Cross-Linguistic Typology of Change-of-State Verbs

@cite{dixon-1982} @cite{levin-1993} @cite{beavers-etal-2021} @cite{rose-nichols-2021}

Empirical data from Beavers, Everdell, Jerro, Kauhanen, @cite{beavers-etal-2021} "States and changes of state: A crosslinguistic study of the roots of verbal meaning." Language 97(3), 439–484.

88-language balanced sample (WALS 100 + additions). For each of 36 property concept (PC) and 36 result root meanings, the authors collected five-item paradigms (underlying root, simple stative, inchoative, causative, result stative) and coded morphological relationships.

Key findings (theory-neutral)

1. Simple statives: PC roots overwhelmingly have simple stative forms (median = 95.67% of languages); result roots overwhelmingly lack them (median = 1.59%). Mann-Whitney U = 1266.5, p < 0.001.

2. Verbal markedness: PC root verbs tend to be marked (median = 56.01%); result root verbs tend to be unmarked (median = 15.20%). Mann-Whitney U = 1291, p < 0.001.

3. Subclass clustering: PC subclasses (dimension, color, value, physical property, speed) cluster near 100% simple statives. Result subclasses (breaking, cooking, killing, destroying, directed motion) cluster near 0%.

inductive Phenomena.Causation.Studies.BeaversEtAl2021.CoSRootClass : Type

Two classes of change-of-state verb roots, defined by morphological and semantic diagnostics (@cite{beavers-etal-2021} §3.1).

Classification criteria:

• PC roots: the root of deadjectival CoS verbs (@cite{levin-1993}:245); describe @cite{dixon-1982}'s basic property types
• Result roots: the root of non-deadjectival CoS verbs; describe specific result states (physical damage, cooking, etc.)

• propertyConcept : CoSRootClass
• result : CoSRootClass

instance Phenomena.Causation.Studies.BeaversEtAl2021.instDecidableEqCoSRootClass : DecidableEq CoSRootClass

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instDecidableEqCoSRootClass x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Causation.Studies.BeaversEtAl2021.instReprCoSRootClass.repr : CoSRootClass → Nat → Std.Format

Equations

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

instance Phenomena.Causation.Studies.BeaversEtAl2021.instReprCoSRootClass : Repr CoSRootClass

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instReprCoSRootClass = { reprPrec := Phenomena.Causation.Studies.BeaversEtAl2021.instReprCoSRootClass.repr }

def Phenomena.Causation.Studies.BeaversEtAl2021.instBEqCoSRootClass.beq : CoSRootClass → CoSRootClass → Bool

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instBEqCoSRootClass.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.Causation.Studies.BeaversEtAl2021.instBEqCoSRootClass : BEq CoSRootClass

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instBEqCoSRootClass = { beq := Phenomena.Causation.Studies.BeaversEtAl2021.instBEqCoSRootClass.beq }

inductive Phenomena.Causation.Studies.BeaversEtAl2021.PCSubclass : Type

PC subclasses (@cite{dixon-1982}; @cite{beavers-etal-2021} ex. 5).

• dimension : PCSubclass
• age : PCSubclass
• value : PCSubclass
• color : PCSubclass
• physicalProperty : PCSubclass
• speed : PCSubclass

instance Phenomena.Causation.Studies.BeaversEtAl2021.instDecidableEqPCSubclass : DecidableEq PCSubclass

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instDecidableEqPCSubclass x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Causation.Studies.BeaversEtAl2021.instReprPCSubclass.repr : PCSubclass → Nat → Std.Format

Equations

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

instance Phenomena.Causation.Studies.BeaversEtAl2021.instReprPCSubclass : Repr PCSubclass

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instReprPCSubclass = { reprPrec := Phenomena.Causation.Studies.BeaversEtAl2021.instReprPCSubclass.repr }

def Phenomena.Causation.Studies.BeaversEtAl2021.instBEqPCSubclass.beq : PCSubclass → PCSubclass → Bool

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instBEqPCSubclass.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.Causation.Studies.BeaversEtAl2021.instBEqPCSubclass : BEq PCSubclass

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instBEqPCSubclass = { beq := Phenomena.Causation.Studies.BeaversEtAl2021.instBEqPCSubclass.beq }

inductive Phenomena.Causation.Studies.BeaversEtAl2021.ResultSubclass : Type

Result root subclasses (@cite{levin-1993}; @cite{beavers-etal-2021} ex. 6).

