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The expression 'a logic of' is correct and usable in written English.
You can use it to describe something that is logical or reasonable in terms of a certain situation, concept, event, or set of circumstances. For example, you could say "We need to develop a logic of understanding that will facilitate productive dialogue and create meaningful change."
Exact(60)
Kyburg has developed a logic of statistical inference based solely on logical direct inference probabilities (Kyburg, 1974).
The novel possesses a logic of conversion.
It all had a logic of interconnectedness".
A Logic of Knowledge C. Rauszer.
American populism operates more by a logic of culture and background than by a logic of present-day circumstances.
A breakthrough on refugees will not arise from a logic of private appeal or persuasion: governments will only respond to a logic of public pressure.
Aristotle's logic is, by contrast, a logic of terms in the sense described above.
Van Horn, K. S. Constructing a logic of plausible inference: a guide to Cox's theorem.
Aristotle's treatment of existence illustrates the sense in which his logic is a logic of terms.
The revolution, I have come to think, has a momentum and a logic of its own.
"Capitalism is based on a notion and a logic of growth.
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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