How to verbify "logic" [duplicate]
How about logicalize? From M-W:
logicalize: logicize
logicize: to make logical : convert to logical form, e.g. logicized the argument
While logicalize is obviously similar to @Noah's answer, "to logicalize a conversation" seems a natural way to describe "the turning of a conversation into a logical conversation".
I think "logicize" may be the correct word.
This dictionary.com entry seems to back that idea up (https://www.dictionary.com/browse/logicize)
The definition states "to make logical; give logical form to".
The definition could be talking about the application of logic abstractly or to something specific.