@cite{kriz-chemla-2015}: Trivalent truth-value judgments for embedded plurals

Empirical data from Manuel Križ and Emmanuel Chemla (2015), "Two methods to find truth-value gaps and their application to the projection problem of homogeneity," Natural Language Semantics. Križ & Chemla introduce a trivalent judgment task ("completely true" / "completely false" / "neither completely true nor completely false") and use it to test how homogeneity gaps for plural definites project under embedding operators (every, no, exactly N).

Empirical contribution

For sentences embedding plural definites under quantifiers:

• every (upward monotonic): gaps DETECTABLE — many "neither" responses in scenarios where every boy found some but not all his presents.
• no (downward monotonic): gaps NOT detectable — few "neither" responses in scenarios where some boys found some but no boy found all presents.
• exactly N (non-monotonic): gaps DETECTABLE — pattern matches every.

The no/every asymmetry is the empirical puzzle that motivates Križ's later formal work (@cite{kriz-2016}) and the extension by @cite{bar-lev-2021} and @cite{augurzky-etal-2023}.

Provenance

This data was previously bundled inside Phenomena/Imprecision/Projection.lean and then Phenomena/Imprecision/Studies/Haslinger2025.lean. Moved here at 0.230.521 because the empirical anchor is Križ & Chemla 2015 — Haslinger 2025 discusses these data points in Ch 7 but as a published-result substrate, not as her own original observation.

inductive Phenomena.Plurals.Studies.KrizChemla2015.EmbeddingOperator : Type

Types of embedding operators for projection studies.

• every : EmbeddingOperator
• no : EmbeddingOperator
• exactlyOne : EmbeddingOperator
• exactlyTwo : EmbeddingOperator
• notEvery : EmbeddingOperator
• atLeastOne : EmbeddingOperator

@[implicit_reducible]

instance Phenomena.Plurals.Studies.KrizChemla2015.instReprEmbeddingOperator : Repr EmbeddingOperator

Equations

• Phenomena.Plurals.Studies.KrizChemla2015.instReprEmbeddingOperator = { reprPrec := Phenomena.Plurals.Studies.KrizChemla2015.instReprEmbeddingOperator.repr }

def Phenomena.Plurals.Studies.KrizChemla2015.instReprEmbeddingOperator.repr : EmbeddingOperator → Nat → Std.Format

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@[implicit_reducible]

instance Phenomena.Plurals.Studies.KrizChemla2015.instDecidableEqEmbeddingOperator : DecidableEq EmbeddingOperator

Equations

• Phenomena.Plurals.Studies.KrizChemla2015.instDecidableEqEmbeddingOperator x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

inductive Phenomena.Plurals.Studies.KrizChemla2015.Monotonicity : Type

Monotonicity of an operator.

• upward : Monotonicity
• downward : Monotonicity
• nonMonotonic : Monotonicity

def Phenomena.Plurals.Studies.KrizChemla2015.instReprMonotonicity.repr : Monotonicity → Nat → Std.Format

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@[implicit_reducible]

instance Phenomena.Plurals.Studies.KrizChemla2015.instReprMonotonicity : Repr Monotonicity

Equations

• Phenomena.Plurals.Studies.KrizChemla2015.instReprMonotonicity = { reprPrec := Phenomena.Plurals.Studies.KrizChemla2015.instReprMonotonicity.repr }

@[implicit_reducible]

instance Phenomena.Plurals.Studies.KrizChemla2015.instDecidableEqMonotonicity : DecidableEq Monotonicity

Equations

• Phenomena.Plurals.Studies.KrizChemla2015.instDecidableEqMonotonicity x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Plurals.Studies.KrizChemla2015.monotonicity : EmbeddingOperator → Monotonicity

