  We prove in a unifying way several equivalent descriptions of Koszul rings,
some of which being well known in the literature. Most of them are stated in
terms of coring theoretical properties of $\Tor_n^A(R,R)$. As an application of
these characterizations we investigate the Koszulity of the incidence rings for
finite graded posets. Based on these results, we describe an algorithm to
produce new classes of Koszul posets (i.e. graded posets whose incidence rings
are Koszul). Specific examples of Koszul posets are included.
