32

Indeterminate: 32 languages.

theorem Core.Modality.DeonticNecessity.pot_more_common_than_nec : languagesWithPot > languagesWithNec

POT markers are more common than NEC markers cross-linguistically. @cite{narrog-2010} p. 406: 156 vs 131.