Equations

• Phenomena.Plurals.Studies.KrizChemla2015.monotonicity Phenomena.Plurals.Studies.KrizChemla2015.EmbeddingOperator.every = Phenomena.Plurals.Studies.KrizChemla2015.Monotonicity.upward
• Phenomena.Plurals.Studies.KrizChemla2015.monotonicity Phenomena.Plurals.Studies.KrizChemla2015.EmbeddingOperator.no = Phenomena.Plurals.Studies.KrizChemla2015.Monotonicity.downward
• Phenomena.Plurals.Studies.KrizChemla2015.monotonicity Phenomena.Plurals.Studies.KrizChemla2015.EmbeddingOperator.exactlyOne = Phenomena.Plurals.Studies.KrizChemla2015.Monotonicity.nonMonotonic
• Phenomena.Plurals.Studies.KrizChemla2015.monotonicity Phenomena.Plurals.Studies.KrizChemla2015.EmbeddingOperator.exactlyTwo = Phenomena.Plurals.Studies.KrizChemla2015.Monotonicity.nonMonotonic
• Phenomena.Plurals.Studies.KrizChemla2015.monotonicity Phenomena.Plurals.Studies.KrizChemla2015.EmbeddingOperator.notEvery = Phenomena.Plurals.Studies.KrizChemla2015.Monotonicity.downward
• Phenomena.Plurals.Studies.KrizChemla2015.monotonicity Phenomena.Plurals.Studies.KrizChemla2015.EmbeddingOperator.atLeastOne = Phenomena.Plurals.Studies.KrizChemla2015.Monotonicity.upward

structure Phenomena.Plurals.Studies.KrizChemla2015.ProjectionDatum : Type

Projection pattern for a plural under an embedding operator.

Source: @cite{kriz-chemla-2015}, Experiments C1-C3. Task: trivalent truth-value judgment ("completely true" / "completely false" / "neither").

• operator : EmbeddingOperator

  The embedding operator

• sentence : String

  Example sentence

• gapScenario : String

  Gap scenario description

• strongReadingAvailable : Bool

  Strong (maximal) reading available?

• weakReadingAvailable : Bool

  Weak (existential) reading available?

• gapDetectable : Bool

  Homogeneity gap detectable (many "neither" responses)?

• nonMaximalAvailable : Bool

  Non-maximal reading available (some "completely true" in gap)?

@[implicit_reducible]

instance Phenomena.Plurals.Studies.KrizChemla2015.instReprProjectionDatum : Repr ProjectionDatum

Equations

• Phenomena.Plurals.Studies.KrizChemla2015.instReprProjectionDatum = { reprPrec := Phenomena.Plurals.Studies.KrizChemla2015.instReprProjectionDatum.repr }

def Phenomena.Plurals.Studies.KrizChemla2015.instReprProjectionDatum.repr : ProjectionDatum → Nat → Std.Format

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def Phenomena.Plurals.Studies.KrizChemla2015.everyProjection : ProjectionDatum

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def Phenomena.Plurals.Studies.KrizChemla2015.noProjection : ProjectionDatum

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def Phenomena.Plurals.Studies.KrizChemla2015.exactlyTwoProjection : ProjectionDatum

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structure Phenomena.Plurals.Studies.KrizChemla2015.EmbeddedTruthConditions : Type

Predicted truth conditions for embedded plurals.

Source: @cite{kriz-chemla-2015} + Križ (2015) dissertation.

• operator : EmbeddingOperator

  Operator

• sentence : String

  Sentence

• truthConditions : String

  Truth conditions (informal)

• falsityConditions : String

  Falsity conditions (informal)

• gapConditions : String

  Gap conditions (informal)

@[implicit_reducible]

instance Phenomena.Plurals.Studies.KrizChemla2015.instReprEmbeddedTruthConditions : Repr EmbeddedTruthConditions

Equations

• Phenomena.Plurals.Studies.KrizChemla2015.instReprEmbeddedTruthConditions = { reprPrec := Phenomena.Plurals.Studies.KrizChemla2015.instReprEmbeddedTruthConditions.repr }

def Phenomena.Plurals.Studies.KrizChemla2015.instReprEmbeddedTruthConditions.repr : EmbeddedTruthConditions → Nat → Std.Format

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def Phenomena.Plurals.Studies.KrizChemla2015.everyTruthConditions : EmbeddedTruthConditions

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def Phenomena.Plurals.Studies.KrizChemla2015.noTruthConditions : EmbeddedTruthConditions

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def Phenomena.Plurals.Studies.KrizChemla2015.exactlyOneTruthConditions : EmbeddedTruthConditions

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def Phenomena.Plurals.Studies.KrizChemla2015.projectionData : List ProjectionDatum

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def Phenomena.Plurals.Studies.KrizChemla2015.truthConditionsData : List EmbeddedTruthConditions

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