No, they won't. Your Playstation Plus subscription is still good on the PS4, but the PS4 is not compatible with any PS3 game content, and therefore can't install any of the PS3 games that have been, or will be, provided free to Plus subscribers; or purchased in the Playstation Store generally. At some point there will probably be a PS4 Instant Game Collection, to complement the existing collections for PS3 and Vita.
You were misinformed. Sony has made it clear from the first announcement that the change from the Cell processor to an AMD processor in the PS4 means that no PS3 games will work on the PS4. Not games on disk. Not games in the Playstation Store. No backward compatibility at launch, at all. Period.
Yeah they said no backwards compatability but they also said they were working on PS3 game collections being available digitally later on after launch. It'll probably take a while and not all of the games will be transferred so if you love your ps3 games then just keep the console.
@gkp it doesnt mean they wont either.
Psp games xfer to other cosoles so do ps1 games, they keep the digital sales across console if they use the same methods they have been. I wouldnt see them stopping using a system they already have in place just to be rude. If its not a remake and just a digital port, than previous owners of that digital game should own it on the new console, but there are no gaurantees and they havent announced any titles as of yet.