The way I see it there are two possibilities:
1) Streaming. Maybe that Gaikai acquisition will result in some sort of pseudo BC, allowing us to stream PS3 games we own. Maybe if the disk is inserted into a PS4 it would make that game available for streaming (1 disc locked to 1 PS4). This could end up being quite expensive for Sony (having people use there hardware/servers for free), but the costs could be offset with paid streaming of PS1/PS2 games, a long with whatever else Gaikai could offer.
2) Separately sold BC dongle. By that I mean a little box of some sort with a cell processor and maybe an RSX in there. Sony could sell it for $50 or so, make a decent profit off it. This was rumoured btw.
Don't count of there being backwards compatibility at all though.
