The PlayStation 4 will not be natively backwards compatible with any previous PlayStation console or title including digital purchases. The hardware inside the PlayStation 4 is vastly different from the PS3 and in its current form, the PS4 cannot play any games from past Sony systems. Sony is currently developing a few workarounds, including the Gaikai cloud-based streaming service as well as the possibility of emulating past titles.
The cloud-gaming company Gaikai was purchased by Sony in July 2012. When the new PlayStation Network launches, the assumption is that Gaikai will be used to render older PlayStation titles and stream them onto your PS4 console.
More information on backwards compatibility can be found here: