In many domains, e.g. in law, priority information cannot be based on logical principles (such as specificity) but is domain information, to be provided by the user. Moreover, priority information is often itself defeasible and subject to conflicts. Therefore, ways have to be found to make prioritised logics 'self-prioritising', i.e. to make them suitable for deriving the priorities as logical consequences of these logics.
Two alternative solutions to this problem have been developed. The first [9] is a modification of an argument-based system and the second [6] can be viewed in two ways: as a modification of extension- or model-based systems, such as default logic or preferential entailment, and as a general criterion on the adequacy of attempts to make prioritised logics self-prioritising.
Our ongoing work on priorities between preferences was continued, the results being published as [1]. This extends our previous work on the lexicographic rule for combining of preference relations. We give proof rules and axioms for manipulating priority operators, a first step towards proof theory for preference semantics. It incorporates work showing that the lexicographic rule is the only possible way of combining relations which has certain properties.