I am studying virtual knot theory. A virtual knot is a knot diagram with real or virtual crossing information. The equivalence relation includes generalized Reidemeister moves. There are premitted virtual Reidemeister moves, and forbbiden moves.
Do the forbidden moves have some validity? How are generalized Reidemeister moves made? For example, If we admit the moves the virtual knot is trivial. Therefore, we make some of the moves forbidden. The moves have two real crossings and one virtual crossing. However, instead of these moves, why the other moves are not selected? For instance, may we exclude classical Reidemeister I move instead of the forbidden moves? I am confused!