The class of logically possible worlds includes everything that has no internal contradictions. I don't think this is difficult. A simple logical non-contradiction makes the world logically possible. So as long as your imagined "world" (or your theory, if we are to speak properly) doesn't contain any internal contradictions it passes the logical test.   

E.g. Is Avatar's Pandora logically possible? Yes, it is logically (but not physically) possible. It is not quite in accord with our accepted physical theories, since it is easy to show that it doesn't fit our accepted conception of gravity. But the world is logically possible, for I see no internal contradictions in it. We can conceive of such a world, with those unique physical laws. So the world is logically possible, but physically impossible (given to the current state of accepted knowledge). 

So to answer your question: No, if the world is physically possible it is logically possible as well.