Blind Mandatory Scalar Implicatures #
@cite{magri-2009}
@cite{magri-2009}. Natural Language Semantics 17(3): 245–297.
Two hypotheses form the core of the paper:
Blindness Hypothesis (BH) (§3.2.2): The exhaustivity operator EXH computes the strengthened meaning using logical entailment (→W), not entailment given common knowledge (→{W_ck}). That is, whether an alternative is excludable is determined without consulting CK.
Mismatch Hypothesis (MH) (§3.2.2, item (33)): If the blind strengthened meaning EXH(φ) is a contradiction given common knowledge (EXH(φ) ∩ W_ck = ∅), then φ sounds odd.
Introductory Example #
"# Some Italians come from a warm country" (ex. (2))
- Literal: some Italians come from a warm country
- Strengthened (blind, via BH): some BUT NOT ALL Italians come from a warm country
- CK: Italy is warm → all Italians come from a warm country
- Strengthened ∩ CK = ∅ → odd (via MH)
Application to Individual-Level Predicates #
The paper's main contribution (§4) derives properties of individual-level predicates (ILPs) from BH + MH via assumption (70): ILPs are homogeneous — if an i-predicate holds at any time in W_ck, it holds at all times. This homogeneity makes blind strengthening systematically contradict CK for i-predicate constructions.
Key applications: "#Sometimes, John is tall" (§4.1), bare plural subject restrictions (§4.2), embedding under universal quantifiers (§4.3), and German word order (§4.5). See §5 below for the Q-adverb formalization.
The ILP/SLP distinction is @cite{carlson-1977}'s PredicateLevel:
individual-level predicates trigger homogeneity (assumption (70)), while
stage-level predicates do not.
A scenario for blind scalar implicature computation.
@cite{magri-2009}'s mechanism needs only literal meanings, scalar alternatives, and common knowledge — no QUD or complexity ordering.
- meaning : U → W → Bool
Literal meaning of each utterance at each world.
- alternatives : U → List U
All scalar alternatives for each utterance. @cite{fox-2007}'s innocent exclusion algorithm (
ieIndices) determines which alternatives are excludable — weaker alternatives (e.g., "some" when the prejacent is "all") are automatically filtered out by the non-weaker check (NW). - context : W → Bool
Common knowledge: which worlds are CK-compatible.
- worlds : List W
Exhaustive world enumeration.
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CK-compatible worlds.
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- s.cWorlds = List.filter s.context s.worlds
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Strengthened meaning via @cite{fox-2007}'s exhaustivity operator.
Implements the Blindness Hypothesis (BH): EXH computes the strengthened meaning using logical entailment over W, not entailment given common knowledge W_ck. The grammar strengthens automatically, even when the result contradicts what speaker and hearer both know.
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- s.strengthened u w = Exhaustification.InnocentExclusion.exhB s.worlds (List.map s.meaning (s.alternatives u)) (s.meaning u) w
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Blind oddness: the exhaustivity operator produced a non-vacuous implicature, yet the strengthened meaning is false at every CK world.
Implements the Mismatch Hypothesis (MH): if EXH(φ) ∩ W_ck = ∅ (the blind strengthened meaning contradicts common knowledge), then φ sounds odd.
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"# Some Italians come from a warm country" (@cite{magri-2009})
Three worlds are needed because the strengthened meaning "some but not all" requires a world where some but not all Italians come from a warm country.
CK: Italy is a warm country → all Italians come from a warm country.
Only allWarm is CK-compatible.
- allWarm : ItalyWorld₃
- someNotAll : ItalyWorld₃
- noneWarm : ItalyWorld₃
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Strengthened "some" at allWarm is false: some(allWarm) ∧ ¬all(allWarm) = true ∧ false = false. The blind implicature "not all" kills the literal meaning at the CK world.
Strengthened "some" at someNotAll is true: some(someNotAll) ∧ ¬all(someNotAll) = true ∧ true = true. But someNotAll is ruled out by CK — no help.
@cite{magri-2009} prediction: "some Italians" is odd. The blind implicature "not all" contradicts CK (Italy is warm).
