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The idea of logic is to have clear rules so that conclusions can be drawn unambiguously and consistently by different people.
Eugenia Cheng • The Art of Logic

In maths the technique we use is logic. We only want to use sheer logical reasoning. Not experiments, not physical evidence, not blind faith or hope or democracy or violence. Just logic. So what are the things we study? We study anything that obeys the rules of logic.
Eugenia Cheng • How to Bake Pi
The following instances of the application of fables to particular occasions are recorded. The fable of The Belly and the Members, which is reputed to be the oldest in existence, is of sterling excellence, as well as of venerable antiquity.[43] Its lucid moral is truth in essence. The logic of its conclusion is as invulnerable as the demonstration
... See moreThomas Newbigging • Fables and Fabulists: Ancient and Modern
Leibniz, in his private thinking, is the best example of a philosopher who uses logic as a key to metaphysics. This type of philosophy begins with Parmenides, and is carried further in Plato’s use of the theory of ideas to prove various extra-logical propositions. Spinoza belongs to the same type, and so does Hegel. But none of these is so clear cu
... See moreBertrand Russell • History of Western Philosophy
Readwise

I have chosen psycho-logic as a neutral and non-judgemental term.