'logical problem' is a correct and usable phrase in written English.
For example, you could use it in a sentence like this: "The professor presented the class with a difficult logical problem to solve."
But there is another logical problem there.
Hacking has negative, Hollywood-influenced connotations, but is just makeshift, logical problem solving.
A logical problem arises from the fact that the subplans may destructively interfere with each other.
Another logical problem arises when you consider the original premise was that everyone would need to marry a supermodel.
Aside from the logical problem here — if tax cuts increase revenue, why do they need to be offset?
They are easier to handle, they don't have the problems that males can have, a very logical problem.
There's also a grammatical and logical problem in using the positive "anyone" in apposition to the negative "no one".
(The logical problem here is that, for a man who wants to get beyond the tyranny of sex, Houellebecq seems unable to avoid endlessly representing it).
But the central logical problem, for the court, was that the order targeted nationals of those countries, even if they had not been to them in years.
It is less harsh than "illegal immigrants", but seems to have the same logical problem, that the actions are illegal/unauthorised, not the people themselves.
There is, if you think about it, an immediate logical problem here: Republicans are saying that job destruction leads to lower wages, which leads to job creation.
