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Putting plural definites into context

Romoli, J., Sudo, Y., Augurzky, P., Bonnet, M., Breheny, R., Cremers, A., Ebert, C., … Mayr, C. (2026). Manuscript, LingBuzz 007987

Source Bibliography Paper

Romoli et al. ask whether a context that makes a non-maximal reading relevant affects a plural definite bound by every, no, not every and exactly two, reanalysing the two experiments of Augurzky et al. (2023) and adding a third on exactly two boys opened their presents. On the symmetric approach, a truth-value gap projected by Strong Kleene and resolved by the question the context raises, the context affects positive and negative environments alike. On the asymmetric approach, Guerrini and Wehbe's presuppositional exhaustification below the quantifier with its presupposition accommodated globally, it affects positive ones only, including the positive part of exactly two. The third experiment found the negative part affected as much as the positive.

pointwise_exactlyTwo_ne_zero_iff and its siblings: the definedness conditions (25).

Implementation notes

A picture is the number of presents each boy opened. The contexts' questions are Augurzky et al.'s, lifted boy by boy, and pex applies at the lowest scope site only, as footnote 7 restricts it. The verdicts are bivalent, so they do not register effect sizes.

TODO

The differences in effect size across quantifiers (Table 12) need graded predictions, and with them the prior bias of §4.2 and the cost of local accommodation of §4.3.

References

Romoli et al. 2026, Putting plural definites into context
Augurzky et al. 2023, Putting plural definites into context formalized
Guerrini & Wehbe 2025, Homogeneity as Presuppositional Exhaustification formalized
Križ 2016, Homogeneity, Non-Maximality, and All formalized
Križ & Chemla 2015, Two Methods to Find Truth-Value Gaps and Their Application to the Projection Problem of Homogeneity formalized
Bar-Lev 2021, An Implicature Account of Homogeneity and Non-Maximality formalized

Sentences and contexts

Strong Kleene projection (25)

Exactly two is defined where two boys opened all presents and the rest none, more than two opened all, or fewer than two any (25d).

theorem pointwise_exactlyTwo_ne_zero_iff L170–177

{d : KrizChemla2015.Display} :

KrizChemla2015.pointwise (Quantifier.NumberTree.cardinal {2}) d ≠ 0 ↔ List.count 1 d = 2 ∧ List.count 0 d = 0 ∨ 2 < List.count 1 d ∨ List.count 1 d + List.count 0 d < 2

The symmetric approach (§2.1, §3.2.1)

L187–190

L192–202

L204–205

Over Strong Kleene and over Spector's supervaluation the symmetric verdict is the same, so the difference between them is immaterial (§3.2.1).

theorem symmetric_iff_nonImplicature L207–211

(q : Quantifier.NumberTree) [DecidableRel q] (ctx : AugurzkyEtAl2023.Context) (d : KrizChemla2015.Display) :

symmetric q ctx d ↔ AugurzkyEtAl2023.nonImplicature q ctx d

Built from

The asymmetric approach (§2.2, §3.2.2)

Guerrini & Wehbe 2025's pex on a boy's he opened his presents, over the alternatives the context leaves, is the value pexCell gives the number of his presents he opened.

theorem pexPlural_alternatives L254–278

(ctx : AugurzkyEtAl2023.Context) (w : Finset ℕ) :

GuerriniWehbe2025.pexPlural AugurzkyEtAl2023.nine AugurzkyEtAl2023.nine BarLev2021.holds (alternatives ctx) w = pexCell ctx (AugurzkyEtAl2023.nine ∩ w).card

Built from ,

In a scope-antitone environment, the asymmetric approach gives the existential reading in every context ((26), (27)).

theorem asymmetric_iff_of_scopeAntitone L335–343

{q : Quantifier.NumberTree} [DecidableRel q] (ctx : AugurzkyEtAl2023.Context) (opened : List ℕ) (hq : q.ScopeAntitone) :

asymmetric q ctx opened ↔ KrizChemla2015.someReading q (List.map KrizChemla2015.cell opened)

