A donkey sentence is a kind of sentence that occurs in natural language, where an anaphoric pronoun (like hó) refers to a quantified variable (like sa ảqshe) even though it is outside of that variable's scope.
It is named after the following prototypical example of such a sentence:
Kỉaı tu hảqpaoche bö hóa sa ảqshe cy, áqshe da.
“Every farmer who owns a donkey, cares for it.”
The English sentence is clearly valid English. But the straightforward translation into logic of such a sentence is not well-formed:
⚠️ ∀f : Farmer(f) ∧ ∃d [Donkey(d) ∧ Owns(f, d)] → Cares(f, d).
The underlined instance of variable d is illegal, because it is outside of the scope of the quantifier ∃d.
Is the above Toaq sentence valid? What does it mean?
Hoemaı considers the case of anaphoric reference to a binding from a previous sentence not so different, and calls such pronouns donkey as well. There is then a "crude handling of donkey pronouns" demonstrated in On quantifiers and variables:
Kảqgaı jí sa gủoso da. Nủo gúoso da.
[∃G : guoso(G)] kaqgaı(J,G). [∀R : raı(R) ∧ guoso(R) ∧ kaqgaı(J,R)] nuo(R).
“I see some cows. They (the cows) are asleep.”
“I see some cows. All the cows that I see are asleep.”
Note the "surprising ∀ quantifier" in the logical translation of the second sentence. For as long as gúoso is logically out of scope, but not explicitly rebound, it refers to "all the cows that I see". “The point of it is to catch the same things as appeared in the previous sentence … instead of just any.”
Applying this same "crude handling" to quantifiers in subclauses, the meaning of the Toaq sentence above is: "All farmers who own some donkeys, care for all the donkeys that they own." This is often sufficient.
"If you have a pet, then the pet in the previously mentioned state of affairs does XYZ." — Hoemaı
"Tu rảı güo kâqgaı jí sa kủsera bı … the one who participates in the guo by seeing something, likes the thing that participates in the guo by being seen." — Hoaqgīo