Comparison Class: Empirical Data

@cite{tessler-goodman-2022} @cite{tessler-goodman-2019} @cite{weicker-schulz-2024}

Theory-neutral empirical patterns for comparison class inference with gradable adjectives.

Phenomena Covered

1. Polarity × Expectations Interaction: Adjective polarity interacts with prior expectations to determine inferred comparison class
2. Linguistic vs Visual Cues: Taxonomic labels dominate visual context
3. RGA vs AGA Distinction: Relative vs absolute gradable adjectives differ in comparison class sensitivity

structure Phenomena.Gradability.ComparisonClass.PolarityExpectationsDatum : Type

Empirical pattern: Polarity and prior expectations interact to determine the inferred comparison class.

Prediction:

• Positive adjective + expected property → superordinate class (e.g., "tall basketball player" → compared to people in general)
• Negative adjective + expected property → subordinate class (e.g., "short basketball player" → compared to basketball players)
• The pattern reverses when expectations reverse (e.g., "short jockey" → compared to people; "tall jockey" → compared to jockeys)

Source: @cite{tessler-goodman-2022}, Section 3

• adjective : String

  The adjective used

• polarity : String

  Polarity of the adjective (positive or negative)

• noun : String

  The noun/kind mentioned

• priorExpectation : String

  Prior expectation direction for this kind ("high" or "low")

• inferredClass : String

  Inferred comparison class

instance Phenomena.Gradability.ComparisonClass.instReprPolarityExpectationsDatum : Repr PolarityExpectationsDatum

Equations

• Phenomena.Gradability.ComparisonClass.instReprPolarityExpectationsDatum = { reprPrec := Phenomena.Gradability.ComparisonClass.instReprPolarityExpectationsDatum.repr }

def Phenomena.Gradability.ComparisonClass.instReprPolarityExpectationsDatum.repr : PolarityExpectationsDatum → Nat → Std.Format

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def Phenomena.Gradability.ComparisonClass.tallBasketball : PolarityExpectationsDatum

"Tall basketball player" → compared to people in general (superordinate).

When you hear someone is a "tall basketball player", the most informative interpretation is that they are tall even compared to people in general, since basketball players are expected to be tall anyway.

Source: @cite{tessler-goodman-2022}, Section 3.2.1, Figure 3

Equations

• Phenomena.Gradability.ComparisonClass.tallBasketball = { adjective := "tall", polarity := "positive", noun := "basketball player", priorExpectation := "high", inferredClass := "superordinate" }

def Phenomena.Gradability.ComparisonClass.shortBasketball : PolarityExpectationsDatum

"Short basketball player" → compared to basketball players (subordinate).

The negative adjective with high prior expectation leads to subordinate comparison: "short for a basketball player".

Source: @cite{tessler-goodman-2022}, Section 3.2.1, Figure 3

Equations

• Phenomena.Gradability.ComparisonClass.shortBasketball = { adjective := "short", polarity := "negative", noun := "basketball player", priorExpectation := "high", inferredClass := "subordinate" }

def Phenomena.Gradability.ComparisonClass.shortJockey : PolarityExpectationsDatum

"Short jockey" → compared to people in general (superordinate).

The pattern reverses for jockeys: negative adjective + low prior → superordinate. "Short for a person" is more informative than "short for a jockey".

Source: @cite{tessler-goodman-2022}, Section 3.2.1, Figure 3

Equations

• Phenomena.Gradability.ComparisonClass.shortJockey = { adjective := "short", polarity := "negative", noun := "jockey", priorExpectation := "low", inferredClass := "superordinate" }

def Phenomena.Gradability.ComparisonClass.tallJockey : PolarityExpectationsDatum

"Tall jockey" → compared to jockeys (subordinate).

Positive adjective + low prior → subordinate comparison class.

Source: @cite{tessler-goodman-2022}, Section 3.2.1, Figure 3

Equations

• Phenomena.Gradability.ComparisonClass.tallJockey = { adjective := "tall", polarity := "positive", noun := "jockey", priorExpectation := "low", inferredClass := "subordinate" }

def Phenomena.Gradability.ComparisonClass.polarityExpectationsExamples : List PolarityExpectationsDatum

All polarity × expectations examples.

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structure Phenomena.Gradability.ComparisonClass.PolarityExpectationsPattern : Type

The polarity × expectations interaction pattern.

