The plan looks sufficient for 4" lights. The spacing doesn't appear to be tto far apart. We use the 4" E26's promarily in bathrooms. In your case an LED not set too deep with the lens flush to the ceiling shoud provide enough ambiant light, witht he major concentration being over the island. It's possible that the lower run of stairs may be a little shadowy, but that is hard to determine from this drawing.

Agree about the ambient light. Am a bit concerned that all of your light is over walkways and none of it is over the places in the kitchen where work is done -- it's a drag to slice things in the shadow of your own body! But maybe the circles with double lines are some kind of under-cabinet lighting which would fit the bill...

Thank you for your comments. @SoHo Kitchen and Bath - noted re the staircase, we will talk to the architect about how to add more lights. @acm - I was also concerned about having no lights above the countertop. We will have two upper cabinets on each side of the range. Maybe we should move the two of the lights closer to the upper cabinets to lit the working surface better? Will it look weird?

I like all the lights about 18" off the side wall, which puts them about 6" in front of the cabinets, above the counters. I'd do that everywhere that you expect to be a real working surface. I can't read the diagram well enough to tell where that is, but I presume at least to the left of the stove -- is everything to the right of the stove full-depth? just to right of fridge? Also be sure that the lights over the island provide task lighting as well as ambiance, as that appears to also be critical working space.

Electricians like everything lined up. Kitchens don't really work that way. :)