For example:
I ate until I was satisfied (not after being satisfied, but at least it arrived to satisfaction by inference, closed limit on the set.)
I ate before I was satisfied (not arriving at satisfaction, open limit on the set)
She sat until I came back (not after, but up to)
We stop working until our manager says so (work before the event, stop after the event)
He can't accept the invitation until I approve it(before, not up to)

Refactor the sentence. Until triggers the action (looks like it triggers an opposite).

satisfied is the trigger which triggers "stop eating."

"came back" is the trigger which triggers "stop sitting"

manager saying so is the trigger which triggers "start working."

So, when you are satisfied you stop eating.

When you come back, they stop sitting.

When the manger says so, you start working.

Wow, that's a brilliant explanation. Kudos to the logic skills.

However, take this for example:

We can't stop working until our manager says so

      'Until' validates this section                                              
|----------------------------------------|-----------------------------------------|
           We can't stop working         |      We stop working
                                Our manager says so

means the same as

We stop working until our manager says so

                                              'Until' validates this section
|----------------------------------------|-----------------------------------------|
                 We work                 |              We stop working
                                Our manager says so

Disgruntling, isn't it?

We stop working until our manager says so

'Until' validates this section
|----------------------------------------|-----------------------------------------|
We work | We stop working
Our manager says so

Disgruntling, isn't it?

No, that's incorrect.

The manager says not to work until he says to work, is what "We stop working until our manager says so" means.

|----------------------------------------|-----------------------------------------|
We don't work | We work
Our manager says so

So the real question is: does the premise refer to the action or state before the until trigger, or the
event that happen because of the trigger?

According to Tom and Tutorial Doctor, it is the former.

"X until Y"

means

X => Y => !X

"not X until Y"

means

!X => Y => X

We stop working until our manager says so (work before the event, stop after the event)

So this is valid english? I had no idea, as a non-native english user, this sentence just confuse me...

No, it's not really. "We stop working..." is simple present tense, and "...until our manager says so." wants a continuous tense instead of a simple one. But "stop" doesn't work with continuous tenses. Stopping is defined as something that happens instantaneously. You can't "keep stopping" for some length of time, which is what continuous tense verbs do. If you say "keep stopping" it implies that you stopped repeatedly, not continuously. Whereas "keep going" means continuously, not repeatedly.

Various rephrasings in proper English include:

"We don't work until our manager says to start."

"We stop working when our manager says to [stop]."

"We work until our manager says otherwise."

"We stood idle until our manager told us to start working."

We stop working until our manager says so (work before the event, stop after the event)

So this is valid english? I had no idea, as a non-native english user, this sentence just confuse me...

Hahaha, yes it is. That's incredibly confusing isn't it?
Just try and read many of the books regarding linguistics and English, you will be surprised how inconsistent English really is (not that other languages aren't as well.)

Actually it's not valid English... ^_^;

We stop working until our manager says so (work before the event, stop after the event)

So this is valid english? I had no idea, as a non-native english user, this sentence just confuse me...

Nope, not valid.

"We stop working" (incorrect)

"We have stopped working." (an event that occurred in the past)

"We won't work, until our manager says so." (continual state of not working until event).

"We will refuse to work, until our manager says so." (continued refusal to work until event)

Until is precise enough to me. It just depends whether you are talking past-tense, or present/future tense.

Your phrases were:

I ate until I was satisfied

"I continued eating up to a fixed point" (past-tense)

I ate before I was satisfied

<The word 'until' doesn't occur in this sentence>

She sat until I came back

"She continued sitting up to a fixed point" (past-tense)

We stop working until our manager says so

<Not grammatically correct>

He can't accept the invitation until I approve it

"He will continue to be unable to accept the invitation up to a fixed point that hasn't yet occurred and may never occur." (present-tense)

As a programmer, what annoys me more is the syntax of the English language, and the inconsistencies (not seen in the above situations) of the rules because of the exceptions. Especially certain usage of quotation marks, commas, and other punctuation.

"until" is sort of like an "if and only if" version of "before". The ongoing state must stop if and only of the condition is met. With "before", the ongoing state can stop if the condition is met, or it can stop earlier:

"We stop working before our manager says so" - Valid
"We stop working until our manager says so" - Not valid

But if you use negation to cause the phrase to become an ongoing state, both are valid:

"We do not stop working before our manager says so" - Valid
"We do not stop working until our manager says so" - Valid


"stop working" is an act which cannot be ongoing, "do not stop working" can be ongoing. "Before" works with momentary acts and ongoing events. "Until" only works with ongoing events.

The difference between "until" and "before" is that one bears a dependency, both timely and logically whereas the other doesn't. The example further becomes confusing in that particular case since "stop" has a negative logic.

"We stop before the manager says so" means "We stop and we give a fuck about what the manager says. Eventually he will (probably) tell us, but we will already have stopped independently".

"We stop until the manager says so" means "We wait for the manager to tell us something, which we will consequently do". Except in this particular example, "do" means "not do", so it is nonsensical, since you cannot abstain from doing something and then stop doing it at a later time, not until you continued doing it, which you didn't according to the wording.

From a timely perspective, "we stop working" as such is also not entirely correct, if you are pedantic, since this implies that you are stopping at the present time when in fact you are already discussing that you are stopping, which means you have already stopped. Unless of course, you are still working with half force while you discuss, but then it would have to be "we will stop working".

Similarly, "until the manager tells us" should actually be "until the manager will be telling us", since obviously he has not told you, nor is he telling you at the present time.

Either way, the incorrect time is "what people are saying", and so it is correct by "what is being spoken is correct".

Ah, I finally see the potential ambiguity. I was parsing the sentence fragment we stop working until our manager says so as having until our manager says so as an adverbial phrase modifying the intransitive verb working, with the word stop as a preposition. The ambiguity comes if the phrase working until our manager says so is parsed as a noun phrase and the object of the transitive verb stop. The latter use is unidiomatic and I would consider it pretty tortured English. It is, however, grammatically valid and the meaning of the word until is still unambiguous, in that it refers to continual action that occurs before an event and has the exact same meaning in both cases.