Scale Generation from Morphological Paradigms

@cite{horn-1972} @cite{kennedy-2007}

Derives Horn scales automatically from adjective paradigms. Given a stem with comparative and superlative rules, we can construct the scale ⟨positive, comparative, superlative⟩ — ordered from weakest to strongest.

This connects morphological infrastructure (Core/Morphology/) to scalar-alternative infrastructure (Theories/Semantics/Alternatives/HornScale.lean), enabling automatic generation of the alternatives needed for scalar implicature computation.

Main definitions

• MorphScale: a Horn scale with its originating forms tracked
• adjectiveScale: extracts a degree scale from a stem's paradigm
• morphologicalAlternatives: returns paradigm-mates as scalar alternatives

structure Core.Morphology.ScaleFromParadigm.MorphScale : Type

A morphologically-derived Horn scale, tracking the positive, comparative, and superlative forms.

• positive : String

  The positive (base) form

• comparative : String

  The comparative form

• superlative : String

  The superlative form

def Core.Morphology.ScaleFromParadigm.instReprMorphScale.repr : MorphScale → ℕ → Std.Format

Equations

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instance Core.Morphology.ScaleFromParadigm.instReprMorphScale : Repr MorphScale

Equations

• Core.Morphology.ScaleFromParadigm.instReprMorphScale = { reprPrec := Core.Morphology.ScaleFromParadigm.instReprMorphScale.repr }

def Core.Morphology.ScaleFromParadigm.instBEqMorphScale.beq : MorphScale → MorphScale → Bool

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• Core.Morphology.ScaleFromParadigm.instBEqMorphScale.beq x✝¹ x✝ = false

instance Core.Morphology.ScaleFromParadigm.instBEqMorphScale : BEq MorphScale

Equations

• Core.Morphology.ScaleFromParadigm.instBEqMorphScale = { beq := Core.Morphology.ScaleFromParadigm.instBEqMorphScale.beq }

def Core.Morphology.ScaleFromParadigm.MorphScale.toHornScale (ms : MorphScale) : Alternatives.HornScale String

Convert a MorphScale to a HornScale String, ordered from weakest (positive) to strongest (superlative).

Equations

• ms.toHornScale = { members := [ms.positive, ms.comparative, ms.superlative] }

def Core.Morphology.ScaleFromParadigm.adjectiveScale {σ : Type} (stem : Stem σ) : Option MorphScale

Extract a degree scale from a stem's paradigm.

Looks for rules with category =.degree and value = "comp" / "super", and builds a 3-point scale [positive, comparative, superlative]. Returns none if either the comparative or superlative rule is missing.

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def Core.Morphology.ScaleFromParadigm.morphologicalAlternatives {σ : Type} (stem : Stem σ) (form : String) : List String

Given a stem and a form (positive, comparative, or superlative), return the paradigm-mates as scalar alternatives.

Returns all scale members except the given form, preserving scale order (weakest to strongest).

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