  We introduce a notion of generalized Auslander-Reiten duality on a Hom-finite
Krull-Schmidt exact category $\mathcal{C}$. This duality induces the
generalized Auslander-Reiten translation functors $\tau$ and $\tau^-$. They are
mutually quasi-inverse equivalences between the stable categories of two full
subcategories $\mathcal{C}_r$ and $\mathcal{C}_l$ of $\mathcal{C}$. A
non-projective indecomposable object lies in the domain of $\tau$ if and only
if it appears as the third term of an almost split conflation; dually, a
non-injective indecomposable object lies in the domain of $\tau^-$ if and only
if it appears as the first term of an almost split conflation.
