No I don't think so. Because Sony decided to be lame about it.
PS3 just used software emulation. I don't see why they couldn't just have converted it to the PS4 OS. Laziness.

****ing whack. I was thinking about getting a PS4 at some point and actually having a current console for one of the only times in my life but PS3's being able to play PS1 games (and PS2 games presumably) is pretty enticing.