"all Italians" is not odd: no stronger alternative to negate, so no blind implicature is generated.
@cite{magri-2009} ex. (3)/(72b): "# Sometimes, John is tall"
The paper's main contribution derives oddness of Q-adverbs with individual-level predicates (ILPs) from BH + MH. The key assumption homogeneity (assumption (70)): if an i-predicate holds of an individual at any time in W_ck, it holds at all times. This rules out mixed worlds (tall at some times but not all) from the common ground.
- Literal: at some times, John is tall
- Strengthened (blind, via BH): at some but NOT ALL times, John is tall
- CK: "tall" is an ILP → homogeneity → John is either always tall or never tall. The "sometimes but not always" world is CK-incompatible.
- Strengthened ∩ CK = ∅ → odd (via MH)
Contrast with the stage-level predicate "Sometimes, John is available": since availability can genuinely vary over time, the "sometimes but not always" world is CK-compatible → strengthened meaning is satisfiable → OK.
The ILP/SLP distinction is @cite{carlson-1977}'s PredicateLevel:
individual-level → homogeneity → oddness; stage-level → no homogeneity → fine.
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@cite{magri-2009} §4.1: Q-adverbs with individual-level predicates.
"Sometimes" and "always" form a ⟨sometimes, always⟩ scale analogous to
⟨some, all⟩. Homogeneity (assumption (70)) rules out sometimesOnly
from the common ground.
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Strengthened "sometimes" at alwaysTall is false: sometimes(alwaysTall) ∧ ¬always(alwaysTall) = true ∧ false = false.
Strengthened "sometimes" at neverTall is also false: sometimes(neverTall) = false.
@cite{magri-2009} prediction: "# Sometimes, John is tall" is odd. The blind implicature "not always" contradicts homogeneity (70).
"Always, John is tall" is fine: no stronger alternative exists.
Homogeneity determines which worlds are CK-compatible.
@cite{magri-2009} assumption (70): if an i-predicate holds of an individual at any time in a CK-compatible world, it holds at all times within that individual's lifespan. This makes the predicate "homogeneous."
This maps @cite{carlson-1977}'s PredicateLevel to a CK context:
- Individual-level → only homogeneous worlds are CK-compatible
- Stage-level → all worlds are CK-compatible (the predicate can genuinely vary over time)
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The context function of tallScenario is exactly what ILP
homogeneity predicts for individual-level predicates.
Stage-level contrast scenario: "Sometimes, John is available."
Same literal semantics and scale as the tall scenario, but CK admits all worlds because availability is stage-level — it CAN genuinely vary over time. The homogeneity assumption (70) does not apply.
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The context of availableScenario matches stage-level homogeneity:
all worlds are CK-compatible.
"Sometimes, John is available" is NOT odd.
Stage-level predicates don't trigger homogeneity (70), so sometimesOnly
is CK-compatible and the strengthened meaning is satisfiable.
The ILP/SLP distinction determines oddness: individual-level + "sometimes" → odd; stage-level + "sometimes" → fine.
This is the structural prediction: @cite{carlson-1977}'s PredicateLevel
feeds into @cite{magri-2009}'s blindness mechanism via homogeneity (70).
The contexts genuinely differ: sometimesOnly is CK-incompatible
for individual-level (tall) but CK-compatible for stage-level (available).
Homogeneity (70) is necessary and sufficient for Q-adverb oddness.
The two scenarios have identical literal semantics, identical scale
structure, and identical worlds. The ONLY difference is the CK context,
which is determined by @cite{carlson-1977}'s PredicateLevel via
homogeneity. Yet this single difference flips the oddness prediction:
- Individual-level ("tall"): context rules out
sometimesOnly→ strengthened meaning contradicts CK → odd - Stage-level ("available"): context admits
sometimesOnly→ strengthened meaning satisfiable at CK world → fine
This proves that @cite{carlson-1977}'s predicate-level classification is doing genuine explanatory work in @cite{magri-2009}'s system: it is the SOLE factor determining oddness for Q-adverb sentences.
