Suppose a father tells his kid that he can play video games whenever he wants.

Then, one day, when the kid fell sick, the father told him that he can play video games until he recovers.

Does this 'until' imply the imperative :"Once you recover, you should stop playing video games'?

In propositional terms, is X until Y equivalent to if Y then not X ?

I ask this question because, my boss told me before that I can work from home whenever I want... as my workplace is far away from home, and when I caught a flu he said : You can work from home until you recover. So, should I stop working from home once I recover?

I am also curious to know what does this word imply (logically speaking).

Suppose a father tells his kid that he can play video games whenever he wants.

Then, one day, when the kid fell sick, the father told him that he can play video games until he recovers.

Does this 'until' imply the imperative :"Once you recover, you should stop playing video games'?

Or does it merely say that : "When you recover, you still can play games or not play games, it is your choice?"

In propositional terms, is X until Y equivalent to if Y then not X ? or is it just equivalent to if Y then X or not X?

I ask this question because, my boss told me before that I can work from home whenever I want... as my workplace is far away from home, and when I caught a flu he said : You can work from home until you recover. So, should I stop working from home once I recover?

I am also curious to know what does this word imply (logically speaking).