In this paper we consider a logical treatment for the ordered disjunctionoperator 'x' introduced by Brewka, Niemel\"a and Syrj\"anen in their LogicPrograms with Ordered Disjunctions (LPOD). LPODs are used to representpreferences in logic programming under the answer set semantics. Theirsemantics is defined by first translating the LPOD into a set of normalprograms (called split programs) and then imposing a preference relation amongthe answer sets of these split programs. We concentrate on the first step andshow how a suitable translation of the ordered disjunction as a derivedoperator into the logic of Here-and-There allows capturing the answer sets ofthe split programs in a direct way. We use this characterisation not only forproviding an alternative implementation for LPODs, but also for checkingseveral properties (under strongly equivalent transformations) of the 'x'operator, like for instance, its distributivity with respect to conjunction orregular disjunction. We also make a comparison to an extension proposed byK\"arger, Lopes, Olmedilla and Polleres, that combines 'x' with regulardisjunction.
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