Best type of joint for recessed, corner edge legs?

As pictured that would be a very week joint for a table. I suppose pocket screws would be one way to achieve it.

heck if it's 8/4 into 4×4's you could do loose tenons or dowels, I'd personally use my dowelmax for that, but not everyone has one, but you could get a pretty beefy loose tenon in there diagonally. You may also want to think about rabbeting the inside edges of the legs 3/8 or so, just so all the weight isn't on the tenons or dowels alone, that way the top would be sitting partially on top of the legs, but most of the top of the legs would still be exposed, that would also make positioning for your reveal easier

You could cut pockets in the bottom side of the top, 1" or more from two sides of the legs and use lag bolts going into the legs horizontally.

I believe you're going to, at least, have to have some aprons if you hope to have any stability. With aprons you can have an additional bolt, lower on the leg, coming in from the diagonal, and could make it every bit as strong as the average dining table.

alex, check this out : http://www.sawmillcreek.org/showthread.php?198561-Dining-room-table

If the table is going to be 40" X 100" I am assuming the table is going to have an apron under the table top to prevent sagging. If this is the case you could mortise and tenon the apron into the legs and attach the top to the apron with connectors that would allow expansion and contraction.

Thanks everyone! So the general consensus is that I will need an apron…. What about if I only made it 80" long by 36" wide?

I in the apron camp also. With the joint you are showing I would worry if you carved the top and legs out of a solid hunk of wood.

Where you are using thick wood that brings weight with it. You need it to be strong enough to tip it on it's side a lift it by the legs.