If the rumored specs are anything to go by, there will be NO backwards compatibility with any of previous PlayStation software. Meaning the PS4 will be running on x86 AMD processors which is incredibly different than current PowerPC Cell architecture, and won't be powerful enough to emulate the PS3, which current PC's can't do eithe, no matter how powerful (Maybe a 12 Core Mac Pro)
It is entirely possible we'll see PS1 and PS2 games on the PS4 however.
It is entirely possible we'll see PS1 and PS2 games on the PS4 however.