  In this paper we consider a logical treatment for the ordered disjunction
operator 'x' introduced by Brewka, Niemel\"a and Syrj\"anen in their Logic
Programs with Ordered Disjunctions (LPOD). LPODs are used to represent
preferences in logic programming under the answer set semantics. Their
semantics is defined by first translating the LPOD into a set of normal
programs (called split programs) and then imposing a preference relation among
the answer sets of these split programs. We concentrate on the first step and
show how a suitable translation of the ordered disjunction as a derived
operator into the logic of Here-and-There allows capturing the answer sets of
the split programs in a direct way. We use this characterisation not only for
providing an alternative implementation for LPODs, but also for checking
several properties (under strongly equivalent transformations) of the 'x'
operator, like for instance, its distributivity with respect to conjunction or
regular disjunction. We also make a comparison to an extension proposed by
K\"arger, Lopes, Olmedilla and Polleres, that combines 'x' with regular
disjunction.
