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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).

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    In English every sentence structure with IF . . . THEN is not a logical relationship. Many are in a logical relationship but some are clearly not in any relationship. It is a mistake to try an say every IF . . . THEN is a Mathematical formula. In philosophy propositions have a proper definition and part is not EXPRESSION. Dont focus on literal words in a sentence but what meaning is being conveyed. We can say equivalent ideas in different sentences & literal words. No matter How it is said the same proposition is in place.The father IF . . . THEN is expressing permission in the circumstance.
    – Logikal
    Commented Feb 12, 2019 at 17:15
  • A reader cannot blame someone else if the reader start making things up in his head. If the message is not clear to a reader then the fault is on the writer. The work from home example CAN BE a deceptive bi-conditional. If you are sick you will just work remotely each time. This basically eliminates the calling out sick option. Why cant you use your computer with a minor illness like the flu? Most Americans who call out sick are not honestly sick. Bosses know this. Pretty soon you will have to Skype your boss so he can literally see your condition. If you are not sick then go to the office.
    – Logikal
    Commented Feb 12, 2019 at 17:21
  • @Logikal I am in Morocco, and the conversation was in French... I do really have a flu, and he already trusts me since I still have about 20 days of vacation that I did not take last year and I worked many holidays, so he believes me when I tell him that I have a flu and I want to take half a day. And since he is very nice, he usually cannot tell me something directly, so I have to make some effort to know what bothers him that he cannot tell me about.
    – SmootQ
    Commented Feb 12, 2019 at 17:34
  • @Logikal he told me before that since I am the only employee who works from this office (because other employees work from an office in another city), and since I am always alone here, he told me that I can work from home whenever I feel like to (since the workplace is very far), unless there are clients who want an appointment, then I should go to the office, but yesterday, he said that I can work from home until I recover, so I wondered what does this until imply.
    – SmootQ
    Commented Feb 12, 2019 at 17:38
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    From what you stated earlier being the only employee at that particular office you can work remotely as normal protocols. The only time you must go in are physical appointments at that office. Working from home will open doors for employers for mandatory Skype sick calls. It may not be the case now but dont ve surprised when it happens. Good general rules should cover cases like this. With well formed rules there are no exceptions to the rules. Poorly formed rules have exceptions
    – Logikal
    Commented Feb 12, 2019 at 18:32

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Neither!

As a general rule, most natural language operators do not have a formal equivalent. In your case, it is even more unlikely, since "until" involves time, while logical implication is blind to time and change.

First Proposed Definition

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

Equivalence is too strong: "If it rains, then the ground is wet" does not imply "The ground is not wet, until it rains".

The left-to-right-direction makes less trouble: in many cases "X until Y" seems to assert that Y is not (yet) the case, which makes the implication true. A necessary condition is obviously not enough for a definition, but see below in Temporal Logic.

Second Proposed Definition

or is it just equivalent to if Y then [(] X or not X [)]?

As above, we can immediately exclude equivalence, since the proposed logical implication is a tautology. That means this is true for any X and Y, and you would be forced to make X until Y a tautology. (You won't be healthy, until you eat ice cream). This refutes both directions!

Why does it not work?

The "until" operator is not truth-functional. There are 16 truth-functional 2-ary operators, and none of them will represent "until" appropriately. One could go through each case and find a counterexample, which seems tedious. But there are several clues why it is not truth-functional: (1) "X until X" seems to be meaningless, not true or false. (2) Nesting "until" does not produce meaningful sentences ("My light is on until (my light is on until the sun rises)" ???). (3) If X can happen only in an instance, then "X until Y" makes no sense. All these cases suggest that the structures of X and Y matter, not only their truth values.

Temporal Logic

Temporal/Modal Logic offers a possibility to add the until operator.

Pragmatics, imperatives and the boss

Uttering the same sentence in different circumstances can mean different things. In your case, without knowing the circumstances, I can see several possible meanings (1) A quite literal one: "Work from home, but as soon as you recover, work in the office" (2) With different intonation it could also mean: "Please work from home even if you are sick" (3) Not much thought was put into the wording, simply meaning: "You are sick, work at home, we will talk when you recover".

Was the conversation in english? It also seems to be a bit strange requesting from a sick person to work...

Get well soon! Also: way to find an interesting philosophical question in everyday life :)

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    Great opening! I think even calling them "operators" is already a stretch in the formalistic direction.
    – Conifold
    Commented Feb 11, 2019 at 23:38
  • @JishinNoben, Thank you so much Jishin, I studied some temporal logic before, but it never occurred to me that I might something useful there as until is far more vague and ambiguous than one can imagine. The conversation was in French (Until = Jusqu'a), and I do not know about the intonation since the conversation was via messaging. Thank you +1
    – SmootQ
    Commented Feb 12, 2019 at 9:11
  • @JishinNoben, this is the exact sentence copy/paste : "tu peux travailler de la maison jusqu'a ce que tu te sens mieux". Also, I feel much better today, thank you. This flu started last Saturday, and I thought it was H1N1 as it is very common recently here, but fortunately it was just a seasonal normal flu. Thanks again.
    – SmootQ
    Commented Feb 12, 2019 at 9:12

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