Unless in a Logic Problem This is a problem from Kenneth H. Rosen's Discrete mathematics and its applications:
Translate the given statement into propositional logic using the propositions provided.
You cannot edit a protected Wikipedia entry unless you are an administrator.
Express your answer in terms of $e$:“You can edit a protected Wikipedia entry” and $a$: “You are an administrator.”
Based on the book, "$q$ unless $\neg p$" is logically equal to $p \rightarrow q$, which was hard to understand, but by accepting this, the solution would be $\neg a \rightarrow \neg e$ or equally $e \rightarrow a$. This means that "if you can edit a Wikipedia entry, then you are (necessarily) an administrator".
Comparing the two statements in bold, this is indeed true, but from my point of view, the converse statement is also true, which is:
"if you are an administrator, then you can (definitely) edit a Wikipedia entry."
In fact, the first answer I came up with was $a \rightarrow e$, and this was my logic; there may be others rather than administrators who can edit Wikipedia entries, but if the person is an administrator, there is no way he/she cannot edit them!
Now I understand that this is only what I imagined and is not based on the statement, but my question is why the biconditional statement is not acceptable? Is this a common natural language mistake which leads me to believe $e \leftrightarrow a$ should be the answer? And if so, then what is the point of solving these problems and using them in Logical Puzzles, while the natural language can make everything confusing?
 A: Confusion often arises in tackling problems like this one. The issue is that in everyday speech language is often (usefully) used to say things that are not literally present in the words if they are interpreted very strictly.
So in problems like this it can help to remember it can be a slightly artificial game. It can help to remove the question from the real world by altering what it is talking about so that your commonsense knowledge about Wikipedia, editing, and administrators does not get in the way.
The form of the problem is:
You cannot do [onething] unless you are [otherthing]
Which means
The only people who can do [onething] are those who are [otherthing]
or, to make it closer to propositional logic:
If you can do [onething] then you are [otherthing]
The tools you are allowed are:
$e$: You can do [onething]
and $a$: you are [otherthing]
As stated in the question, the translation into propostional logic is
$e \to a$. The problem says nothing about whether $a \to e$ or not, but it looks like it might because of the familiar context.
A: Typically 'not $P$ unless $Q$' translates to $\neg Q \to \neg P$ (or what is indeed the same: $P \to Q$) ... but there are certainly cases where we use this expression to also mean that $Q \to P$ ... and thus we would have the biconditional $P \leftrightarrow Q$.
This particular case may indeed be one of those cases where I think it makes sense to have a biconditional, as also pointed out by the commenter.
However, in general, it is typically a safe bet to go with just $P \to Q$. Consider this example:
'You will not pass the course unless you do all the homeworks'
For this, we can definitely say that as long as you do not do the course homeworks, you will not pass the course, i.e. $\neg H \to \neg P$ or $P \to H$: if we know that a student passes the course, then we know that they must have done all the homeworks, since this is apprently a necessary condition for passing the course.
However, just because a student does do all of the homeworks, that does not mean that they will now definitely pass the course: they could still fail all the quizzes, for example. So, we should not, in addition, also have that $H \to P$: doing all the homeworks may not be a sufficient condition to pass the course.
So this is why we typically only use a one-way conditional expressing the nessary condition, rather than using the biconditional. Indeed, even in this case, one could think of a scenario where someone is required to be an adminstrator in order to edit a protected Wikipedia page ... but other conditions need to be satisfied as well (e.g. One needs to have paid the Special Wikipedia Fee or recited the Secret Wikipedia Pledge)
