Zimmermann (2026): African Lambdas I, The Nominal Domain

Zimmermann's review of formal semantic work on African languages compares two marked indefinites in its §3.3. Akan bí and Hausa wani have nearly the same distribution, but under negation a wani phrase takes either scope, (13), while a bí phrase takes only wide scope, (15). The review concludes that they need different analyses, (16): a choice function skolemized to a situation for bí, after Owusu, and an existential quantifier for wani, after Zimmermann's earlier work. It explains the scope of bí by negation not being an intensional operator, so that negation cannot shift the situation argument of the function.

Main results

• wani_scopings_diverge: under the existential analysis the two scopings of wani under negation differ, on the passenger model of Zimmermann2008.
• bi_reading_not_narrow: under the choice-function analysis bí under negation does not give the narrow reading when the restrictor has two members.
• bi_negation_construals_collapse: under negation the free and bound construals of the situation argument of bí coincide.

Implementation notes

• Only the comparison the review itself draws is formalized; the two analyses are consumed from the studies of their primary sources.
• Bare noun phrases, which take obligatory narrow scope in both languages, are outside the classification of (16).

TODO

• The Ga markers ko and kome of (17) and the co-occurrence of definite and indefinite markers of (18).

References

• [Zim26]
• [Zim14]
• [Zim08]
• [Owu22]

theorem Zimmermann2026.wani_scopings_diverge : ¬((¬∃ (x : Zimmermann2008.Faasinjee), Zimmermann2008.Daura x) ↔ Quantifier.GQ.some (fun (x : Zimmermann2008.Faasinjee) => True) fun (x : Zimmermann2008.Faasinjee) => ¬Zimmermann2008.Daura x)

Under the existential analysis (16b) the two scopings of wani under negation in (13) differ, since on the passenger model of [Zim08] the wide scoping holds and the narrow one fails.

theorem Zimmermann2026.bi_reading_not_narrow {S : Type u_1} {E : Type u_2} (f : S → Reference.ChoiceFunction E) {s : S} {P : S → E → Prop} {a b : E} (ha : P s a) (hb : P s b) (hab : a ≠ b) : ¬∀ (VP : E → Prop), ¬VP ((f s) (P s)) ↔ ¬Quantifier.GQ.some (P s) VP

Under the choice-function analysis (16a) bí under negation, as in (15), is not the narrow reading. When the restrictor has two members, the negated pick and the negated existential differ on some predicate.

theorem Zimmermann2026.bi_negation_construals_collapse {S : Type u_1} {E : Type u_2} (f : S → Reference.ChoiceFunction E) (s₀ : S) (P : S → E → Prop) (VP : E → S → Prop) : (fun (p : S → Prop) (s : S) => ¬p s) (fun (s : S) => VP ((f s) (P s)) s) s₀ ↔ (fun (p : S → Prop) (s : S) => ¬p s) (fun (s : S) => VP ((f s₀) (P s₀)) s) s₀

The review explains (15) by negation not being an intensional operator, so that it cannot shift the situation argument of the choice function away from the resource situation. An operator is extensional exactly when it cannot tell an argument whose situation it binds from the same argument with the situation fixed (ModalLogic.isExtensionalAt_iff_forall_diag), and pointwise negation is extensional, so under negation the bound and the free construals of the situation argument of bí coincide, for any function and restrictor.