Kennedy Framework on Comparative Data

@cite{kennedy-2007} @cite{kennedy-mcnally-2005} @cite{schwarzschild-2005} @cite{solt-2015} @cite{winter-2005}

Bridge connecting @cite{kennedy-2007}'s measure function approach to the comparative construction data in Phenomena/Comparison/.

Key Bridges

1. Morphological distribution: Kennedy's ⟦-er⟧ and ⟦more⟧ are the same degree morpheme (comparative DegP head) with different spell-out — the framework is morphology-neutral.

2. Scale structure predictions: Kennedy's Interpretive Economy predicts that open-scale comparatives use contextual standards while closed-scale comparatives use endpoint standards.

3. Measure phrase licensing: Kennedy's approach naturally accounts for measure phrase differentials ("3 inches taller") because the degree argument IS a measure.

Differential Comparative Data

Empirical data on differential comparatives (@cite{schwarzschild-2005}, @cite{solt-2015}): constructions that specify the extent of the comparison ("3 inches taller", "twice as expensive", "much faster").

1. Measure phrase differentials require specific scale structure: "3 inches taller" ✓ but "*3 units more beautiful" ✗ (ratio scale needed).
2. Factor phrases ("twice as tall") require the equative, not the comparative (*"twice taller than").
3. Degree modifiers ("much", "slightly", "a lot") are less restrictive than measure phrases — they work with open scales.

theorem Phenomena.Comparison.Studies.Kennedy2007.open_scale_contextual : Semantics.Degree.interpretiveEconomy Core.Scale.Boundedness.open_ = Semantics.Degree.PositiveStandard.contextual

Open-scale adjectives (Kennedy's "relative"; Class A here) use contextual standards.

theorem Phenomena.Comparison.Studies.Kennedy2007.closed_scale_endpoint : Semantics.Degree.interpretiveEconomy Core.Scale.Boundedness.closed = Semantics.Degree.PositiveStandard.maxEndpoint

Closed-scale adjectives (Kennedy's "absolute"; Class B here) use endpoint standards.

theorem Phenomena.Comparison.Studies.Kennedy2007.lower_bounded_minEndpoint : Semantics.Degree.interpretiveEconomy Core.Scale.Boundedness.lowerBounded = Semantics.Degree.PositiveStandard.minEndpoint

Lower-bounded adjectives use minimum endpoint.

structure Phenomena.Comparison.Studies.Kennedy2007.MeasurePhraseComparativeDatum : Type

A measure phrase differential datum: a numeric amount specifying the extent of comparison.

• sentence : String
• acceptable : Bool
• scaleType : String

  What kind of scale does the adjective have?

• measurePhrase : String

  The measure phrase

instance Phenomena.Comparison.Studies.Kennedy2007.instReprMeasurePhraseComparativeDatum : Repr MeasurePhraseComparativeDatum

Equations

• Phenomena.Comparison.Studies.Kennedy2007.instReprMeasurePhraseComparativeDatum = { reprPrec := Phenomena.Comparison.Studies.Kennedy2007.instReprMeasurePhraseComparativeDatum.repr }

def Phenomena.Comparison.Studies.Kennedy2007.instReprMeasurePhraseComparativeDatum.repr : MeasurePhraseComparativeDatum → ℕ → Std.Format

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def Phenomena.Comparison.Studies.Kennedy2007.measurePhraseExamples : List MeasurePhraseComparativeDatum

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theorem Phenomena.Comparison.Studies.Kennedy2007.measure_phrases_require_subtraction (d : MeasurePhraseComparativeDatum) : d ∈ measurePhraseExamples → d.acceptable = true → d.scaleType = "ratio (height)" ∨ d.scaleType = "interval (temperature)"

Kennedy's approach predicts measure phrases are licensed when the degree type has subtraction (ratio/interval scale). The comparative data measurePhraseExamples reflects this: height (ratio) ✓, beauty (open, no conventional unit) ✗.

This is a type-theoretic prediction: differentialComparative requires ℚ (with subtraction), not just an ordered type.

structure Phenomena.Comparison.Studies.Kennedy2007.FactorPhraseDatum : Type

Factor phrase data: multiplicative comparison ("twice", "three times").

• sentence : String
• acceptable : Bool
• factor : String

  Factor ("twice", "three times", etc.)

• construction : String

  Equative or comparative?

def Phenomena.Comparison.Studies.Kennedy2007.instReprFactorPhraseDatum.repr : FactorPhraseDatum → ℕ → Std.Format

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instance Phenomena.Comparison.Studies.Kennedy2007.instReprFactorPhraseDatum : Repr FactorPhraseDatum

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• Phenomena.Comparison.Studies.Kennedy2007.instReprFactorPhraseDatum = { reprPrec := Phenomena.Comparison.Studies.Kennedy2007.instReprFactorPhraseDatum.repr }

def Phenomena.Comparison.Studies.Kennedy2007.factorPhraseExamples : List FactorPhraseDatum

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structure Phenomena.Comparison.Studies.Kennedy2007.DegreeModifierDatum : Type

Degree modifier data: "much", "slightly", "a lot", "far".

• sentence : String
• acceptable : Bool
• modifier : String
• requiresComparison : Bool

  Does the modifier require a comparison construction?

instance Phenomena.Comparison.Studies.Kennedy2007.instReprDegreeModifierDatum : Repr DegreeModifierDatum

Equations

• Phenomena.Comparison.Studies.Kennedy2007.instReprDegreeModifierDatum = { reprPrec := Phenomena.Comparison.Studies.Kennedy2007.instReprDegreeModifierDatum.repr }

def Phenomena.Comparison.Studies.Kennedy2007.instReprDegreeModifierDatum.repr : DegreeModifierDatum → ℕ → Std.Format

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def Phenomena.Comparison.Studies.Kennedy2007.degreeModifierExamples : List DegreeModifierDatum

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