Context characterization theorem #
The existing proofs show that specific context functions (homogeneity, stage-level) produce or prevent oddness. But what characterizes the oddness- producing contexts in general?
For the ⟨sometimes, always⟩ scale, oddness of "sometimes" depends on a single
Boolean condition: whether the "mixed" world (sometimesOnly) is CK-compatible.
This is because the strengthened meaning "sometimes but not always" is true
only at the mixed world — so EXH(φ) ∩ W_ck = ∅ iff the mixed world is
excluded from CK.
This theorem is universally quantified over all possible context functions, not just the two tested above. It explains why @cite{carlson-1977}'s predicate-level classification does the right work: individual-level predicates produce oddness precisely because homogeneity rules out the mixed world.
For any context function on the ⟨sometimes, always⟩ scale, oddness of "sometimes" is equivalent to ruling out the mixed world from CK.
This characterizes EXACTLY which contexts produce oddness, independently of any specific predicate-level classification. The proof factors the abstract context into its 3 constructor values (8 cases) and verifies each computationally.
Homogeneity (70) produces oddness because it rules out the mixed world.
SLP permits "sometimes" because it admits the mixed world.
Bare plural subject restrictions #
@cite{magri-2009} §4.2: the BPS firemen of the s-predicate available admits both the existential and generic readings (ex. (84a)):
- ∃-BPS: "There are firemen who are available"
- GEN-BPS: "Firemen are generally available"
But the BPS of the i-predicate tall lacks the existential reading (84b):
- #∃-BPS: "There are firemen who are tall"
- GEN-BPS: "Firemen are (generally) tall"
@cite{magri-2009}'s key insight: the ∃-BPS reading of an ILP has the SAME abstract structure as "#Sometimes, John is tall" (§4.1). This is because existential BPs always take narrowest scope (@cite{carlson-1977}), making narrow-scope ∃ over times equivalent to "sometimes." The definite description alternative plays the role of "always." Homogeneity (70) rules out the partial world, so the strengthened meaning contradicts CK.
We model this with independent types and prove the meaning table is isomorphic to the Q-adverb scenario from §5.
Worlds for the bare plural ∃-reading of "Firemen are tall."
@cite{magri-2009} §4.2: the truth conditions (91b)/(92b) involve ∃ over firemen and time. The three worlds correspond to whether any fireman is tall throughout his lifespan within the contextually supplied restrictor.
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The bare plural reading and its definite-description alternative.
Following the Heim-Diesing framework: the BP introduces a free variable bound by a default existential operator (DEO) with VP scope.
The Horn scale is ⟨bare plural, definite description⟩ (eq. (94)):
the BP firemen alternates with the fireman P for each specific
fireman P. In the 3-world model, the definite-description alternative
ψ (eq. (95)) is extensionally equivalent to the GEN-BPS reading φ
(eq. (91b)), so we model both as generic_.
- existential_ : BPSReading
- generic_ : BPSReading
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@cite{magri-2009} §4.2: bare plural existential reading of an ILP.
existential_(φ', (92b)): ∃_t[C̄(t)][∃x(fireman(x) ∧ tall(x,t))] "for some time t in C̄, there exists a fireman who is tall at t"generic_(φ, (91b)): GEN_t[C̄(t)][∃x(fireman(x) ∧ tall(x,t))] "for generically all times t in C̄, there exists a fireman who is tall at t"
Homogeneity (70) rules out partialOnly: if fireman d is tall at
any time, d is tall at ALL times within his lifespan.
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The ∃-BPS reading of ILP "Firemen are tall" is odd. Blind strengthening derives "∃ fireman tall at some times BUT no fireman tall throughout" — contradicting homogeneity (70).
The GEN-BPS reading of ILP "Firemen are tall" is fine.
Stage-level counterpart: ∃-BPS reading of "Firemen are available."
Same meaning structure, but all worlds CK-compatible because availability can genuinely vary over time (no homogeneity).
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The ∃-BPS reading of SLP "Firemen are available" is fine.
