I've come to the conclusion that the AI is prone to being suicidally stupid about when to declare war, whether it be against me or another AI. Time and again, the AI players in my current game would DOW me or another AI despite it being plainly obvious that the DOWer is too weak to defend itself from its target, let alone attacking said target.
I assume this is an endemic problem in this game? Civ5's AI was a lot smarter when it came to this.
I've seen similar behavior, and yes, it is different from the Civ5 AI. I'm not sure how or why they changed the logic for declaring war from Civ5, but it is very puzzling.
For me, it happens at two distinct parts of the game --
Mid-game (turns 90-200) one of the smaller AI decides they don't like me and declares on me. Sometimes this happens because our affinities differ, sometimes this happens because I don't have lots of veteran units. They DOW, I fight them, and they refuse to accept peace for...a...long...time.
End-game, once I've started my victory wonder. They are blinded by the rage of war, regardless of our relative military strength. More than a few times, I have taken all but 1 or 2 of their cities, destroyed their army, and they still re-declare after a few turns.
I've also seen AI fighting each other in the latter stages of the game. Big AI stomps on the little AI, leaving them with one city. Little AI waits just enough turns to build 2 offensive units and declares war, trying to get their original capital back. Hopeless case.