Yes and no

I've traditionally given ia and na as the Koa translations of "yes" and "no," but the situation is actually quite a bit more complex with some fairly neat opportunities for nuance. Na is a decent all-purpose "no," being the general negative particle, but ia is actually a veridical often used in verum focus: as such its true meaning is "definitely, certainly, absolutely." There's a negative corollary ianá that means "definitely not, absolutely not," and there are many other modal particles that can be used analogously for different shades of meaning.

For example, ku classifies the information within its scope as already known, whether it really factually is or the speaker deems that it should be so. The following sentence might be uttered if the speaker had just returned from out of town, and been asked if they'd done something, or heard something, that implied more time at home than they had yet had:

ni-ku-lai he-ele i mono
1SG-KNOWN-return TIME-yesterday FIN only
"I mean, I only came back yesterday, after all"

As an interjection, then, ku means something like "obviously," "clearly" or "of course," and the negative form kuná would be "obviously not," "of course not," "clearly not."

For those particles that do not have veridical or evidential force -- that is, other than ia, li, pu, vu -- the positive form can also be combined with ia for emphasis, thus kuiá "clearly yes," "well of course it is." All of these particles are modular and can be combined freely in whatever ways their meanings would allow: so iaté "yes, that very well may be," "it is definitely true that that is possible" vs teiá "yes, perhaps," "it's possible that that's true." Or even stacked with other modals, like kuté, kuteiá "yes, that may indeed be possible."

Below are the particles that can be used as interjections and their approximate English meanings. One note for the following examples: "I" in the translations is only illustrative, and could be replaced with any other referent relevant to the discourse (e.g. oená could also mean "no, she shouldn't" in the appropriate context).

ea "yes, let's"
     eaná "no, let's not"

hoiá "yes, actually, counter to expectations" (ho alone indicates surprise)
     honá "no, actually not, counter to expectations"

ia "yes, definitely"
     ianá "no, definitely not"

io "that's right, there it is, aha!, bingo, there we go"
     ioná "no, no way, no longer, no more of that"

ki "yes, I have to; yes, it must be"
     kiná "no, I mustn't; no, it must not be"
     nakí "no, I don't have to; no, there's no need"

ku "yes, obviously; yes, of course"
     kuná "no, obviously not, of course not"

li "yes, I suppose so, might be, probably"
     liná "no, I suppose not, probably not"

lu "yes, I want to"
     luná "no, count me out"
     nalú "no, I don't want to"

oe "yes, I should"
     oená "no, I shouldn't"

pu "yes, apparently; yes, so I hear"
     puná "no, apparently not; no, so I hear"

te "yes, I can; yes, maybe"
     tená "no, maybe not"
     naté "no, I can't; no, it can't be"

vi "yes, do it! yes, let it be so!"
     navi, naví "no, don't do it! ojalá que no"

vu "yeah, I guess so"
     vuná "no, I guess not"

I'm really pretty pleased with the amount of subtlety and precision that Koa has developed in this area sort of by accident, just by virtue of its system of modal particles. I know I keep saying this but it's been continually fascinating to keep discovering the language's emergent complexity as it's come into greater and greater use this year.