Need a good, Latin-based word for “logical reasoning”? Try this one: ratiocination.
This comes from the Latin verb ratiocinare "to calculate, deliberate".
There is also and English verb form of ratiocination: ratiocinate: “to think or argue logically and methodically; reason”
“For the inhibition of the process of ratiocination leaves the mind in a state to carry out the one idea which has been placed in it.” –William Breathes
“His ratiocination on this subject is, however, purely speculative, and does not touch the ordinary obligations of men considered as social or patriotic duties.” –John Owen Evenings with the Skeptics, Or, Free Discussion on Free Thinkers, Volume 1