As Sony promised when they announced the PlayStation 4, their solution for playing PlayStation 3 games going forward will be through Gaikai game streaming. The newly named PlayStation Now service will allow gamers to stream PS3 games to their PS4, PS3, and Vita, and eventually to their smart TVs, tablets, and phones as well. The service will launch only with PS3 games, but Sony says they are considering access to older platform libraries in the future.
There is no mention of using your PS3 discs to access the streamed version of PS3 games. Nor does ownership seem possible. Your options appear to be to rent specific games or pay a subscription fee for the entire service. Beta will begin at the end of January and the service will be available for public use sometime this summer. A 5Mb/s internet connection is a recommended minimum to use the service.