It's highly unlikely that they will have backwards compatibility however they plan to have a cloud-computing service for older games. How this would work is still unconfirmed.
"Backwards compatibility The PlayStation 4 hardware will not include the ability to natively play or emulate PlayStation 3 titles. This is a consequence of moving away from the Cell architecture of the PlayStation 3, in favor of x86 for the PlayStation 4. While not available at launch, there is a plan to launch a cloud-based streaming service via Gaikai, Sony's recently-purchased cloud company, to play PlayStation, PlayStation 2 and PlayStation 3 games via its streaming service, at some point in the lifecycle of the PlayStation 4."
That's according to Wikipedia's page. It's possible they could have "emulated backwards compatibility" like they did with the PS3 for the PS2 when it first came out, but because of the drastic architecture change you'd probably see substantial framerate drops and it would be even worse than the support for PS2 on the PS3. Hence it is unlikely they'd even offer it as an option.