The phrase "about the logic behind" is correct and usable in written English.
You can use it when discussing the reasoning or rationale for a particular idea, action, or concept.
Example: "In this paper, I will explore the logic behind the decision-making process in organizations."
Alternatives: "regarding the reasoning behind" or "concerning the rationale for".
(a nice bit of trivia: I have always wondered about the logic behind revolving doors).
Press him on what he means by that, and he launches into a passionate, pub-polemic about the logic behind the end of the Union.
He said that while talks were "probably getting closer to succeeding," he was still sceptical about the logic behind the acquisition.
At the time, I wondered about the logic behind ending the lockdown, but, eager for something to do, I decided to go to J. J. Foley's, a nearby Irish bar.
It wasn't the case that there was no evidence for the answer to this question about the logic behind suicide terrorism, but [that] everybody thought we knew the answer.
While some liberals expressed glee at the Democrats' decision, the CNN host Chris Cuomo on Wednesday subjected Mr. Perez to an on-air grilling about the logic behind his decision.
On momentum for a Taliban revolution in Pakistan: I usually agree with Steve Coll about AfPak but the logic behind this scenario is murky, at best.
By about 3.30pm though, the logic behind not bringing a jam butty for a quick snack was beginning to show flaws.
A company can avoid those traps by focusing on customers, recognizing that strategy is about making bets, and articulating the logic behind strategic choices.
Many nerds are defined by their ability — some say habit — to question the information they receive until they are satisfied about its authenticity or understand the logic behind it.
Almost everyone had been bearish about the dollar's prospects, for the logic behind its fall has seemed impeccable.
