Evaluativity: Empirical Patterns

@cite{rett-2015} @cite{lassiter-goodman-2017} @cite{tessler-franke-2019}

Evaluativity distribution across adjectival constructions. Positive constructions are evaluative, comparatives are not, equatives show asymmetry.

Main definitions

EvaluativityStatus, EvaluativityDatum, EvaluativityPrediction

AdjectivalConstruction is defined in Theories.Semantics.Degree.Core.

inductive Phenomena.Gradability.EvaluativityBridge.EvaluativityStatus : Type

Evaluativity status.

• evaluative : EvaluativityStatus
• nonEvaluative : EvaluativityStatus
• markedOnly : EvaluativityStatus
• ungrammatical : EvaluativityStatus

def Phenomena.Gradability.EvaluativityBridge.instReprEvaluativityStatus.repr : EvaluativityStatus → ℕ → Std.Format

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instance Phenomena.Gradability.EvaluativityBridge.instReprEvaluativityStatus : Repr EvaluativityStatus

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• Phenomena.Gradability.EvaluativityBridge.instReprEvaluativityStatus = { reprPrec := Phenomena.Gradability.EvaluativityBridge.instReprEvaluativityStatus.repr }

instance Phenomena.Gradability.EvaluativityBridge.instDecidableEqEvaluativityStatus : DecidableEq EvaluativityStatus

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• Phenomena.Gradability.EvaluativityBridge.instDecidableEqEvaluativityStatus x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Gradability.EvaluativityBridge.instBEqEvaluativityStatus.beq : EvaluativityStatus → EvaluativityStatus → Bool

Equations

• Phenomena.Gradability.EvaluativityBridge.instBEqEvaluativityStatus.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.Gradability.EvaluativityBridge.instBEqEvaluativityStatus : BEq EvaluativityStatus

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• Phenomena.Gradability.EvaluativityBridge.instBEqEvaluativityStatus = { beq := Phenomena.Gradability.EvaluativityBridge.instBEqEvaluativityStatus.beq }

structure Phenomena.Gradability.EvaluativityBridge.EvaluativityDatum : Type

Evaluativity judgment datum.

• construction : Semantics.Degree.AdjectivalConstruction
• adjective : String
• isPositivePolar : Bool
• exampleSentence : String
• status : EvaluativityStatus
• presupposition : Option String
• notes : String

def Phenomena.Gradability.EvaluativityBridge.instReprEvaluativityDatum.repr : EvaluativityDatum → ℕ → Std.Format

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instance Phenomena.Gradability.EvaluativityBridge.instReprEvaluativityDatum : Repr EvaluativityDatum

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• Phenomena.Gradability.EvaluativityBridge.instReprEvaluativityDatum = { reprPrec := Phenomena.Gradability.EvaluativityBridge.instReprEvaluativityDatum.repr }

def Phenomena.Gradability.EvaluativityBridge.positive_tall : EvaluativityDatum

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def Phenomena.Gradability.EvaluativityBridge.positive_short : EvaluativityDatum

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Comparatives

Comparatives are NEVER evaluative, regardless of adjective polarity.

"Adam is taller than Doug" does NOT presuppose either is tall. "Adam is shorter than Doug" does NOT presuppose either is short.

This is a key contrast with positive constructions.

def Phenomena.Gradability.EvaluativityBridge.comparative_tall : EvaluativityDatum

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def Phenomena.Gradability.EvaluativityBridge.comparative_short : EvaluativityDatum

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def Phenomena.Gradability.EvaluativityBridge.comparative_entails_equative : String

Comparatives entail their equative counterpart but not vice versa.

"Adam is taller than Doug" → "Adam is as tall as Doug" "Adam is as tall as Doug" ↛ "Adam is taller than Doug"

Equations

• Phenomena.Gradability.EvaluativityBridge.comparative_entails_equative = "Adam is taller than Doug → Adam is as tall as Doug"

Equatives

Equatives show an ASYMMETRY based on adjective polarity:

• "Adam is as tall as Doug" → NOT evaluative
• "Adam is as short as Doug" → evaluative (presupposes both are short)

This asymmetry is evidence for a marked/unmarked distinction, but the effect emerges from pragmatic competition, not lexical stipulation.

Source: @cite{rett-2015}, @cite{bierwisch-1989}

def Phenomena.Gradability.EvaluativityBridge.equative_tall : EvaluativityDatum

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def Phenomena.Gradability.EvaluativityBridge.equative_short : EvaluativityDatum

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Measure Phrase Constructions

Measure phrases are NOT evaluative - they specify exact degrees.

