@cite{alexandropoulou-gotzner-2024} — Gradable Adjective Interpretation Under Negation: The Role of Competition #
@cite{alexandropoulou-gotzner-2024}
In: Glossa: a journal of general linguistics 9(1), pp. 1–33.
Thesis #
@cite{alexandropoulou-gotzner-2024} (Glossa) tests whether the asymmetric vs. symmetric interpretation patterns of negated relative vs. absolute gradable adjectives — established in their @cite{alexandropoulou-gotzner-2024-jos} companion paper — depend on overt contextual competition between alternative expressions. The Glossa paper finds that contextual competition is necessary to surface the polarity asymmetry of relative adjectives but does not discriminate the symmetric interpretation patterns of weak absolute adjectives.
The structural precondition for the asymmetry remains the extension gap between contrary antonyms (two thresholds, with a borderline region) versus the absence of a gap for contradictory antonyms (single threshold, complementary partition). The competition mechanism the Glossa paper isolates operates on top of this structural distinction.
The paper situates its findings in the @cite{horn-1989} vs. @cite{krifka-2007b}
controversy over the source of negative strengthening; that controversy is
the central topic of the companion JoS paper, formalised in
AlexandropoulouGotzner2024JoS.lean. The Krifka-2007 hidden-agreement bridge
theorem (lexical commitment ↔ output of pragmatic strengthening) lives there.
Substrate consumed #
Theories/Semantics/Degree/Basic.lean—positiveMeaning,antonymMeaning,positiveMeaning_monotone(allProp-valued, decidable).Theories/Semantics/Gradability/Theory.lean—ThresholdPair,positiveMeaning',contraryNegMeaning,notContraryNegMeaning,inGapRegion(allabbrevs over the Core primitives).Theories/Semantics/Gradability/Antonymy.lean—contradictory_exhaustive,contradictory_is_complement(used in §4).Fragments/English/Predicates/Adjectival.lean—large/small/gigantic/tinyandclean/dirty/pristine/filthylexical entries.
Verified citations #
PDF audit of glossa-9919-alexandropoulou.pdf confirms: the precision-shift
mechanism (§7 here) is Glossa §4.2; equations (6a-b) are the contrary
non-entailments. The paper has five sections (ending at §5 Conclusion) — no
§6/§7/§9 paper-section refs exist; any internal "§N" labels in this file
refer to the Lean file's own structure, not to the paper.
Out of scope (deferred to JoS file) #
The three-case typology (weak relative / weak absolute / strong gradable),
the @cite{horn-1989} vs. @cite{krifka-2007b} prediction signatures, the
strong-adjective challenge to Horn, and the Krifka 2007 hidden-agreement
bridge theorem all live in AlexandropoulouGotzner2024JoS.lean.
A four-cell stimulus design: two pairs of antonymic adjectives at the weak/strong informational levels for a single dimension. The Glossa paper uses size (large/small/gigantic/tiny) as the relative case and cleanliness (clean/dirty/pristine/filthy) as the absolute case.
- weakPos : Semantics.Gradability.GradableAdjEntry
- weakNeg : Semantics.Gradability.GradableAdjEntry
- strongPos : Semantics.Gradability.GradableAdjEntry
- strongNeg : Semantics.Gradability.GradableAdjEntry
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A quadruple's relative-vs-absolute classification is derived from the
Fragment's scaleType: open scales (no inherent bounds) are relative;
bounded scales (lower/upper/closed) are absolute. The Fragment is the
single source of truth — this avoids the duplicate-stipulation pattern
the cross-framework reconciler flagged in the original audit.
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- q.isRelative = (q.weakPos.scaleType == Core.Scale.Boundedness.open_)
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5-degree scale (matching the 1–5 Likert response scales used in the Glossa experiments).
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Reference threshold pair: substrate-imposed θ_pos = 2, θ_neg = 1, giving a one-degree gap at deg 2. The Glossa paper does not commit to specific threshold values; this choice is a substrate convenience for stating Lean-checkable predictions.
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For contrary antonyms (ThresholdPair), the scale partitions into three
regions: positive, gap, negative. The gap is where "not positive"
diverges from "negative" — the structural basis for polarity asymmetry.
Every degree falls in at least one of {positive, gap, negative}.
Gap region excludes the positive region.