The BPS scenario's meaning table is isomorphic to the Q-adverb scenario: "∃-BPS at world w" has the same truth value as "sometimes at the corresponding Q-adverb world."
This is @cite{magri-2009}'s reduction (p. 275): "the existential reading of the BPS of sentence (84b) can be ruled out in exactly the same way as sentence (46a)."
The context functions match: homogeneity rules out the same "mixed" world in both scenarios.
Universal quantifier rescue #
@cite{magri-2009} §4.3, building on @cite{fox-1995}: the ∃-BPS reading of an i-predicate becomes available when the BP is embedded under a universal quantifier.
- (102a) "Jewish women are related to Chomsky" — no ∃ reading
- (102b) "Jewish women are related to every Jewish man" — ∃ reading available
In (102b) the existential over Jewish women takes wide scope over both the generic operator AND the universal quantifier every Jewish man. This creates a "distributed witnesses" world — woman a₁ related to man b₁, a₂ to b₂ — where EXH(φ) = φ ∧ ¬ψ is satisfiable.
Under homogeneity, "related" is permanent: once a₁ is related to b₁, she always is. But this doesn't prevent different women from being related to different men. The distributed-witnesses world is CK-compatible, so the strengthened meaning is not vacuous at CK worlds → not odd.
The structural insight: the rescue scenario has the SAME context as the stage-level scenario (all worlds CK-compatible), despite a different reason. For SLPs, variability over time admits the mixed world. For universal embedding, distributed witnesses admit the mixed world. @cite{magri-2009}'s mechanism produces the correct prediction in both cases: the mixed world survives in CK.
@cite{magri-2009} §4.3: universal quantifier rescue of ∃-BPS reading.
The meaning table matches the ⟨some, all⟩ pattern:
sometimes_(φ): "for every Jewish man, ∃ a related Jewish woman"always_(ψ): "∃ a Jewish woman related to EVERY Jewish man"
The three worlds under the correspondence:
alwaysTall→ "concentrated": one woman related to all men (φ ∧ ψ)sometimesOnly→ "distributed": different women for different men (φ ∧ ¬ψ)neverTall→ "none": some man has no related woman (¬φ ∧ ¬ψ)
All worlds are CK-compatible because homogeneity for "related" (each woman-man relationship is permanent) is compatible with distributed witnesses.
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The ∃-BPS reading under a universal quantifier is NOT odd. The distributed-witnesses world is CK-compatible, so the strengthened meaning is satisfiable at a CK world.
The rescue context matches the SLP context: both admit all worlds.
For SLPs: the predicate can genuinely vary over time → no worlds ruled out. For universal rescue: distributed witnesses are CK-compatible → no worlds ruled out. Different reasons, same abstract effect.
Three-way structural comparison:
| Scenario | Context type | Mixed world CK? | Odd? |
|---|---|---|---|
| ILP Q-adverb | Homogeneity (70) | No | Yes |
| SLP Q-adverb | All worlds | Yes | No |
| ILP + ∀ | All worlds | Yes | No |
All three share the same meaning table and alternatives. Oddness is
entirely determined by whether the context rules out the mixed world —
as proved by oddness_iff_mixed_excluded.
BH_prs and MH_prs #
@cite{magri-2009} extends BH and MH to presuppositions (§3.4, eqs. 64–66):
BH_prs (65): The strengthened presupposition EXH_prs(φ) is computed using logical entailment, not entailment given common knowledge.
MH_prs (66): If the blind strengthened presupposition contradicts common knowledge (EXH_prs(φ) ∩ W_ck = ∅), then φ sounds odd.
The strengthened presupposition mirrors standard EXH but operates on the presupposition dimension:
EXH_prs(φ) = φ_prs ∧ ∧_{ψ ∈ Excl_prs(φ)} ¬ψ_prs
where Excl_prs uses @cite{fox-2007}'s innocent exclusion applied to
presuppositions. This reuses exhB/ieIndices directly — the same
algorithm, applied to a different dimension of meaning.
A scenario with both meanings and presuppositions for blind SI computation.