"Adam is 6ft tall" does NOT presuppose Adam is tall.

However, measure phrases are RESTRICTED to positive-polar adjectives:

• "Adam is 6ft tall" ✓
• *"Adam is 4ft short" ✗

Source: @cite{schwarzschild-2005}, @cite{kennedy-mcnally-2005}

def Phenomena.Gradability.EvaluativityBridge.mp_tall : EvaluativityDatum

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def Phenomena.Gradability.EvaluativityBridge.mp_short : EvaluativityDatum

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Degree Questions

Degree questions show a similar asymmetry to equatives:

• "How tall is Adam?" → neutral (no presupposition)
• "How short is Adam?" → presupposes Adam is short

The unmarked form is used for neutral information-seeking. The marked form presupposes the property holds.

Source: @cite{rett-2015}

def Phenomena.Gradability.EvaluativityBridge.question_tall : EvaluativityDatum

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def Phenomena.Gradability.EvaluativityBridge.question_short : EvaluativityDatum

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def Phenomena.Gradability.EvaluativityBridge.allEvaluativityData : List EvaluativityDatum

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def Phenomena.Gradability.EvaluativityBridge.evaluativitySummary : String

Summary table: Evaluativity by construction and polarity.

	Positive-polar (tall)	Negative-polar (short)
Positive	evaluative	evaluative
Comparative	non-evaluative	non-evaluative
Equative	non-evaluative	EVALUATIVE
Measure Phrase	non-evaluative	*ungrammatical
Degree Question	non-evaluative	EVALUATIVE

The asymmetries in equatives and questions are the key evidence for the marked/unmarked distinction.

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Theoretical Predictions

A theory of evaluativity should derive:

1. Positive constructions are evaluative

   • This falls out of threshold semantics + pragmatic inference (RSA)
   • Listener infers threshold jointly with degree

2. Comparatives are non-evaluative

   • The comparative morpheme (-er) binds the degree argument
   • No free threshold to infer

3. Equative asymmetry

   • "as tall as" and "as short as" are semantically equivalent
   • But pragmatic competition makes "as short as" marked
   • Using marked form implicates evaluativity

4. MP restriction to positive adjectives

   • @cite{schwarzschild-2005}: MPs measure "gaps" (bounded intervals)
   • Negative adjectives have unbounded intervals
   • *"4ft short" would measure an infinite interval

5. Question asymmetry

   • Parallel to equative: marked form presupposes property
   • "How short?" is only felicitous if shortness is salient

structure Phenomena.Gradability.EvaluativityBridge.EvaluativityPrediction : Type

Predictions a pragmatic (RSA-style) theory should derive.

• name : String
• claim : String
• mechanism : String

def Phenomena.Gradability.EvaluativityBridge.instReprEvaluativityPrediction.repr : EvaluativityPrediction → ℕ → Std.Format

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instance Phenomena.Gradability.EvaluativityBridge.instReprEvaluativityPrediction : Repr EvaluativityPrediction

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• Phenomena.Gradability.EvaluativityBridge.instReprEvaluativityPrediction = { reprPrec := Phenomena.Gradability.EvaluativityBridge.instReprEvaluativityPrediction.repr }

def Phenomena.Gradability.EvaluativityBridge.prediction_positive : EvaluativityPrediction

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def Phenomena.Gradability.EvaluativityBridge.prediction_comparative : EvaluativityPrediction

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def Phenomena.Gradability.EvaluativityBridge.prediction_equative_asymmetry : EvaluativityPrediction

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def Phenomena.Gradability.EvaluativityBridge.prediction_mp_restriction : EvaluativityPrediction

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def Phenomena.Gradability.EvaluativityBridge.prediction_question_asymmetry : EvaluativityPrediction

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def Phenomena.Gradability.EvaluativityBridge.allPredictions : List EvaluativityPrediction

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Connections

To FlexibleNegation:

• "not unhappy" ≠ "happy" involves evaluativity
• "unhappy" is evaluative (degree below θ_neg)
• "not unhappy" covers gap + positive region

To Scalar Implicatures:

• Evaluativity in equatives may be a manner implicature
• Using costly marked form signals something extra

To Threshold Semantics:

• Positive construction evaluativity derives from threshold inference
• RSA listener infers threshold jointly with degree