• entitySpecificCoS : ResultSubclass
• cooking : ResultSubclass
• breaking : ResultSubclass
• bending : ResultSubclass
• killing : ResultSubclass
• destroying : ResultSubclass
• calibratableCoS : ResultSubclass
• inherentlyDirectedMotion : ResultSubclass

instance Phenomena.Causation.Studies.BeaversEtAl2021.instDecidableEqResultSubclass : DecidableEq ResultSubclass

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instDecidableEqResultSubclass x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Causation.Studies.BeaversEtAl2021.instReprResultSubclass.repr : ResultSubclass → Nat → Std.Format

Equations

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

instance Phenomena.Causation.Studies.BeaversEtAl2021.instReprResultSubclass : Repr ResultSubclass

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instReprResultSubclass = { reprPrec := Phenomena.Causation.Studies.BeaversEtAl2021.instReprResultSubclass.repr }

instance Phenomena.Causation.Studies.BeaversEtAl2021.instBEqResultSubclass : BEq ResultSubclass

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instBEqResultSubclass = { beq := Phenomena.Causation.Studies.BeaversEtAl2021.instBEqResultSubclass.beq }

def Phenomena.Causation.Studies.BeaversEtAl2021.instBEqResultSubclass.beq : ResultSubclass → ResultSubclass → Bool

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instBEqResultSubclass.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

inductive Phenomena.Causation.Studies.BeaversEtAl2021.ParadigmPosition : Type

The five positions in a CoS verb paradigm (@cite{beavers-etal-2021} eq. 40). Every root meaning is associated with (up to) five forms.

• underlyingRoot : ParadigmPosition
• simpleStative : ParadigmPosition
• inchoative : ParadigmPosition
• causative : ParadigmPosition
• resultStative : ParadigmPosition

instance Phenomena.Causation.Studies.BeaversEtAl2021.instDecidableEqParadigmPosition : DecidableEq ParadigmPosition

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instDecidableEqParadigmPosition x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Causation.Studies.BeaversEtAl2021.instReprParadigmPosition.repr : ParadigmPosition → Nat → Std.Format

Equations

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

instance Phenomena.Causation.Studies.BeaversEtAl2021.instReprParadigmPosition : Repr ParadigmPosition

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instReprParadigmPosition = { reprPrec := Phenomena.Causation.Studies.BeaversEtAl2021.instReprParadigmPosition.repr }

def Phenomena.Causation.Studies.BeaversEtAl2021.instBEqParadigmPosition.beq : ParadigmPosition → ParadigmPosition → Bool

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instBEqParadigmPosition.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.Causation.Studies.BeaversEtAl2021.instBEqParadigmPosition : BEq ParadigmPosition

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instBEqParadigmPosition = { beq := Phenomena.Causation.Studies.BeaversEtAl2021.instBEqParadigmPosition.beq }

inductive Phenomena.Causation.Studies.BeaversEtAl2021.MorphRelation : Type

Morphological relationship codes between forms (@cite{beavers-etal-2021} eq. 41, generalizing @cite{haspelmath-1993}:90–92).

