Probabilistic Default Reasoning with Strict and Defeasible Conditional Constraints Probabilistic Default Reasoning with Strict and Defeasible Conditional Constraints

We present an approach to reasoning about statistical knowledge and degrees of belief, which is based on a combination of probabilistic reasoning from conditional constraints and default reasoning from conditional knowledge bases. More precisely, we generalize the notions of Pearl's entailment in system , Lehmann's lexicographic entailment, and Geffner's conditional entailment to strict and defeasible conditional constraints. We show that the new notions of Þ-, lexicographic, and conditional entailment are proper generalizations of their classical counterparts. Moreover, they coincide with the classical notion of logical entailment as far as satisfiable sets of conditional constraints are concerned. We then show that the new notions of Þ-, lexicographic, and conditional entailment have similar properties like their classical counterparts. In particular, they all satisfy the rationality postulates proposed by Kraus, Lehmann, and Magidor, and have some general irrelevance and direct inference properties. Moreover, the new notions of Þ-and lexicographic entailment satisfy the property of rational monotonicity. Finally, we analyze the computational complexity of some representative decision and optimization problems.