Alexandropoulou and Gotzner (2024b): adjective interpretation and competition

Alexandropoulou and Gotzner re-run the rating experiments of their 2024a paper with one statement per trial, removing the overt competition among the eight forms of an item. The polarity asymmetry of weak relative antonyms persists and is larger without competition, absolute antonyms stay symmetric in both modes, and negated weak absolutes (not dirty, not clean) are nonetheless rated differently from their truth-conditionally equivalent simple antonyms (clean, dirty).

The relative pattern is Horn's: R-strengthening of not large needs no competitor, while the middling reading of not small rides on the semantic gap. For absolutes the paper proposes that competition among equivalent forms invites a precision-level reasoning: clean is read at a high precision, opening a gap the complex forms fill. On a two-threshold scale this is exactly the observed profile — both negated weak forms come apart from their simple antonyms (relative_like) yet the residues are mirror images (residues_symmetric), whereas at a single threshold neither distinction exists (Degree.AntonymForm.contradictoryDenotation_synonymy).

References

• [AG24a]
• [AG24b]
• [Hor89]
• [Ken07b]

Precision-level gap

theorem AlexandropoulouGotzner2024b.residues_symmetric {D : Type u_1} [LinearOrder D] (tp : Degree.ThresholdPair D) : Degree.AntonymForm.strengthenedDenotation tp Degree.AntonymForm.notNegative \ Degree.AntonymForm.strengthenedDenotation tp Degree.AntonymForm.positive = Degree.AntonymForm.strengthenedDenotation tp Degree.AntonymForm.notPositive \ Degree.AntonymForm.strengthenedDenotation tp Degree.AntonymForm.negative

The two residues are the same region, the gap, so the distinctions are symmetric across polarity.

theorem AlexandropoulouGotzner2024b.relative_like {D : Type u_1} [LinearOrder D] (tp : Degree.ThresholdPair D) (h : tp.neg ≤ tp.pos) : (Degree.AntonymForm.strengthenedDenotation tp Degree.AntonymForm.notNegative \ Degree.AntonymForm.strengthenedDenotation tp Degree.AntonymForm.positive).Nonempty ∧ (Degree.AntonymForm.strengthenedDenotation tp Degree.AntonymForm.notPositive \ Degree.AntonymForm.strengthenedDenotation tp Degree.AntonymForm.negative).Nonempty

Under a precision-opened gap, not dirty is not clean and not clean is not dirty, the relative-like distinctions of the single-statement data.

Rows

theorem AlexandropoulouGotzner2024b.entails_iff_complementaryStandards (row : Datum) : row ∈ Examples.all → row.feature? "modifier" = none → row.feature? "negation" = some "negated" → ∀ p ∈ (row.feature? "adjective").bind English.Adjectives.pairOf, row.feature? "relation" = some "entails" ↔ p.ComplementaryStandards

An unmodified negated adjective entails its antonym exactly when the Fragment's pair takes complementary standards.

theorem AlexandropoulouGotzner2024b.readings_are_horn_ranges (row : Datum) : row ∈ Examples.all → ∀ f ∈ AlexandropoulouGotzner2024a.formOf row, ∀ i ∈ row.feature? "inference", (i = "negative_strengthening" ↔ AlexandropoulouGotzner2024a.hornRanges f = {Krifka2007b.Region.negative}) ∧ (i = "middling" ↔ AlexandropoulouGotzner2024a.hornRanges f = {Krifka2007b.Region.plateauLow, Krifka2007b.Region.plateauHigh})

The paper's two pragmatic readings are Horn's ranges, negative strengthening landing not large on the antonym and the middling reading landing not small on the gap.