If I said:
Yell only if I fall.
Would the person have to yell once I fell?
Sources of confusion
Recall that in formal logic, your expressions are used as follows:
For example if in the morning I tell my wife "I'll buy that shirt we saw yesterday only if it costs less than 40 dollars" and she sees me wear it in the evening, she can deduce that I paid less than 40 dollars.
"Only If" is not a stronger version of "If" that keeps what it implies.
This is the illustration for the two equivalent statements:
Each circle represents a set of instances of "I fall" or "Yell".
Disclaimer: English is not my first language. I'm only talking about the mathematical sense.
Yes, the person would yell once you fell, but only if you fell.
"If" and "Only if" used in the same way means the same thing, except that "only if" is more forceful, more compelling.
"If and only if" is the most obligatory of the three, in which the action has been distinguished and emphasised, "If, and only if" It's the most forceful of the three
Practically speaking, it's an ambiguous command, and if you really want to be clear in your request, you would phrase it in an unambiguous way.
Technically speaking... well, who cares? The goal of language is to communicate with humans. There may be some arcane rules of language that provide for a definitive answer to your question, but since few people are familiar with it, knowing the rule won't do you any good.
Edit: First time visiting/posting so I'm not sure how this community leans between looking for technical grammar rules as opposed to practicality. In real life and in a lot of writing I find "Just say what you mean in a way that people will understand you!" to be the underlying answer to a lot of grammatical questions. Since I've been downvoted already, I can see that at least one person prefers the former.
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