  We study Koszul homology over Gorenstein rings. If an ideal is strongly
Cohen-Macaulay, the Koszul homology algebra satisfies Poincar\'e duality. We
prove a version of this duality which holds for all ideals and allows us to
give two criteria for an ideal to be strongly Cohen-Macaulay. The first can be
compared to a result of Hartshorne and Ogus; the second is a generalization of
a result of Herzog, Simis, and Vasconcelos using sliding depth.
