The "logic of war" is an English translation of a French phrase, la logique de la guerre, which refers to the dynamic of how wars begin despite the fact that the war itself will be horrendous, counterproductive, and possibly end in complete defeat.
As applied to North Korea, the U.S. has made it clear that if it is forced into a preemptive attack to destroy North Korea's nuclear weapons and missile programs, it will not stop there. The U.S. will aim to decapitate the regime and replace it with something more reasonable.
This could be the start of a gradual reunification of the Korean peninsula on terms favorable to the U.S. In effect, we would be winners in the original Korean War fought from 1950 to 1953.
North Korea has made it equally clear that any attack by the U.S. will result in massive artillery and missile bombardment of South Korea, and possibly Japan and U.S. bases in the region.
Even if North Korea has not yet produced nuclear armed missiles, it does have enormous conventional firepower and missiles. It could possibly detonate a nuclear "device" even if it does not yet have a miniaturized nuclear warhead.