Like many of his predecessors, Barack Obama seems to have decided what military action he wants to take and then worked out the legal details. The Obama administration continued its air campaign against Islamic State group (ISIS) and Khorasan targets in Syria and Iraq on Wednesday, as the White House tried to clarify the basis for the strikes. Legal scholars want to establish the justification for using military force absent authorization from Congress or the United Nations -- and clear answers are hard to come by.

President Obama has relied on his Constitutional powers as commander-in-chief – also known as his Article II powers -- to justify the airstrikes. But “it’s pretty clear that the administration is interested in bringing its activity under some statutory authority rather than relying on Article II,” said Ashley Deeks, an associate law professor at the University of Virginia and former legal adviser with the State Department. “Presidents almost always prefer to have statutory authority to use force.”

And over the past weeks, officials have put forth a variety of legal rationales for the air campaigns. U.S. Ambassador to the United Nations Samantha Power justified the airstrikes under international law in a letter to U.N. Secretary-General Ban Ki-moon this week by citing Article 51 of the U.N. Charter, which gives nations the right to attack one another in cases of “individual or collective self-defense” in the wake of an armed attack. In the case of Iraq, which has explicitly asked for U.S. assistance in containing ISIS, U.S. military force can comfortably fall under Iraq’s right to collective self-defense.

But Syria presents a thornier case, as Bashar Assad’s government has not explicitly allowed the U.S. to use military force on its territory. Power invoked a legal theory that allows for military intervention in cases where a state is “unwilling or unable” to counter threats inside its borders.

“The ‘unwilling or unable’ test is already a (controversial) exception to international law’s prohibition on the use of force in another state’s territory,” wrote legal scholar Ryan Goodman of New York University for Just Security. “It would be hard, to say the least, to suggest there is an additional ‘exception to the exception.’”

As for domestic law, the War Powers Resolution, first passed in 1973, requires the president to end military uses of force abroad within 60 days or else seek Congressional authorization to continue. But White House officials argue that the administration already has Congressional authorization for the strikes under the broad powers of the 2001 and 2002 Authorization to Use Military Force (AUMF). The 2001 AUMF specifically authorizes the president to use force against groups, nations or persons involved in the Sept. 11, 2001, attacks, which could include Khorasan, a branch of al Qaeda in Syria.

It’s much less likely that could apply to ISIS, which has broken with al Qaeda and is now one of its biggest rivals. In a New York Times op-ed, Yale law professor Bruce Ackerman adamantly argued against invoking the 2001 AUMF to justify attacks against ISIS. “It’s preposterous to suggest that a congressional vote 13 years ago can be used to legalize new bombings in Syria and additional (noncombat) forces in Iraq,” he wrote.

Still, the 2002 AUMF could conceivably apply to ISIS. That document gives the president authority to use force to defend U.S. national security interests against the “continuing threat posed by Iraq.” Some scholars, such as Harvard University’s Jack Goldsmith, have argued that that wording means Obama would have the authority to strike outside the geographic limitation of Iraq to defend U.S. national security “from the threat posed by the ISIS-induced collapse of Iraq.” But Yale University’s Harold Koh, in an op-ed for Politico Magazine, wrote that the 2002 AUMF clearly was aimed at the regime of Saddam Hussein and the possible threat of his regime's possession of weapons of mass destruction, not ISIS.

There are no easy answers in determining the legality of the air campaign in Syria and Iraq, but previous administrations have been inconsistent as well in seeking Congressional or U.N. authorization for using military force abroad. Congress has not formally declared war since the days of Franklin D. Roosevelt, although it has issued resolutions granting the president power to use force abroad; such was the case with the 1964 Gulf of Tonkin Resolution, which allowed President Lyndon Johnson to escalate the war in Vietnam, as well as the resolutions giving George W. Bush authorization for the 2001 and 2003 invasions of Afghanistan and Iraq.

President George H. W. Bush secured both Congressional and U.N. authorization for the Persian Gulf War, but President Bill Clinton never received Congressional or U.N. authorization for the 1999 bombing campaign in Kosovo, and Obama’s 2011 air campaign against Libya received U.N. approval but not Congressional authorization. Meanwhile, Obama invoked his Article II powers under the Constitution in 2013 to declare he did not need Congressional authorization to launch an offensive in Syria after international inspectors showed the Assad regime had crossed a “red line” in using chemical weapons against its citizens.