Last February, however, al-Qaeda publicly dissociated itself from Islamic State, partly because of Islamic State’s brutality, including beheadings. So now the question is: Does this mean that Islamic State can no longer be treated as part of an “organization” responsible for the attacks of 9/11, such that the president cannot act (in the words of the AUMF) “to prevent any future acts of international terrorism against the United States”?

Skeptics may think so, but it’s hard to see why. Imagine that in 2012, al-Qaeda split into two organizations: the original one and a new, more brutal group with a new name. Under the AUMF, the president would plainly have the authority to use force against both.

True, the Islamic State situation is not precisely the same, because it has always had its own name and identity. But if it was part of al-Qaeda for a significant period, it’s not easy to argue that al-Qaeda’s announcement of dissociation last February (for excessive brutality, no less) suddenly deprives the president of the authority he had in January. Keep in mind that the group insists it is the true inheritor of the legacy of Osama bin Laden.