Operators and Laws for Combining

The paper concerns the use of the lexicographic rule for combining preference relations with diierent priorities. We use it to interpret defaults with priorities. We present four kinds of results. We show that the lexicographic rule is the only way of combining preference relations which satisses conditions proposed by Arrow 1. We show in what circumstances the lexicographic rule propagates various conditions on preference relations, thus extending Grosof's 7 results. We give necessary and suucient conditions on the priority relation to determine various relationships between combinations of preferences. We give an algebraic treatment of generalized prioritization. Two operators, called but and on the other hand, are suucient to express any prioritization. We present a complete equational axiomatization of these two operators.