@cite{magri-2009} §3.4: presupposition strengthening runs in parallel to meaning strengthening, using the same @cite{fox-2007} algorithm.
- alternatives : U → List U
- presup : U → W → Bool
Presupposition carried by each utterance.
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Strengthened presupposition via @cite{fox-2007}'s EXH applied to presuppositions.
Implements BH_prs: the strengthening uses logical entailment over W, not entailment given common knowledge.
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- s.strengthenedPresup u w = Exhaustification.InnocentExclusion.exhB s.worlds (List.map s.presup (s.alternatives u)) (s.presup u) w
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Blind presuppositional oddness: EXH_prs(φ) ∩ W_ck = ∅.
Implements MH_prs (66): if the blind strengthened presupposition contradicts common knowledge, the sentence sounds odd.
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"#John is always tall" via presuppositional mismatch #
@cite{magri-2009} §4.6: always and covert GEN are Horn-mates with the same denotation but different presuppositions. Overt always carries no homogeneity presupposition; covert GEN carries the homogeneity presupposition (eq. (137)): either ALL atomic parts of the restrictor satisfy the scope or NONE do (YES ∪ NO).
The oddness of "#John is always tall" is derived via MH_prs (66):
- φ_prs (always) = W (trivial presupposition)
- ψ_prs (GEN) = YES ∪ NO (homogeneity presupposition)
- ψ_prs asymmetrically entails φ_prs (YES ∪ NO ⊂ W)
- EXH_prs(φ) = φ_prs ∧ ¬ψ_prs = ¬(YES ∪ NO) = mixed worlds only
- CK (from assumption (70)): W_ck = YES ∪ NO (homogeneity for ILPs)
- EXH_prs(φ) ∩ W_ck = ∅ → odd via MH_prs
The contrast with "John is tall" (= covert GEN): GEN has no stronger presuppositional alternative, so EXH_prs is vacuous and no mismatch arises.
The reuse of TallWorld is structural: the three worlds — alwaysTall,
sometimesOnly, neverTall — serve double duty across meaning (§5)
and presupposition (§10).
Utterance type for the ⟨always, GEN⟩ Horn scale.
- always_ : AlwaysGENUtt
- gen_ : AlwaysGENUtt
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@cite{magri-2009} §4.6: always vs covert GEN.
The two utterances have IDENTICAL denotation (both mean "at all times, John is tall") but DIFFERENT presuppositions:
- always: φ_prs = W (no homogeneity presupposition)
- GEN: ψ_prs = {alwaysTall, neverTall} (homogeneity: YES ∪ NO)
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GEN's presupposition matches homogeneity: the same predicate as the CK context. This is not coincidence — assumption (70) says W_ck is exactly the set of homogeneous worlds, and GEN presupposes homogeneity.
always has trivial (universal) presupposition.
The strengthened presupposition of always asserts ¬(YES ∪ NO), i.e., that there ARE mixed worlds — which is exactly what homogeneity rules out.
@cite{magri-2009} §4.6: "#John is always tall" is odd via MH_prs.
The blind strengthened presupposition (= ¬homogeneity = mixed worlds only) contradicts CK (= homogeneity = no mixed worlds).
"John is tall" (= covert GEN) is NOT odd via MH_prs.
GEN has no stronger presuppositional alternative — always is presuppositionally weaker (trivial presupposition ⊂ homogeneity presupposition is backwards). Since GEN's presupposition entails always's, always is not excludable w.r.t. GEN.
Meanings are identical but oddness differs — the presupposition is doing ALL the work. This is a pure presuppositional effect: the same mechanism (BH + MH) applied to a different dimension of meaning.
Predictions match empirical BPS data #
@cite{magri-2009}'s theory predicts that individual-level predicates block
the existential reading of bare plural subjects. The data in
Phenomena.Generics.BarePlurals independently records these judgments
as empirical observations (@cite{cohen-erteschik-shir-2002}).
The bridge theorems verify that every ILP datum with
existentialOK = false is correctly predicted by the BH+MH mechanism,
and every SLP-with-locative-argument datum with existentialOK = true
is correctly predicted as non-odd.
