Derivatives

[Ollie.ha]

So I have “Γ⊢P”
How do I figure out Γ from P?

[Radagast]

Took me a while to work out even what your question means. Embarrassingly, I had to turn to AI to help me. I hope the mods will excuse me, just this once, for posting AI output but what it told me was:

The notation Γ⊢P signifies that formula P is provable from the set of assumptions Γ in a formal proof system (natural deduction). It indicates that P can be derived from the assumptions Γ using valid inference rules. Γ can represent multiple, one, or zero assumptions, and if empty, it is written as ⊢P.

Which is nice and concise. Did AI in this case get it right, or is the above incorrect in some subtle way?

Assuming it is correct, you are asking how you can figure out the set of assumptions from the formula? That sounds quite a profound question, but might it not be the case that more than one set of assumptions might entail P?

[puto]

Interference and it is sound.