Does quantum mechanics separate ontology from gnoseology? I mean this answer here. Laws present to us what we know (what we may know). But what we know cannot define what is real; it only defines our actions & assumptions. We may know only probabilities of events (such and such observable takes on this value or that value in an experiment), but we may not know the real values, which nevertheless exist. (As shown by the fact that once we know the value by observation, not by laws, then we can build different assumptions about the results of the next experiments with this very particle than those we had before, and we may not ignore the new knowledge for some reason, as we ought to know that there was an interaction; apparently, the probabilstic laws present the ways in which the real values change…) It seems that quantum mechanics is unique in this regard; for all other theories, we may freely not differentiate ontology and gnoseology, there is no difference. For all other theories, we may even say, for example, that nothing exists, and we only deal with rules of our knowledge (laws). Or that what exists and what we may know is the same thing, so knowledge defines both a) what is real and b)  our actions. Or I am on a completely false track here? Thank you.
 A: 
Laws present to us what we know (what we may know). 

There two meanings of the word law.
One is the description scientists make of the regularities of observations. The other is the actual regularity which is postulated.

But what we know cannot define what is real; it only defines our actions & assumptions. 

The above sounds like a completely specious statement. There isn't a physical world and then people floating outside of it like some mystical whatever. The world is an actual way such that we (a part of the world) are in the state we are in. So your knowledge does mean the world has to be consistent with yourself being in a state of having that knowledge. It's a real and physical constraint and you and your brain are real and physical things. Not important things, but you can't go to the other extreme and pretend like people aren't physical.

We may know only probabilities of events (such and such observable takes on this value or that value in an experiment), but we may not know the real values, which nevertheless exist.

This could be completely wrong. There is a tradition in physics to use the word observation and the word measurement to describe interactions that provably change the state of the subject. For instance different components of spin, when you "observe" or "measure" you actually change the state. And assuming that these post interaction results existed before you did the interaction and that your interaction merely passively revealed it is provably wrong. For instance it won't explain the fact that changing the order measurements ate completed can affect whether two measurements agree.

As shown by the fact that once we know the value by observation, not by laws, then we can build different assumptions about the results of the next experiments with this very particle than those we had before, 

But the same holds when you create results. This doesn't mean the results existed before you created them.

It seems that quantum mechanics is unique in this regard; for all other theories, we may freely not differentiate ontology and gnoseology, there is no difference. 

There is zero difference between quantum mechanics and any other theory, except of course for the unfortunate tradition of using the words measurement and observation for interactions that don't deserve the name.

“There is a tradition in physics to use the word observation and the word measurement to describe interactions that provably change the state of the subject”. Whom or what do you mean by the “subject”? 

For instance if there is a spin 1/2 particle, then you can say that you measure or observe the so called z component of the spin, or the so called x component of the spin. When you do the corresponding interactions you make it interact with other things in a way that both gives information and puts it into a state. That state had the property that a repeated interaction of the same type on the same subject (e.g. the same spin 1/2 particle that just came out of the interaction) you get the same result (and don't change the state). 

What do you mean by creation of results, and which results are you referring to?

But if you did the directions z, then z, then x (in that order) you will find the two z interactions always agree with each other. So the result of the first z interaction clearly puts it into a state that yields that particular result for z interactions with 100% certainty. However, if you do interactions in the z direction, then the x direction, and then the z direction (in that order) then you find the two z interactions only produce identical results 50% of the time. So the intervening x interaction clearly changed the state of the subject.
And assuming it was in such a state (one that produces particular results with 100% certain for z interactions) and that x interactions don't change it would lead to completely wrong results.
This isn't a problem except that the mere words measurement and observation can mislead you onto thinking this a passive information gathering process instead of active interaction that physically and probably changes the state of the subject.

QM had no effect on the status of realism in science, because the most important thing about “measurement” is it discusses interaction, not getting knowledge per the usual sense of this word.

You do get knowledge. You get knowledge about the state you just changed it into. And realism has no status in science. For any observations whatsoever, you can have a realist theory that agrees or a non realist theory that agrees.
But there is another poor tradition when it comes to realism. You can only have as much realism as is required to explain all observations (an example is that you could be a realist about position or momentum, but not both). But some people try to be a realist about more things than is required to explain observations (I don't know why, they like a bigger class of symmetries than nature allows you to be realist about). And inevitably they then make mistakes and sometimes blame the whole idea of realism rather than their greed.
You can be realist or not. And when you are a realist you can be careless about what you choose to be realist about, up until you have a completely deterministic theory but if you then start carelessly being a realist further you risk being inconsistent. So you have to restrain yourself. If you are not a realist then you can be a non realist pretty much without restraint.