This captures the core empirical generalization:

• positive adjective + high prior → superordinate
• negative adjective + high prior → subordinate
• positive adjective + low prior → subordinate
• negative adjective + low prior → superordinate

Source: @cite{tessler-goodman-2022}, Section 3.2.1, Figure 3

• examples : List PolarityExpectationsDatum

  Examples demonstrating the pattern

• positivePlusHighYieldsSuperordinate : Bool

  Does pattern show expected-leads-to-superordinate for positive adjectives?

• negativePlusHighYieldsSubordinate : Bool

  Does pattern show expected-leads-to-subordinate for negative adjectives?

instance Phenomena.Gradability.ComparisonClass.instReprPolarityExpectationsPattern : Repr PolarityExpectationsPattern

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• Phenomena.Gradability.ComparisonClass.instReprPolarityExpectationsPattern = { reprPrec := Phenomena.Gradability.ComparisonClass.instReprPolarityExpectationsPattern.repr }

def Phenomena.Gradability.ComparisonClass.instReprPolarityExpectationsPattern.repr : PolarityExpectationsPattern → Nat → Std.Format

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def Phenomena.Gradability.ComparisonClass.tesslerGoodmanPattern : PolarityExpectationsPattern

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inductive Phenomena.Gradability.ComparisonClass.AdjectiveType : Type

Adjective type: Relative Gradable (RGA) vs Absolute Gradable (AGA).

• RGA: Requires comparison class for interpretation (big, tall, expensive)
• AGA: Has inherent standard, less dependent on comparison class (wet, closed, full)

Source: @cite{weicker-schulz-2024}, Section 1.2

• RGA : AdjectiveType
• AGA : AdjectiveType

def Phenomena.Gradability.ComparisonClass.instReprAdjectiveType.repr : AdjectiveType → Nat → Std.Format

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instance Phenomena.Gradability.ComparisonClass.instReprAdjectiveType : Repr AdjectiveType

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• Phenomena.Gradability.ComparisonClass.instReprAdjectiveType = { reprPrec := Phenomena.Gradability.ComparisonClass.instReprAdjectiveType.repr }

instance Phenomena.Gradability.ComparisonClass.instDecidableEqAdjectiveType : DecidableEq AdjectiveType

Equations

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

structure Phenomena.Gradability.ComparisonClass.AdjectiveTypeDatum : Type

Structure capturing the difference in comparison class dependency between RGA and AGA adjectives.

Source: @cite{weicker-schulz-2024}, Section 1.2

• adjective : String

  The adjective

• adjType : AdjectiveType

  Adjective type

• example1 : String

  Example showing context-sensitivity (or lack thereof)

• example2 : String

  Another example

• thresholdShifts : Bool

  Does threshold shift with comparison class?

def Phenomena.Gradability.ComparisonClass.instReprAdjectiveTypeDatum.repr : AdjectiveTypeDatum → Nat → Std.Format

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instance Phenomena.Gradability.ComparisonClass.instReprAdjectiveTypeDatum : Repr AdjectiveTypeDatum

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• Phenomena.Gradability.ComparisonClass.instReprAdjectiveTypeDatum = { reprPrec := Phenomena.Gradability.ComparisonClass.instReprAdjectiveTypeDatum.repr }

def Phenomena.Gradability.ComparisonClass.bigRGA : AdjectiveTypeDatum

"Big" is an RGA - threshold shifts with comparison class.

Source: @cite{weicker-schulz-2024}, citing @cite{kennedy-2007}

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def Phenomena.Gradability.ComparisonClass.wetAGA : AdjectiveTypeDatum

"Wet" is an AGA - has inherent minimum standard.

Source: @cite{weicker-schulz-2024}, Section 1.2

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def Phenomena.Gradability.ComparisonClass.adjectiveTypeExamples : List AdjectiveTypeDatum

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• Phenomena.Gradability.ComparisonClass.adjectiveTypeExamples = [Phenomena.Gradability.ComparisonClass.bigRGA, Phenomena.Gradability.ComparisonClass.wetAGA]

inductive Phenomena.Gradability.ComparisonClass.CueType : Type

Cue type for comparison class determination.

