[Solved]: Real life description for (~A->A)->A

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

$\qquad\begin{align*} &(\lnot A \to A) \to A \\ \equiv &\lnot(\lnot A \to A) \lor A \\ \equiv &\lnot(A \lor A) \lor A \\ \equiv &\lnot A \lor A, \end{align*}$

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.

Best Answer from StackOverflow

Question Source : http://cs.stackexchange.com/questions/26164

 Ask a Question

 Download Related Notes/Documents