noun
logic
LAH-jik/ˈlɑːdʒɪk/
The consistent rules by which conclusions follow from information.
The linked gears illustrate the logic of cause and effect in an orderly mechanism.

Etymology
“Pertaining to reason” originally described the “reasoning art,” the study of how to distinguish true from false reasoning. The word also came to name sound argumentation itself.
In context
the proposed proofs that in virtue of the laws of logic such and such things must exist and such and such others cannot are not capable of surviving a critical scrutiny
More examples
- I understand your goal, but I can't follow your logic.
- Students study logic to learn what makes a conclusion valid.
- The program's logic determines which requests receive approval.
Forms
logical adjective — Following consistent rules of sound reasoning.
logician noun — A specialist in the study of logic.