Source: @cite{weicker-schulz-2024}, Section 1.3

• linguistic : CueType
• visual : CueType

def Phenomena.Gradability.ComparisonClass.instReprCueType.repr : CueType → Nat → Std.Format

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instance Phenomena.Gradability.ComparisonClass.instReprCueType : Repr CueType

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• Phenomena.Gradability.ComparisonClass.instReprCueType = { reprPrec := Phenomena.Gradability.ComparisonClass.instReprCueType.repr }

instance Phenomena.Gradability.ComparisonClass.instDecidableEqCueType : DecidableEq CueType

Equations

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

inductive Phenomena.Gradability.ComparisonClass.NounLevel : Type

Noun level in taxonomic hierarchy (Rosch & Mervis, 1975).

This is distinct from @cite{tessler-goodman-2022}'s ComparisonClass (subordinate/superordinate reference population). NounLevel classifies the noun's position in a conceptual taxonomy; ComparisonClass classifies the reference population used for adjective threshold computation. They are related — basic-level nouns tend to trigger subordinate comparison classes — but the mapping is not identity: "basketball player" (basic-level noun) is the subordinate comparison class, while "people" (superordinate noun) is the superordinate comparison class.

Source: @cite{weicker-schulz-2024}, Section 2

• basic : NounLevel
• superordinate : NounLevel

def Phenomena.Gradability.ComparisonClass.instReprNounLevel.repr : NounLevel → Nat → Std.Format

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instance Phenomena.Gradability.ComparisonClass.instReprNounLevel : Repr NounLevel

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• Phenomena.Gradability.ComparisonClass.instReprNounLevel = { reprPrec := Phenomena.Gradability.ComparisonClass.instReprNounLevel.repr }

instance Phenomena.Gradability.ComparisonClass.instDecidableEqNounLevel : DecidableEq NounLevel

Equations

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

structure Phenomena.Gradability.ComparisonClass.LinguisticVsVisualDatum : Type

Empirical pattern: Linguistic cues dominate visual cues for comparison class.

When taxonomic label conflicts with visual context, both children and adults privilege the linguistic information.

• "The big animal" + visual context of mice → compare to animals (linguistic wins)
• Basic-level nouns trigger subordinate class, superordinate nouns trigger superordinate class

Source: @cite{weicker-schulz-2024}, Section 4

• adjective : String

  The adjective used

• noun : String

  The noun used (determines linguistic cue)

• nounLevel : NounLevel

  Level of the noun

• visualContext : String

  Visual context description

• inferredClass : String

  What comparison class is inferred?

• dominantCue : CueType

  Which cue dominates?

instance Phenomena.Gradability.ComparisonClass.instReprLinguisticVsVisualDatum : Repr LinguisticVsVisualDatum

Equations

• Phenomena.Gradability.ComparisonClass.instReprLinguisticVsVisualDatum = { reprPrec := Phenomena.Gradability.ComparisonClass.instReprLinguisticVsVisualDatum.repr }

def Phenomena.Gradability.ComparisonClass.instReprLinguisticVsVisualDatum.repr : LinguisticVsVisualDatum → Nat → Std.Format

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def Phenomena.Gradability.ComparisonClass.bigAnimalMice : LinguisticVsVisualDatum

"The big animal" with mice visible → animal comparison class.

The superordinate noun "animal" triggers the superordinate comparison class, overriding the visual context of only mice being present.

Source: @cite{weicker-schulz-2024}, Experiment 1

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def Phenomena.Gradability.ComparisonClass.bigMouseAnimals : LinguisticVsVisualDatum

"The big mouse" with various animals visible → mouse comparison class.

The basic-level noun "mouse" triggers the subordinate comparison class (compared to mice), even when other animals are visually salient.

Source: @cite{weicker-schulz-2024}, Experiment 1

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def Phenomena.Gradability.ComparisonClass.linguisticVsVisualExamples : List LinguisticVsVisualDatum

Equations

• Phenomena.Gradability.ComparisonClass.linguisticVsVisualExamples = [Phenomena.Gradability.ComparisonClass.bigAnimalMice, Phenomena.Gradability.ComparisonClass.bigMouseAnimals]

structure Phenomena.Gradability.ComparisonClass.DevelopmentalDatum : Type

Empirical pattern: Children show same linguistic > visual preference as adults.

Both 4-6 year olds and adults privilege linguistic over visual information, though adults show larger subordinate selections with basic-level nouns (possible scalar implicature contribution).

