In this paper, we present several approaches to default reasoning in a possibilistic framework which all are based on purely structural information, encoded by the conditional structures of worlds. Conditional structures symbolize the effects conditionals have on worlds and make conditional interactions transparent and computable, providing a sound algebraic framework for default inferences. Even the weakest of our inference relations, which merely demands a compatibility with conditional structures, proved to be quite well-behaved, according to widely accepted standards. The other two inference relations investigated here are based on faithful possibilistic realizations of conditional structures. Both these approaches allow to handle implicit priorities among the default rules under consideration and thereby combine structural with qualitative information.
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