Is the purpose of dihedral to add 'self-righting characteristics' to the plane?

Does this work by lowering the center of mass away from where the fuse meets the wings (creating a moment arm), so that the force of gravity on the fuse has a greater moment about the axis where the wings meet the fuse?

I have seen both low-wing commercial planes with dihedral, and a high-wing military plane with 'reversed dihedral'. Would this be to nearly eliminate the moment arm and thus the moment about the plane caused by gravity so that the plane does what the pilot tells it to, and not what gravity wants it to do?

Thanks.