Yes, formal logic (rationality) and informal logic (reasonableness) are not actually the same thing and can't replace each other; logic works in its own world (which has finite/enumerable factors) and reasonableness works in the real world (which doesn't). This was tried several times under "logical positivism", "AI expert systems", and "rationalism", all of which were failures. Some people haven't noticed the last two failed and are still trying to do them though.

See: https://metarationality.com

Of course there is. In AI domain (and philosophy) for e.g you have associative logic: "Grass is a plant. Plant is green. Grass should be green". There is symbolic logic too where relationships are established based on rules of observable world.

Logic isn't treated as the CS logic per se, but as a high level concept although at a fundamental level they will be compositional of the mathematical logic rules. That is still an ongoing goal - a unification of "world models" which can be modeled and explained