Battlefield 4 for PS3 will include a one-time use voucher allowing you to upgrade to the PS4 digital version of the game for a small price. This is how the "discounted" upgrade scheme will work, first announced by Sony president Andrew House last month during the company's Gamescom keynote.
Presumably this is how other eligible PS3 games can transition into their PS4 counterparts, though we've followed up with Sony for confirmation.
Only four games are participating in this promotion as of right now: Call of Duty: Ghosts, Assassin's Creed 4: Black Flag, Watch Dogs and Battlefield 4. The pricing to go from PS3 to PS4 version for each game is determined by the publishers.