Distributivity

In plural logic, a predicate $P$ is distributive over its argument $xx$ if and only if these two statements are equivalent:

1. $P(xx)$.
2. For all $x$ among $xx$, $P(x)$.

For example, ${\textsf {dua}}(x,y)$ distributes over both its arguments since if all of a group of people know several things, this means that each of them knows each of those things. Meanwhile, ${\textsf {gu}}(x)$ is non-distributive because each of two things are not themselves two.

Being explicit

Forcing distributivity

If you have a non-distributive verb like hao, how do you distribute it over some plural constant?

One way is to use the word shıcha “▯ satisfy property ▯ individually/one by one,” in a serial verb.

Shıcha hao náq.
The guys hao one by one.

Another is to use tú mea X “each among X”.

Hao tú mea náq.
Each of the guys haos.

Forcing non-distributivity

If you have a distributive verb like geı, how do you apply it to a plural subject without getting a distributive meaning?

😕 Geı ké deo gu tíefuq.
The two children (each) wear the coat.
Both D₁ wears T and D₂ wears T — nonsense.

One way is to use the word mecha “▯ satisfy property ▯ as a group,” in a serial verb.

Mecha geı ké deo gu tíefuq.
The two children wear the coat together.
(D₁+D₂) considered as a unit wears T

Another is to use me “an aggregate of….” An aggregate is a plural value wrapped in a singularizing wrapper, shielding it from effects like distributivity.

Geı ké me kê deo gu tíefuq.
The two-child-bundle wears the coat.
(D₁+D₂) considered as a unit wears T