Andréka, H., Ryan,M., and Schobbens, P-Y.

Operators and laws for combining preference relations

The paper incorporates explicit priorities on defaults onto the framework of preferential logics. It does so by using the lexicographic rule for putting together preference relations with different priorities, to yield a single preference relation. We present four kinds of results.

- We show that the lexicographic rule is the only way of combining preference relations which satisfies 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 sufficient conditions on the priority relation to determine various relationships between combinations of preferences.

- We give an algebraic treatment of this form of generalized prioritization. Two operators, called *but* and *on the other hand*, are sifficient to express any prioritization. We present a complete equational axiomatization of these two operators.

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