Built from

L346–352

Accommodated below the quantifier, the asymmetric approach gives the symmetric verdict, so only a cost of local accommodation keeps its asymmetry (§4.3) ((35)).

theorem localAccommodation_iff_symmetric L354–360

{q : Quantifier.NumberTree} [DecidableRel q] (ctx : AugurzkyEtAl2023.Context) (opened : List ℕ) :

localAccommodation q ctx opened ↔ symmetric q ctx (List.map KrizChemla2015.cell opened)

Built from ,

L363–366

L369–374

L379–383

Without pruning, exactly two boys opened their presents says after accommodation that two boys opened all of theirs and every other boy none (30).

theorem asymmetric_exactlyTwo_universal_iff L385–391

(opened : List ℕ) :

asymmetric (Quantifier.NumberTree.cardinal {2}) AugurzkyEtAl2023.Context.universal opened ↔ List.count 1 (List.map KrizChemla2015.cell opened) = 2 ∧ List.count 0 (List.map KrizChemla2015.cell opened) = 0

Built from

L394–398

The experiments

On the symmetric approach every sentence is accepted on its target pictures exactly in its lax context, Tables 1, 3, 6 and 9.

theorem predictions_symmetric L428–433

(p : Item) :

p ∈ pictures → ∀ pol ∈ p.targetFor, ∀ (c : Context), symmetric (sentences p.experiment pol).quantifier.tree c.raises p.display ↔ c = Recoding.lax.context pol

Built from , , , ,

On the asymmetric approach, target pictures are accepted only for the positive sentence in the prohibiting context (Tables 2, 4, 7 and 10).

theorem predictions_asymmetric L435–440

(p : Item) :

p ∈ pictures → ∀ pol ∈ p.targetFor, ∀ (c : Context), asymmetric (sentences p.experiment pol).quantifier.tree c.raises p.opened ↔ pol = Polarity.positive ∧ c = Context.prohibited

Built from , ,

The implicature approach as Augurzky et al. 2023 state it treats exactly two as it treats every, accepting the negative target of Experiment 3 where the presents are required to be opened, which the asymmetric approach rejects.

theorem implicature_negativeTarget L442–449

(p : Item) :

p ∈ pictures → p.experiment = Experiment.three → Polarity.negative ∈ p.targetFor → AugurzkyEtAl2023.implicature Quantifier.exactlyTwo.tree AugurzkyEtAl2023.Context.universal p.display ∧ ¬asymmetric Quantifier.exactlyTwo.tree AugurzkyEtAl2023.Context.universal p.opened

Built from , ,

The reanalysis and Table 12

L453–456

L458–463

The reanalysis of Experiments 1 and 2 excludes 4 and 6 participants where Augurzky et al. 2023 excluded 7 and 10, and changes every χ², but no test's significance at the .05 level.

theorem significant_iff_augurzky L465–471

(t : AugurzkyEtAl2023.Test) :

t ∈ AugurzkyEtAl2023.tests → t.model = AugurzkyEtAl2023.Model.mixed → ∀ e ∈ Effect.ofAugurzky t.effect, (tests (Experiment.ofAugurzky t.experiment) e).p.Significant (1 / 20) ↔ t.p.Significant (1 / 20)

Built from ,

L473–481

The Likert effect sizes of Table 12 are the lax-minus-strict differences of the target means of Figures 4, 6 and 8.

theorem effectSizes_likert L483–487

(x : Experiment) (pol : Polarity) :

∃ l ∈ targetMean x pol Recoding.lax, ∃ s ∈ targetMean x pol Recoding.strict, l - s = (effectSizes x pol).likert.toRat

Built from

The log-odds effect sizes of Table 12 are the CONTEXT estimate, plus the interaction for the positive condition, up to rounding (Tables 5, 8 and 11).

theorem effectSizes_logOdds L489–495

(x : Experiment) (pol : Polarity) :

|((estimates x Term.context).beta.toRat + if pol = Polarity.positive then (estimates x Term.interaction).beta.toRat else 0) - (effectSizes x pol).logOdds.toRat| ≤ 1 / 100