Can a house have a 'roof' but no 'ceiling' in its upper floor?

Solution 1:

No. A room will always have a celling.

However a celling may not be a roof. A first floor room in a two story building will have a celling, but the structure that forms the celling of that room will be the floor of the room above it.

The shape, size, material, design, etc., of it doesn't matter. Only whether or not it covers the room. If it does then it is a celling.

A roof is the structure that goes on top of the building. The 'lid' if you will. The underside of that roof will be the celling of that room.

Another point worth noting is that this definition really only applies to a building. For example, a car has a roof, but it would be a strange (although proably technically correct) statement to talk about the celling of a car.

EDIT

From some of the other comments:

So an attic is a room, got no problem with that. I'm just wondering whether an uncovered roof can be considered a surface. If so, then it's a ceiling according to this definition, no?

Yes - it is a celling. The physical form is not what we need to define. The concept of it covering the room and providing a barrier from whatever is above that room is the celling. We would say something like "the celling of the attic is made up of wooden beams and the underside of the roof tiles"

Let's say you have a bedroom on the second floor of your house. It has a ceiling. There is also a hatch in the bedroom closet that goes to an attic. Now let's say you rip down the bedroom ceiling, exposing the bedroom directly to the attic. What are you left with? A bedroom without a ceiling that has nothing between it and the roof of the house?

Exactly. You are left with a bedroom that has a very high celling. A celling which is made up of beautiful old beams and cobwebs (I'm taking some aritisc license to illustrate how the 'raw' roof is also the celling).