Indirect question

An indirect question (or more linguistically, embedded interrogative or interrogative content clause) is a subclause that looks like a question.

In Toaq, this is a content clause starting with mä (if/whether) or tïo (how much), or containing a question word like hí (which?) or rí (this or that?).

Bu dua jí, mä ao cho súq ní lua da.
I don't know if you'd like this story.

Duashao jí, ꝡä tısha nháo râo hí da.
I wonder when they'll arrive.

Overview

Rogative predicates are predicates like wonder/ask/be curious about, that only make sense with interrogative complements (I wonder which boat is his, not *I wonder that the SS Toaq is his boat).
Responsive predicates are predicates like know/remember/forget/be certain/conjecture, that appear to accept both declarative complements (I know the SS Toaq is his boat) and interrogative complements (I know which boat is his).
- Within this category, veridical predicates are predicates like know/remember/forget, which when used with an interrogative complement, entail that they hold of the declarative complement that correctly answers the question (given I know which boat is his and his boat is the SS Toaq, we can conclude I know the SS Toaq is his).
- And non-veridical predicates are predicates like be certain/agree/conjecture, which when used with an interrogative complement, do not entail that they hold of the "correct answer".
The theory that top-level questions (Which boat is yours?) are reduceable to an imperative statement with an indirect question (Bring it about that I know which boat is yours!) is known as the imperative-epistemic theory of wh-questions, and seems to be pretty widely accepted.
The issue that questions that happen to have the same answer shouldn't be considered equivalent (e.g. I know which boat is his vs. I know who owns the SS Toaq), is known as the problem of convergent knowledge.

Semantics

A popular starting point is that an indirect question denotes a set of possible answers, correct or not:

⟦ꝡä tıshaı hí⟧ = {‘tıshaı mí A’, ‘tıshaı mí B’, ‘tıshaı mí C’, …}

Exhaustivity

The first question is: what counts as an answer? When we say “I know who left”, what knowledge are we purporting to have?

There are various levels of exhaustivity one could demand of an answer. Suppose that only A and B left. Then increasingly exhaustive answers to the question “who left” are the following:

Mention-some answers: ‘A left’
Weakly-exhaustive answer: ‘A left and B left’
Strongly-exhaustive answer: ‘A left and B left, and no one else left.’

Predicates

How can the second slot of dua accept both a regular content clause, which denotes a proposition, and an interrogative clause that denotes a whole set of propositions? Doesn't this make dua polysemous?

There are a few possible answers to this question:

Maybe dua is really a family of predicates, and dua_P “to know a fact” is a different predicate from dua_Q “to know the answer to a question”, and Toaq's grammar selects the right one automatically.
Maybe dua in its purest form takes propositions, and there is some reduction from question complements to proposition complements. This is Q-to-P reduction.
Maybe dua in its purest form takes questions, and there is a P-to-Q reduction.

The Wataru Uegaki (2019) paper in #See also is all about this.