"No," Yoshida said, when asked about any current-gen PSN game being natively supported on the PS4. "Unless, somehow, some games work on emulation. The easiest thing technically would be to make PS1 games work on PS4 through emulation. But we aren't talking about our emulation plans as yet. There are two ways: emulation or cloud service. But native support, no, sorry. We could do so if we choose to. We know who purchased what as a record. But we are working on service plans, and we haven't decided."
In last night's PS4 announcement, Sony revealed the new console won't have backwards compatibility for PS1, PS2, or PS3 discs, although the company aims to use the PS Cloud service to stream previous-gen games as a workaround.
Update: Revised with clarifying quotes from Yoshida