Constraints in Nonmonotonic Reasoning

We report on the use of constraints to govern partial models of rst-order logic. These models are constructed using systems of default rules, as in the default logic of Reiter, but where Reiter's rules build logical theories, our rules build models. Our approach takes advantage of domain-theoretic notions. A system of default rules is a straightforward generalization of Scott's notion of information system, already an important tool in understanding constraint programming. We apply our theory to resolve an anomaly due to Poole on the meaning of defaults. Using nite default models, constraints, and a constructive, rule-based notion of conditional degree of belief, we give a probabilistic way of interpreting default statements.