inductive Phenomena.Imprecision.Projection.EmbeddingOperator : Type

Types of embedding operators for projection.

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

def Phenomena.Imprecision.Projection.instReprEmbeddingOperator.repr : EmbeddingOperator → Nat → Std.Format

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instance Phenomena.Imprecision.Projection.instReprEmbeddingOperator : Repr EmbeddingOperator

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• Phenomena.Imprecision.Projection.instReprEmbeddingOperator = { reprPrec := Phenomena.Imprecision.Projection.instReprEmbeddingOperator.repr }

instance Phenomena.Imprecision.Projection.instDecidableEqEmbeddingOperator : DecidableEq EmbeddingOperator

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• Phenomena.Imprecision.Projection.instDecidableEqEmbeddingOperator x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

inductive Phenomena.Imprecision.Projection.Monotonicity : Type

Monotonicity of an operator.

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

def Phenomena.Imprecision.Projection.instReprMonotonicity.repr : Monotonicity → Nat → Std.Format

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instance Phenomena.Imprecision.Projection.instReprMonotonicity : Repr Monotonicity

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• Phenomena.Imprecision.Projection.instReprMonotonicity = { reprPrec := Phenomena.Imprecision.Projection.instReprMonotonicity.repr }

instance Phenomena.Imprecision.Projection.instDecidableEqMonotonicity : DecidableEq Monotonicity

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• Phenomena.Imprecision.Projection.instDecidableEqMonotonicity x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Imprecision.Projection.monotonicity : EmbeddingOperator → Monotonicity

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• Phenomena.Imprecision.Projection.monotonicity Phenomena.Imprecision.Projection.EmbeddingOperator.every = Phenomena.Imprecision.Projection.Monotonicity.upward
• Phenomena.Imprecision.Projection.monotonicity Phenomena.Imprecision.Projection.EmbeddingOperator.no = Phenomena.Imprecision.Projection.Monotonicity.downward
• Phenomena.Imprecision.Projection.monotonicity Phenomena.Imprecision.Projection.EmbeddingOperator.exactlyOne = Phenomena.Imprecision.Projection.Monotonicity.nonMonotonic
• Phenomena.Imprecision.Projection.monotonicity Phenomena.Imprecision.Projection.EmbeddingOperator.exactlyTwo = Phenomena.Imprecision.Projection.Monotonicity.nonMonotonic
• Phenomena.Imprecision.Projection.monotonicity Phenomena.Imprecision.Projection.EmbeddingOperator.notEvery = Phenomena.Imprecision.Projection.Monotonicity.downward
• Phenomena.Imprecision.Projection.monotonicity Phenomena.Imprecision.Projection.EmbeddingOperator.atLeastOne = Phenomena.Imprecision.Projection.Monotonicity.upward

structure Phenomena.Imprecision.Projection.ProjectionDatum : Type

Projection pattern for a plural under an embedding operator.

• 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?

• nonMaximalAvailable : Bool

  Non-maximal reading available?

def Phenomena.Imprecision.Projection.instReprProjectionDatum.repr : ProjectionDatum → Nat → Std.Format

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instance Phenomena.Imprecision.Projection.instReprProjectionDatum : Repr ProjectionDatum

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• Phenomena.Imprecision.Projection.instReprProjectionDatum = { reprPrec := Phenomena.Imprecision.Projection.instReprProjectionDatum.repr }

def Phenomena.Imprecision.Projection.everyProjection : ProjectionDatum

Križ & @cite{kriz-chemla-2015} tested these conditions experimentally.

Task: Trivalent truth-value judgment

• "completely true"
• "completely false"
• "neither completely true nor completely false"

Source: Križ & @cite{kriz-chemla-2015}, Experiments C1-C3

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def Phenomena.Imprecision.Projection.noProjection : ProjectionDatum

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def Phenomena.Imprecision.Projection.exactlyTwoProjection : ProjectionDatum

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structure Phenomena.Imprecision.Projection.QUDManipulationDatum : Type

@cite{augurzky-etal-2023} manipulated QUD between participants.

Strict context: QUD targets strongest reading. Lax context: QUD targets weakest reading.

no is less sensitive to QUD manipulation than every.

Source: @cite{augurzky-etal-2023}, Experiments 1-2

• operator : EmbeddingOperator

  The embedding operator

• sentence : String

  Sentence

• strictReading : String

  Strict reading (QUD = strong)

• laxReading : String

  Lax reading (QUD = weak)

• gapScenario : String

  Gap scenario

• strictContextAcceptance : String

  Acceptance rate in STRICT context (gap scenario)

• laxContextAcceptance : String

  Acceptance rate in LAX context (gap scenario)

• contextEffect : Bool

  Is there an interaction (context effect differs by operator)?

def Phenomena.Imprecision.Projection.instReprQUDManipulationDatum.repr : QUDManipulationDatum → Nat → Std.Format

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instance Phenomena.Imprecision.Projection.instReprQUDManipulationDatum : Repr QUDManipulationDatum

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• Phenomena.Imprecision.Projection.instReprQUDManipulationDatum = { reprPrec := Phenomena.Imprecision.Projection.instReprQUDManipulationDatum.repr }

def Phenomena.Imprecision.Projection.everyQUDEffect : QUDManipulationDatum

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def Phenomena.Imprecision.Projection.noQUDEffect : QUDManipulationDatum

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def Phenomena.Imprecision.Projection.notEveryQUDEffect : QUDManipulationDatum

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structure Phenomena.Imprecision.Projection.NoNotEveryAsymmetryDatum : Type

no resists non-maximality but not every permits it, which is surprising because both are downward-entailing.

