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The phrase "its underlying logic" is correct and can be used in written English
It is used to refer to the principles or rationale that form the foundation of an idea or argument. An example sentence could be: "The professor clarified its underlying logic to the students."
Exact(8)
Yet if the mood in fashion changed, its underlying logic remained immutable.
But it is certainly not unreasonable -- and surely not outside the legal mainstream -- to question its underlying logic.
Today, though, I and others regularly explain its underlying logic to students by focusing on the simplest imaginable system to which that logic applies: the qubits that make up a quantum computer.
This paper summarizes the recommended strategy and its underlying logic.
The participants could ask the tutor to repeat the process until they had memorized the whole procedure and its underlying logic.
It should be born in mind that the very idea of axiomatic set theory is to dispense with higher-order logic; its underlying logic is taken to be FO.
Similar(52)
Succumbing to a strange frequency in his underlying logic, Kharms begins Kharmsifying: "He didn't have hair either, so he was called a redhead arbitrarily".
The combined results of our analysis, summarized in Table 6, along with our earlier work [12] [15], indicate that the script has a rich syntax with an underlying logic in its structure which needs to be explored further.
In addition to describing the model and explaining the underlying logic, we demonstrate its parameterization potential using simulated data and investigate the robustness of its predictions over a wide range of temporal and spatial sampling scales.
He writes: The underlying logic is that no country defaults on its domestic bonds if it retains the right to set the printing presses in motion.
We explored this underlying logic — and path to it — a couple years ago in The Ultimate Answer.
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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