As you'd expect from the people that are involved with this project, Caligula looks a lot like Persona. At least Persona 3 and Persona 4 given the game's style and the fact that it actually takes place in a school.
In any case, Caligula is an upcoming RPG set in a virtual world that you're trying to exit. Featuring modern pathology and trauma, it will explore a variety of themes that are meant to make the player think.
You'll also explore dungeons and battle monsters in turn based battles.
You can see all that and more in the game's first teaser trailer: