PlayStation 3 Game Titles can be only 'emulated' via their PlayStation Now-Service - where you already now those Games doesn't get emulated at all - and while the PS3 had many 'PS2 Classics' available at their PSN Store, the PS4 share a few of them as well, but sadly only about >50 Game Titles and the last one added was also already over two years ago. In fact, it seems that Sony isn't interested anymore nowadays to make the PS4 a 'fully' Backwards Compatible Console.
Emulation on todays Sony Home Consoles wasn't always a easy task compared with the older days such for the PS3 for instance.