• input : MorphRelation
• derived : MorphRelation
• transitive : MorphRelation
• labile : MorphRelation
• equipollent : MorphRelation
• unrelated : MorphRelation
• unattested : MorphRelation
• suppletive : MorphRelation

instance Phenomena.Causation.Studies.BeaversEtAl2021.instDecidableEqMorphRelation : DecidableEq MorphRelation

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instDecidableEqMorphRelation x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Causation.Studies.BeaversEtAl2021.instReprMorphRelation : Repr MorphRelation

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instReprMorphRelation = { reprPrec := Phenomena.Causation.Studies.BeaversEtAl2021.instReprMorphRelation.repr }

def Phenomena.Causation.Studies.BeaversEtAl2021.instReprMorphRelation.repr : MorphRelation → Nat → Std.Format

Equations

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

instance Phenomena.Causation.Studies.BeaversEtAl2021.instBEqMorphRelation : BEq MorphRelation

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instBEqMorphRelation = { beq := Phenomena.Causation.Studies.BeaversEtAl2021.instBEqMorphRelation.beq }

def Phenomena.Causation.Studies.BeaversEtAl2021.instBEqMorphRelation.beq : MorphRelation → MorphRelation → Bool

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instBEqMorphRelation.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

structure Phenomena.Causation.Studies.BeaversEtAl2021.RootMeaning : Type

A root meaning with its crosslinguistic attestation.

• gloss : String

  English gloss(es)

• rootClass : CoSRootClass

  PC or result root

• subclass : Option (PCSubclass ⊕ ResultSubclass)

  Subclass, if applicable

• nSimpleStative : Nat

  Number of languages with a simple stative for this root (Table A1)

• nLanguages : Nat

  Number of languages with any data for this root (Table A1)

• nMarkedVerbal : Nat

  Number of languages with a marked verbal paradigm (Table A2)

• nVerbalLanguages : Nat

  Number of languages with verbal paradigm data (Table A2)

def Phenomena.Causation.Studies.BeaversEtAl2021.instReprRootMeaning.repr : RootMeaning → Nat → Std.Format

Equations

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

instance Phenomena.Causation.Studies.BeaversEtAl2021.instReprRootMeaning : Repr RootMeaning

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instReprRootMeaning = { reprPrec := Phenomena.Causation.Studies.BeaversEtAl2021.instReprRootMeaning.repr }

def Phenomena.Causation.Studies.BeaversEtAl2021.RootMeaning.pctSimpleStative (r : RootMeaning) : Float

Percentage of languages with simple stative.

Equations

• r.pctSimpleStative = if r.nLanguages = 0 then 0.0 else r.nSimpleStative.toFloat / r.nLanguages.toFloat * 100.0

def Phenomena.Causation.Studies.BeaversEtAl2021.RootMeaning.pctMarkedVerbal (r : RootMeaning) : Float

Percentage of languages with marked verbal paradigm.

Equations

• r.pctMarkedVerbal = if r.nVerbalLanguages = 0 then 0.0 else r.nMarkedVerbal.toFloat / r.nVerbalLanguages.toFloat * 100.0

def Phenomena.Causation.Studies.BeaversEtAl2021.coldRoot : RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.largeRoot : RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.redRoot : RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.longRoot : RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.goodRoot : RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.dryRoot : RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.oldRoot : RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.whiteRoot : RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.brokenRoot : RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.cookedRoot : RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.deadRoot : RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.meltedRoot : RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.shatteredRoot : RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.bentRoot : RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.burnedRoot : RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.tornRoot : RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.goneRoot : RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.destroyedRoot : RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.pcRoots : List RootMeaning

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.resultRoots : List RootMeaning

Equations

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

structure Phenomena.Causation.Studies.BeaversEtAl2021.TypologicalComparison : Type

Summary of a crosslinguistic comparison between PC and result roots.