Source: @cite{augurzky-etal-2023}, @cite{bar-lev-2021a}

• noSentence : String

  no sentence

• notEverySentence : String

  not every sentence

• gapScenario : String

  Gap scenario

• noPermitsWeak : Bool

  no permits weak reading in gap?

• notEveryPermitsWeak : Bool

  not every permits weak reading in gap?

• explanation : String

  Theoretical explanation

def Phenomena.Imprecision.Projection.instReprNoNotEveryAsymmetryDatum.repr : NoNotEveryAsymmetryDatum → Nat → Std.Format

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instance Phenomena.Imprecision.Projection.instReprNoNotEveryAsymmetryDatum : Repr NoNotEveryAsymmetryDatum

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• Phenomena.Imprecision.Projection.instReprNoNotEveryAsymmetryDatum = { reprPrec := Phenomena.Imprecision.Projection.instReprNoNotEveryAsymmetryDatum.repr }

def Phenomena.Imprecision.Projection.noNotEveryAsymmetry : NoNotEveryAsymmetryDatum

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structure Phenomena.Imprecision.Projection.EmbeddedTruthConditions : Type

Predicted truth conditions for embedded plurals.

Source: Križ & @cite{kriz-chemla-2015}, Križ (2015)

• operator : EmbeddingOperator

  Operator

• sentence : String

  Sentence

• truthConditions : String

  Truth conditions (informal)

• falsityConditions : String

  Falsity conditions (informal)

• gapConditions : String

  Gap conditions (informal)

instance Phenomena.Imprecision.Projection.instReprEmbeddedTruthConditions : Repr EmbeddedTruthConditions

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• Phenomena.Imprecision.Projection.instReprEmbeddedTruthConditions = { reprPrec := Phenomena.Imprecision.Projection.instReprEmbeddedTruthConditions.repr }

def Phenomena.Imprecision.Projection.instReprEmbeddedTruthConditions.repr : EmbeddedTruthConditions → Nat → Std.Format

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def Phenomena.Imprecision.Projection.everyTruthConditions : EmbeddedTruthConditions

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def Phenomena.Imprecision.Projection.noTruthConditions : EmbeddedTruthConditions

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def Phenomena.Imprecision.Projection.exactlyOneTruthConditions : EmbeddedTruthConditions

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structure Phenomena.Imprecision.Projection.RestrictorScopeDatum : Type

Plurals in restrictor vs nuclear scope behave differently.

Source: @cite{kriz-2016}

• sentence : String

  Sentence

• pluralPosition : String

  Position of plural

• universalReading : Bool

  Reading available

• existentialReading : Bool

  Existential reading?

• notes : String

  Notes

def Phenomena.Imprecision.Projection.instReprRestrictorScopeDatum.repr : RestrictorScopeDatum → Nat → Std.Format

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instance Phenomena.Imprecision.Projection.instReprRestrictorScopeDatum : Repr RestrictorScopeDatum

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• Phenomena.Imprecision.Projection.instReprRestrictorScopeDatum = { reprPrec := Phenomena.Imprecision.Projection.instReprRestrictorScopeDatum.repr }

def Phenomena.Imprecision.Projection.pluralInRestrictor : RestrictorScopeDatum

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def Phenomena.Imprecision.Projection.pluralInScope : RestrictorScopeDatum

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structure Phenomena.Imprecision.Projection.ProjectionGeneralizations : Type

Core empirical generalizations about projection.

• upwardMonotonicGapsProject : Bool

  Upward monotonic operators: gaps project

• noResistsGaps : Bool

  Downward monotonic operators: gaps don't project (for no)

• notEveryDifferentFromNo : Bool

  not every different from no

• nonMonotonicGapsProject : Bool

  Non-monotonic operators: gaps project

• strongReadingsUniversal : Bool

  Strong readings in all cases

instance Phenomena.Imprecision.Projection.instReprProjectionGeneralizations : Repr ProjectionGeneralizations

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• Phenomena.Imprecision.Projection.instReprProjectionGeneralizations = { reprPrec := Phenomena.Imprecision.Projection.instReprProjectionGeneralizations.repr }

def Phenomena.Imprecision.Projection.instReprProjectionGeneralizations.repr : ProjectionGeneralizations → Nat → Std.Format

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def Phenomena.Imprecision.Projection.mainGeneralizations : ProjectionGeneralizations

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def Phenomena.Imprecision.Projection.krizChemlaData : List ProjectionDatum

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def Phenomena.Imprecision.Projection.augurzkyData : List QUDManipulationDatum

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def Phenomena.Imprecision.Projection.truthConditionsData : List EmbeddedTruthConditions

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