The phrase "a logical rationale" is correct and usable in written English.
It can be used when discussing the reasoning or justification behind a decision or argument that is based on logical principles.
Example: "In order to support our proposal, we need to present a logical rationale that clearly outlines the benefits of our approach."
Alternatives: "a sound justification" or "a coherent reasoning".
The candidacies — at least in retrospect — seemed to provide voters with a logical rationale.
England did not pick the strongest squad possible but that was a decision with a logical rationale behind it and one in line with other teams.
Instead of espousing reasonable, moderate solutions to complicated problems (ala the Democratic Leadership Council of old), they have chased the illusion of compromise while often failing to provide a logical rationale for their stated objectives.
She refuses to believe that the snatcher is a stranger, "someone lurching out of nowhere, out of dreaming space" — as if an act of violence had to have a logical rationale.
Those who presented a logical rationale (I'm late for class) got what they wanted 94% of the time.
While this philosophy has a logical rationale behind it, the forecasting of how that will turn out is something that not even Musk knows with certainty.
Since most HIV infections are sexually transmitted or associated with pregnancy, childbirth and breast-feeding, there is a strong and logical rationale to integrate care.
In response, the Trump Administration had offered nothing no logical rationale, no indication, even, of a "deliberative process" behind the order.
However, the aim of CT is usually the verification of the efficacy of a new treatment modality based on preclinical study and logical rationale that the CT therapy could be superior to or at least not inferior to conventional therapy.
He said there was "no logical rationale" behind closing the station, which had an average weekly reach of 695,000 listeners in the final three months of last year.
Bacon, who presents a Saturday afternoon show on 6 Music as well as a weekday afternoon show on BBC Radio 5 Live, said: "There's no logical rationale behind any decision [if that's true] to close 6 Music.
