She MIGHT be dead...but she is more than likely dead, unless John's luck has rubbed off on her...or they found a piece of her core and can give the new Cortana the old one's memories, but John doesn't want what happened before to happen again, in other words, he despised her when they were first paired, and the feeling was mutual, but over time they grew to know, trust, and depend on each other...but she is more than likely GONE since the Reclaimer Saga is about an emotional and characteristic growth and development for John
She really does die, though. That's why my friend Karsyn and I (We are both girls) cried at the end of Halo 4. On top of that, I look almost exac tly like Cortana. No joke. She was my favorite Character because I could relate to her feelings easier than the Chief's.
I was shocked by the ending of Halo 4, but by the time the final cutscene was over, I had come up with at least three different theories explaining how Cortana might not be dead. Even today I don't believe she's going to stay dead for long.