Gap region excludes the contrary-negative region.
Gap holds iff the degree is neither positive nor contrary-negative.
For contradictory antonyms (single θ), positive and antonym partition the scale with no gap: every degree satisfies exactly one. This is why absolute adjectives like clean/dirty show symmetric negation patterns in the Glossa experiments.
Contradictory antonyms exhaust the scale. Delegates to the substrate
lemma in Antonymy.lean.
antonymMeaning is the propositional complement of positiveMeaning.
Delegates to the substrate lemma in Antonymy.lean.
positiveMeaning_monotone (Core): higher threshold ⇒ informationally
stronger. This single substrate theorem grounds both:
1. Strong adjectives entail weak (gigantic ⇒ large).
2. Precision upshift entails standard (pristine-precision ⇒ standard
precision; cf. Glossa §4.2 precision-shift mechanism in §7 below).
Strong adjectives entail weak.
Concrete witness: degree 4 is positive at the weak threshold (thr 2) BECAUSE it is positive at the strong threshold (thr 3) and monotonicity propagates.
Precision upshift entails the standard reading: a degree satisfying "clean" at pristine precision (θ = 3) satisfies "clean" at standard precision (θ = 1). Same monotonicity theorem, different reading.
Lean-checkable witnesses for the structural predictions the Glossa paper makes about negated contrary antonyms. Theorem names describe what the proofs actually establish, not the pragmatic phenomena the names might suggest in informal exposition (negative strengthening, middling readings) — those are pragmatic inferences from the structural facts witnessed here, not the structural facts themselves.
At defaultTP, the bottom of the scale satisfies both "not positive" (the
antonym predicate) and the contrary-negative predicate. This overlap is a
necessary condition for negative strengthening (Glossa §1, Horn 1989)
but does not derive the pragmatic inference.
At defaultTP, degree 2 is in the gap: neither positive nor
contrary-negative. This is the structural basis for the "middling"
reading of not small discussed in the Glossa paper.
Polarity asymmetry: there exist witnesses for both (i) "not positive ⇒ negative" overlap (deg 0) and (ii) "not negative ⇏ positive" gap (deg 2).
Contrary non-entailment witnesses (Glossa eqs. 6a–b): (i) "not positive" does not entail "contrary negative" (deg 2 is a counterexample to not large ⇒ small). (ii) "not negative" does not entail "positive" (deg 2 is a counterexample to not small ⇒ large).
The contrary/contradictory split depends on antonym type, not on informational strength: weak (large/small) and strong (gigantic/tiny) relative adjectives both have contrary antonyms.
For contradictory antonyms, every degree is positive or in the antonym
region — no gap. Hence symmetric negation. Demonstrated at θ = thr 2
on Deg5 via contradictory_complement.
The Glossa paper's §4.2 proposes that absolute adjectives behaving relative-like under negation results from a precision-level shift driven by the availability of more-precise alternatives: clean in competition with a more demanding alternative reading (≈ pristine) takes the high-precision threshold, creating a structural gap.
The precision-shifted scale is encoded as a `ThresholdPair` with the
positive threshold raised. Note: the Glossa paper does not give an
operational specification for *which* precision parameter applies in
*which* discourse context; the mechanism is sketched, not formalised.
@cite{haslinger-2025}'s *potential p-equivalence* substrate addresses
related precision-shift phenomena via a different competition formalism;
bridging the two accounts is out of scope here.
ThresholdPair for the precision-upshifted "clean" scale: θ_pos = 3
(pristine precision), θ_neg = 1 (filthy threshold) — defaultTP with the
positive threshold raised one notch.
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Precision upshift creates a gap at degree 2.
The precision gap is genuine: degree 2 satisfies neither positive (at
pristine precision) nor contrary-negative. Reuses §3's gap_iff_neither
and the precision_gap witness.
Relative-adjective Fragment entries are classified as contrary.
Weak absolute Fragment entries are classified as contradictory.
Strong absolute Fragment entries are classified as contrary (extreme absolutes have a gap, per Glossa §3 / Kennedy & McNally 2005).
AdjQuadruple.isRelative agrees with the experimental design: size is
relative (open scale), cleanliness is absolute (closed scale). The
classification is structural — it reads off the Fragment's scaleType.
Size quadruple shares a dimension.
Cleanliness quadruple shares a dimension.