• measure : String

  What is being measured

• pcMedian : Float

  PC root median percentage

• resultMedian : Float

  Result root median percentage

• uStatistic : Float

  Mann-Whitney U statistic

• pThreshold : Float

  One-tailed p-value threshold

• nPC : Nat

  Sample sizes (PC roots, result roots)

• nResult : Nat

def Phenomena.Causation.Studies.BeaversEtAl2021.instReprTypologicalComparison.repr : TypologicalComparison → Nat → Std.Format

Equations

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

instance Phenomena.Causation.Studies.BeaversEtAl2021.instReprTypologicalComparison : Repr TypologicalComparison

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instReprTypologicalComparison = { reprPrec := Phenomena.Causation.Studies.BeaversEtAl2021.instReprTypologicalComparison.repr }

def Phenomena.Causation.Studies.BeaversEtAl2021.simpleStativeComparison : TypologicalComparison

Simple stative form comparison (§6, Fig. 1).

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.verbalMarkednessComparison : TypologicalComparison

Verbal markedness comparison (§7, Fig. 5).

Equations

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

theorem Phenomena.Causation.Studies.BeaversEtAl2021.both_comparisons_significant : simpleStativeComparison.pcMedian > simpleStativeComparison.resultMedian ∧ verbalMarkednessComparison.pcMedian > verbalMarkednessComparison.resultMedian

Both comparisons are statistically significant.

inductive Phenomena.Causation.Studies.BeaversEtAl2021.DiagnosticResult : Type

Empirical diagnostics for classifying roots. Each diagnostic independently sorts roots into two classes that align with the PC vs result distinction.

• positive : DiagnosticResult
• negative : DiagnosticResult

instance Phenomena.Causation.Studies.BeaversEtAl2021.instDecidableEqDiagnosticResult : DecidableEq DiagnosticResult

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instDecidableEqDiagnosticResult x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Causation.Studies.BeaversEtAl2021.instReprDiagnosticResult : Repr DiagnosticResult

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instReprDiagnosticResult = { reprPrec := Phenomena.Causation.Studies.BeaversEtAl2021.instReprDiagnosticResult.repr }

def Phenomena.Causation.Studies.BeaversEtAl2021.instReprDiagnosticResult.repr : DiagnosticResult → Nat → Std.Format

Equations

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

instance Phenomena.Causation.Studies.BeaversEtAl2021.instBEqDiagnosticResult : BEq DiagnosticResult

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instBEqDiagnosticResult = { beq := Phenomena.Causation.Studies.BeaversEtAl2021.instBEqDiagnosticResult.beq }

def Phenomena.Causation.Studies.BeaversEtAl2021.instBEqDiagnosticResult.beq : DiagnosticResult → DiagnosticResult → Bool

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instBEqDiagnosticResult.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

def Phenomena.Causation.Studies.BeaversEtAl2021.changeDenialTest : CoSRootClass → DiagnosticResult

Stative form + change denial test (§3.3, ex. 10–11). "The bright photo has never brightened" → OK (PC) "#The shattered vase has never shattered" → contradictory (result)

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.restitutiveAgainTest : CoSRootClass → DiagnosticResult

Restitutive 'again' test (§3.4, ex. 15–16). "John sharpened the knife again" → can be just one sharpening (PC) "#Chris thawed the meat again" → necessarily two thawings (result)

Equations

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

theorem Phenomena.Causation.Studies.BeaversEtAl2021.diagnostics_agree (rc : CoSRootClass) : changeDenialTest rc = restitutiveAgainTest rc

The two diagnostics always agree.

structure Phenomena.Causation.Studies.BeaversEtAl2021.LanguageProfile : Type

A language's CoS verb typological profile.

• language : String
• family : String
• nPCParadigms : Nat

  Number of PC root verbal paradigms with data

• nResultParadigms : Nat

  Number of result root verbal paradigms with data

• pctPCMarked : Float

  % of PC paradigms that are marked

• pctResultMarked : Float

  % of result paradigms that are marked

instance Phenomena.Causation.Studies.BeaversEtAl2021.instReprLanguageProfile : Repr LanguageProfile

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instReprLanguageProfile = { reprPrec := Phenomena.Causation.Studies.BeaversEtAl2021.instReprLanguageProfile.repr }

def Phenomena.Causation.Studies.BeaversEtAl2021.instReprLanguageProfile.repr : LanguageProfile → Nat → Std.Format

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.kakataibo : LanguageProfile

The six in-depth case study languages (§4).

