Check out this video from Bisohock Infinite which was shown at the Tokyo Games Show 2011. This footage is from the PlayStation 3 version and is pretty similar to what we have seen at E3 in June.
The player assumes the role of former Pinkerton agent Booker DeWitt, sent to the lost city to rescue Elizabeth, a young woman imprisoned there since childhood. He develops a relationship with Elizabeth, augmenting his abilities with hers so the pair may escape from a city that is literally falling from the sky. DeWitt must learn to fight foes in high-speed Sky-Line battles, engage in combat both indoors and amongst the clouds, and harness the power of dozens of new weapons and abilities.
The game is due on the PS3, Xbox 360 and PC in 2012. The game is being developed by Irrational Games and published by 2K games.