  We propose a hierarchy of Bell-type inequalities for arbitrary $n$-partite
systems that identify the different degrees of nonlocality ranging from
standard to genuine multipartite nonlocality. After introducing the definition
of nonsignaling $m$-locality, we show that the observed joint probabilities in
any nonsignaling $m$-local realistic models should satisfy the $(m-1)$-th
Bell-type inequality. When $m=2$ the corresponding inequality reduces to the
one shown in [Phys. Rev. Lett. 112, 140404 (2014)] whose violation indicates
genuine multipartite nonlocality, and when $m=n$ the corresponding inequality
is just Hardy's inequality whose violation indicates standard multipartite
nonlocality. Furthermore, several examples are provided to demonstrate their
hierarchy of multipartite nonlocality.