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.kinyarwanda : LanguageProfile

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.hebrew : LanguageProfile

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.marathi : LanguageProfile

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.marathi = { language := "Marathi", family := "Indic", nPCParadigms := 40, nResultParadigms := 35, pctPCMarked := 20.41, pctResultMarked := 21.33 }

def Phenomena.Causation.Studies.BeaversEtAl2021.greek : LanguageProfile

Equations

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

def Phenomena.Causation.Studies.BeaversEtAl2021.english : LanguageProfile

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.english = { language := "English", family := "Germanic", nPCParadigms := 43, nResultParadigms := 60, pctPCMarked := 0.0, pctResultMarked := 0.0 }

def Phenomena.Causation.Studies.BeaversEtAl2021.caseStudyLanguages : List LanguageProfile

Equations

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

inductive Phenomena.Causation.Studies.BeaversEtAl2021.LanguageType : Type

Attested language types (§7.2, §8).

• asymmetric : LanguageType
• highMarking : LanguageType
• lowMarking : LanguageType

instance Phenomena.Causation.Studies.BeaversEtAl2021.instDecidableEqLanguageType : DecidableEq LanguageType

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instDecidableEqLanguageType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Causation.Studies.BeaversEtAl2021.instReprLanguageType.repr : LanguageType → Nat → Std.Format

Equations

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

instance Phenomena.Causation.Studies.BeaversEtAl2021.instReprLanguageType : Repr LanguageType

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instReprLanguageType = { reprPrec := Phenomena.Causation.Studies.BeaversEtAl2021.instReprLanguageType.repr }

def Phenomena.Causation.Studies.BeaversEtAl2021.instBEqLanguageType.beq : LanguageType → LanguageType → Bool

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instBEqLanguageType.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.Causation.Studies.BeaversEtAl2021.instBEqLanguageType : BEq LanguageType

Equations

• Phenomena.Causation.Studies.BeaversEtAl2021.instBEqLanguageType = { beq := Phenomena.Causation.Studies.BeaversEtAl2021.instBEqLanguageType.beq }

def Phenomena.Causation.Studies.BeaversEtAl2021.LanguageType.allAttested : List LanguageType

The fourth logically possible type (result marked, PC unmarked) is UNATTESTED — predicted by the markedness generalization.

Equations

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

theorem Phenomena.Causation.Studies.BeaversEtAl2021.three_attested_types : LanguageType.allAttested.length = 3

Three and only three types are attested.

theorem Phenomena.Causation.Studies.BeaversEtAl2021.pcRoots_all_pc : (pcRoots.all fun (x : RootMeaning) => x.rootClass == CoSRootClass.propertyConcept) = true

All entries in our PC root sample are classified as PC.

theorem Phenomena.Causation.Studies.BeaversEtAl2021.resultRoots_all_result : (resultRoots.all fun (x : RootMeaning) => x.rootClass == CoSRootClass.result) = true

All entries in our result root sample are classified as result.

theorem Phenomena.Causation.Studies.BeaversEtAl2021.most_pc_roots_have_statives : (List.filter (fun (r : RootMeaning) => decide (r.nSimpleStative * 2 ≥ r.nLanguages)) pcRoots).length ≥ pcRoots.length - 1

Most PC roots in the sample have ≥ 50% simple stative attestation.

theorem Phenomena.Causation.Studies.BeaversEtAl2021.result_roots_rare_statives : (resultRoots.all fun (r : RootMeaning) => decide (r.nSimpleStative * 10 ≤ r.nLanguages)) = true

No result root in the sample exceeds 10% simple stative attestation.