Guerrini and Wehbe (2025): Homogeneity as presuppositional exhaustification #
Guerrini and Wehbe derive homogeneity by presuppositional exhaustification. A plural definite
contributes Bar-Lev's existential pluralization, and the operator pex of Del Pinal, Bassi and
Sauerland asserts it while presupposing that its subdomain alternatives are all true or all false.
Accommodating the presupposition yields the universal reading as long as no alternative for a single
atom is pruned (pexPlural_eq_one_iff), and pruning those yields non-maximal readings, at least
two of three students for the pairs of (21) (pexPlural_pairs_eq_one_iff). Under negation the
presupposition projects and the negated existential already entails it, so pruning has no effect
(pexPlural_eq_neg_one_iff).
Non-maximality under negation needs local accommodation below negation and a second pex over the
negated universal, which is the positive case for the negated predicate
(localAccommodation_nonMaximal).
Homogeneity is thus a presupposition, which a constraint on accommodation detects: a sentence is
felicitous only if its assertion is informative once its presupposition is accommodated
(Informative, the paper's (8)). She read the books is infelicitous where Mary is known to have
read some of them, the candidates lost where at most one candidate can win, and their negations
where the universal is known to fail, while the quantified counterparts are fine
(judgments_10, judgments_13).
Implementation notes #
A plurality is the domain of Bar-Lev's existential pluralization, the disjunction of its atoms,
and the alternatives are his subdomain alternatives, the sub-disjunctions, all of which are
innocently includable (Exhaustification.II_eq_self_of_subset_supClosure).
The common ground is a set of worlds and accommodation intersects it with the presupposition.
The higher pex of (24) and (27) does not change the truth conditions of a negated plural and
is not modelled.
TODO #
- The comparison with Križ and Chemla's gap judgments (§5.1) and with Paillé (§5.2).
- Projection from non-monotonic quantifiers, free choice and the modal cases of §6.
References #
Presuppositional exhaustification of plural predication (§4) #
A plural predication under pex, (19), asserts Bar-Lev's existential pluralization and
presupposes that its relevant subdomain alternatives are homogeneous.
Equations
- GuerriniWehbe2025.pexPlural D x P R = Exhaustification.pexIEII (supClosure (BarLev2021.atom P '' ↑(x ∩ D))) (⋃ b ∈ x ∩ D, BarLev2021.atom P b) R
Instances For
The presupposition (19b) is that the relevant subdomain alternatives are all true or all false.
In (20), after accommodation, a plural predication is universal as long as no alternative for a single atom is pruned.
In (25) and (28), a negated plural predication is true exactly where no atom satisfies the predicate, however the alternatives are pruned.
Post-Accommodation Informativity (§3) #
A sentence is informative in the common ground c after accommodation, Post-Accommodation
Informativity (8), when it is false at some world of c, its presupposition holding there.
Equations
- GuerriniWehbe2025.Informative c S = ∃ w ∈ c, S w = -1
Instances For
Where the existential is common ground, a plural predication asserts nothing new, (10a) and (13d).
Where the universal is known to fail, the negated plural predication asserts nothing new once homogeneity is accommodated, (10b), (12b), (13c) and (23).
Three students (§4, §5) #
Worlds record who smiled, and holds a w says that a smiled at w.
In (21), pruning to the alternatives over pairs of the three students makes the students smiled true after accommodation where at least two of them smiled.
Student a did not smile at w.
Equations
- GuerriniWehbe2025.notSmiled a w = (a ∉ w)
Instances For
In (31), with homogeneity accommodated below negation and no pruning, the students didn't smile is true where none of them smiled.
In (32)–(34), pruning the alternative for the third student makes the students didn't smile true when only that student smiled, a non-maximal reading under negation.
The judgments of §3 #
Each sentence is judged against the common ground its context sets up. Worlds record which books Mary read, which teammates John is married to, which candidates won, or which students smiled.
In (9), with John's kids known to be adopted, all 10 of John's kids are adopted asserts nothing once its presupposition that he has 10 kids is accommodated, while John has 10 adopted kids is informative. A world records how many kids John has and whether they are all adopted.
In (10), with Mary known to have read some of the books, she read the books asserts nothing new, and with her known not to have read all of them, neither does she didn't read the books.
In (12), since John is not married to all of his teammates, John isn't married to any of his teammates is informative, but John isn't married to his teammates asserts nothing new once homogeneity is accommodated.
In (13), where at most one candidate can win, none of the candidates won and all of the candidates lost are informative, but the candidates didn't win and the candidates lost assert nothing new once homogeneity is accommodated.
In (23), with the students known not to have all smiled, the students didn't smile asserts nothing new once homogeneity is accommodated.