“Ducks are mammals” contradicts “mammals have mammary glands”. When this type of contradiction happens, we call the logical system inconsistent.
You hand me an egg to put in my own incubator and raise myself? Well someone swapped the duck while I wasn't looking before the mammary glands developed.
No,valid, not sound. Soundness is validity plus true premises, and any sound conclusion is true of logical necessity. A valid conclusion is true contingent on the truth of the supporting premises.
> but axioms don't have to correspond to reality for the logic to be sound.
False, premises being true is part of the definition of soundness.