Source: @cite{weicker-schulz-2024}, Section 4

• ageGroup : String

  Age group

• nounLevel : NounLevel

  Condition (noun level)

• subordinateSelection : Float

  Proportion selecting subordinate interpretation

• superordinateSelection : Float

  Proportion selecting superordinate interpretation

instance Phenomena.Gradability.ComparisonClass.instReprDevelopmentalDatum : Repr DevelopmentalDatum

Equations

• Phenomena.Gradability.ComparisonClass.instReprDevelopmentalDatum = { reprPrec := Phenomena.Gradability.ComparisonClass.instReprDevelopmentalDatum.repr }

def Phenomena.Gradability.ComparisonClass.instReprDevelopmentalDatum.repr : DevelopmentalDatum → Nat → Std.Format

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def Phenomena.Gradability.ComparisonClass.adultBasicLevel : DevelopmentalDatum

Adults with basic-level nouns strongly prefer subordinate interpretation.

Source: @cite{weicker-schulz-2024}, Figure 2

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def Phenomena.Gradability.ComparisonClass.adultSuperordinate : DevelopmentalDatum

Adults with superordinate nouns prefer superordinate interpretation.

Source: @cite{weicker-schulz-2024}, Figure 2

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def Phenomena.Gradability.ComparisonClass.childBasicLevel : DevelopmentalDatum

Children with basic-level nouns prefer subordinate interpretation.

Source: @cite{weicker-schulz-2024}, Figure 2

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def Phenomena.Gradability.ComparisonClass.childSuperordinate : DevelopmentalDatum

Children with superordinate nouns prefer superordinate interpretation.

Source: @cite{weicker-schulz-2024}, Figure 2

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def Phenomena.Gradability.ComparisonClass.developmentalExamples : List DevelopmentalDatum

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structure Phenomena.Gradability.ComparisonClass.ComparisonClassGeneralizations : Type

Main empirical generalizations about comparison class inference.

Source: @cite{tessler-goodman-2022}, @cite{weicker-schulz-2024}

• polarityExpectationsInteraction : Bool

  Polarity interacts with prior expectations

• linguisticDominatesVisual : Bool

  Linguistic cues dominate visual cues

• basicLevelYieldsSubordinate : Bool

  Basic-level nouns trigger subordinate classes

• superordinateYieldsSuperordinate : Bool

  Superordinate nouns trigger superordinate classes

• developmentallyStable : Bool

  Pattern holds across development (adults and children)

• rgaMoreContextSensitive : Bool

  RGAs more context-sensitive than AGAs

def Phenomena.Gradability.ComparisonClass.instReprComparisonClassGeneralizations.repr : ComparisonClassGeneralizations → Nat → Std.Format

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instance Phenomena.Gradability.ComparisonClass.instReprComparisonClassGeneralizations : Repr ComparisonClassGeneralizations

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• Phenomena.Gradability.ComparisonClass.instReprComparisonClassGeneralizations = { reprPrec := Phenomena.Gradability.ComparisonClass.instReprComparisonClassGeneralizations.repr }

def Phenomena.Gradability.ComparisonClass.mainGeneralizations : ComparisonClassGeneralizations

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def Phenomena.Gradability.ComparisonClass.AdjectiveType.ofDomain (d : Core.PropertyDomain) : AdjectiveType

Map PropertyDomain to AdjectiveType: domains that require comparison-class computation are RGA; others are AGA.

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theorem Phenomena.Gradability.ComparisonClass.size_is_rga : AdjectiveType.ofDomain Core.PropertyDomain.size = AdjectiveType.RGA

Size domain → RGA (e.g., "big", "tall").

theorem Phenomena.Gradability.ComparisonClass.state_is_aga : AdjectiveType.ofDomain Core.PropertyDomain.state = AdjectiveType.AGA

State domain → AGA (e.g., "wet", "full").

theorem Phenomena.Gradability.ComparisonClass.rga_threshold_shift_predicted : bigRGA.thresholdShifts = true ∧ Core.PropertyDomain.size.requiresComparisonClass = true

The empirical observation that RGA thresholds shift with comparison class is predicted by requiresComparisonClass = true for the size domain.

theorem Phenomena.Gradability.ComparisonClass.aga_no_threshold_shift_predicted : wetAGA.thresholdShifts = false ∧ Core.PropertyDomain.state.requiresComparisonClass = false

The empirical observation that AGA thresholds do NOT shift is predicted by requiresComparisonClass = false for the state domain.