All individual-level predicates in the BarePlurals data lack the existential reading — matching @cite{magri-2009}'s prediction that the ∃-BPS of an ILP is odd (BH + MH + homogeneity).
All stage-level predicates with locative arguments in the BarePlurals data HAVE the existential reading — matching @cite{magri-2009}'s prediction that the ∃-BPS of an SLP is fine (no homogeneity → no mismatch).
The BPS scenario for ILPs is odd, AND the ILP data independently confirms no existential reading. Cross-validation between theory (BH+MH) and empirical observation.
The BPS scenario for SLPs is fine, AND the SLP-argument data independently confirms existential reading available.
German BPS word order matches BH+MH predictions #
@cite{magri-2009} §4.5 argues that @cite{diesing-1992}'s German BPS word order contrast (BPS left vs right of ja doch) follows from BH+MH:
- S-predicate BPS both positions OK → BH+MH: no mismatch (SLP)
- I-predicate BPS left only → BH+MH: right-of-ja doch = VP-internal = existential reading only → mismatch with homogeneity → odd
The data in Fragments.German.BarePluralWordOrder independently records
this pattern. The bridge theorem confirms that the oddness pattern in
the German data aligns with the model scenarios.
The German ja doch data confirms the same ILP/SLP split: the ONLY unacceptable configuration is ILP + right of ja doch (= VP-internal = existential-only reading).
- ILP right of ja doch → odd: matches
bpsScenario.blindOdd .existential_ - SLP both positions → fine: matches
bpsSLPScenario.blindOdd .existential_ - ILP left of ja doch → fine: the GEN reading is available (not blocked)
"Firemen are always tall" is fine (§4.6.2 Remark) #
@cite{magri-2009} §4.6.2: "#John is always tall" is odd (§10 above), but "Firemen are always tall" is FINE when the definite John is replaced by a bare plural.
The key difference: with a bare plural subject, the strengthened presupposition ¬ψ_prs asserts that homogeneity fails for the restrictor (some firemen are tall, others aren't). This is NOT a contradiction given common knowledge — there are CK-compatible worlds where some firemen are tall and others aren't.
This shows the presuppositional mechanism is sensitive to the logical form of the subject: definite subjects (John) produce oddness because homogeneity must hold for a single individual; bare plural subjects (firemen) don't because different individuals can differ.
Worlds for "Firemen are always tall" with bare plural subject.
With a bare plural, the homogeneity presupposition of GEN quantifies over firemen: either ALL firemen are tall or NONE are. But CK for a bare plural does NOT rule out mixed worlds (some tall, some not).
- allTall : BPAlwaysWorld
- mixedFiremen : BPAlwaysWorld
- noneTall : BPAlwaysWorld
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@cite{magri-2009} §4.6.2: always vs GEN with bare plural subject.
Meanings are identical (both: "all firemen are always tall"), but presuppositions differ. GEN's homogeneity presupposition says either all firemen are tall or none are (YES ∪ NO). But with a bare plural, the mixed world (some tall, some not) IS CK-compatible.
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"Firemen are always tall" is NOT odd via MH_prs.
The strengthened presupposition ¬ψ_prs = {mixedFiremen} is satisfiable at a CK world (mixedFiremen is CK-compatible for bare plurals), so MH_prs does not fire.
Contrast: same logical structure, different subjects, different oddness.
- "#John is always tall" (definite): odd via MH_prs (§10)
- "Firemen are always tall" (bare plural): fine (§4.6.2)
The difference: CK for a definite (John) rules out the mixed world (homogeneity for one individual), while CK for a bare plural does not (different firemen can differ).
AlternativeSource instance for the Italian ⟨some, all⟩ scale.
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Exhaustifying via AlternativeSource agrees with BlindScenario.strengthened.
BlindScenario carries its own alternatives field; here we show that
deriving alternatives from the AlternativeSource typeclass produces
the same exhaustified meaning. The key: including the assertion in the
alternative list (AlternativeSource convention) doesn't change the
result — exhB filters it out via the non-weaker check.