We provide a semantic framework for preference handling in answer setprogramming. To this end, we introduce preference preservingconsequence operators. The resulting fixpoint characterizationsprovide us with a uniform semantic framework for characterizingpreference handling in existing approaches. Although our approach isextensible to other semantics by means of an alternating fixpointtheory, we focus here on the elaboration of preferences under answerset semantics. Alternatively, we show how these approaches can becharacterized by the concept of order preservation. These uniformsemantic characterizations provide us with new insights aboutinter-relationships and moreover about ways of implementation.