View source for Donkey sentence

A '''donkey sentence''' is a kind of sentence that occurs in natural language, where an anaphoric pronoun (like {{t|hó}}) refers to a quantified variable (like {{t|sa ảqshe}}) even though it is outside of that variable's scope.

It is named after the following prototypical example of such a sentence:

{{Example|Kỉaı tu hảqpaoche bö hóa sa ảqshe cy, <u>áqshe</u> da.|“Every farmer who owns a donkey, cares for <u>it</u>.”}}

The English sentence is clearly valid English. But the straightforward translation into logic of such a sentence is not well-formed:

<blockquote>⚠️ ∀''f'' : Farmer(''f'') ∧ ∃''d'' [Donkey(''d'') ∧ Owns(''f'', ''d'')] → Cares(''f'', <u>''d''</u>).</blockquote>

The underlined instance of variable ''d'' is illegal, because it is outside of the scope of the quantifier ∃''d''.

== In Toaq ==
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 "[https://discord.com/channels/311223912044167168/311223912044167168/877607261684518922 crude handling of donkey pronouns]" demonstrated in [https://toaqlanguage.wordpress.com/2019/07/24/on-quantifiers-and-variables-grammar-update/ ''On quantifiers and variables'']:

<blockquote>{{t|Kảqgaı jí sa gủoso da. Nủo gúoso da.}}<br>[∃G : guoso(G)] kaqgaı(J,G). [∀R : raı(R) ∧ guoso(R) ∧ kaqgaı(J,R)] nuo(R).<br>“I see some cows. They (the cows) are asleep.”<br>“I see some cows. All the cows that I see are asleep.”</blockquote>

Note the "surprising ∀ quantifier" in the logical translation of the second sentence. For as long as {{t|gúoso}} is logically out of scope, but not explicitly rebound, it refers to "'''all''' the cows that I see". [https://discord.com/channels/311223912044167168/311223912044167168/877608075857637386 “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.

Hoemāı remarked that [https://discord.com/channels/311223912044167168/311223912044167168/877608281156243487 "donkey anaphora can't really be allowed in Toaq, unless you use a separate set of pronouns or a donkey conversion mechanism. Otherwise you get ambiguity."]

One idea is to explicitly anaphorically refer back to the construct containing the now-unbound variable and talk about its participants, as proposed [https://discord.com/channels/311223912044167168/311223912044167168/877609515267260437 by Hoemāı] and [https://discord.com/channels/311223912044167168/311223912044167168/887013492371099688 by Hoaqgīo].

<blockquote>"If you have a pet, then the pet in the previously mentioned state of affairs does XYZ." — Hoemaı<br>"{{t|Tu rảı güo kâqgaı jí sa kủsera bı}} … the one who participates in the {{t|guo}} by seeing something, likes the thing that participates in the {{t|guo}} by being seen." — Hoaqgīo</blockquote>

== External links ==
* [https://en.wikipedia.org/wiki/Donkey_sentence ''Donkey sentence'' on Wikipedia]
* [https://mw.lojban.org/papri/All_about_poi_and_noi#PA_da_noi ''All about poi and noi'' on the Lojban wiki]. The ''PA da noi'' section demonstrates a similar "surprising ∀ quantifier".