Problem Detail: It can be shown that the logical preposition [ :- (~A->A)->A ] is a theorem (always true). I want to know if anybody knows a real life description for the preposition above? I mean an expression in computer, economics, mathematics, politics or anything that fits in that preposition.
Asked By : n.Perception
Answered By : Raphael
Since $A$ is always the same atomic statement, every direkt translation is going to be weird. Also, natural language does not do well with (nested) implications; we typically say “leads to” not “logically implies” in reality. I suggest you transform the formula to $qquadbegin{align*} &(lnot A to A) to A equiv &lnot(lnot A to A) lor A equiv &lnot(A lor A) lor A equiv &lnot A lor A, end{align*}$ which is, of course, a tautology (as you’ve stated):
You will help me, or you won’t [, your choice].
Coming up with more complicated sentences won’t give you more (logical) meaning — all tautologies are equivalent (in Boolean logic), after all.
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