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