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"without logic" is a perfectly correct and usable phrase in written English, and is often used to imply something is unreasonable, illogical, or irrational.
For example, you might say: "Sometimes the decisions of our government seem to be made without logic."
Exact(45)
It is without logic.
It is completely irrational and without logic".
In a city without logic, that is without logic and then some".
He has had a thing about her that is without logic.
But it's a cry without logic now: not one way or another, but failure in between.
Batista's strategy, batty and vulgar though it sounds, is not entirely without logic.
Similar(15)
Without justice or logic, without sense, you survived.
This work is the continuation of our published works in [1] and [2] where the former proposed CAC in 5G C-RAN without fuzzy logic while the latter proposed CAC in 5GC-RAN using fuzzy logic without preemption.
At first, the images flood through my mind without much logic or coherence.
So the approach I offer here is necessarily selective, though not without its logic.
Steps put together in this way may seem unrelated, just as a dancer's body can include movements pasted together without obvious logic or preparation.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com