General patterns in nonmonotonic reasoning
Handbook of logic in artificial intelligence and logic programming (vol. 3)
Revision rules for convex sets of probabilities
Mathematical models for handling partial knowledge in artificial intelligence
On the logic of iterated belief revision
Artificial Intelligence
Confidence relations and ordinal information
Information Sciences: an International Journal
The Principle of Conditional Preservation in Belief Revision
FoIKS '02 Proceedings of the Second International Symposium on Foundations of Information and Knowledge Systems
A behavioural model for vague probability assessments
Fuzzy Sets and Systems
On consistent approximations of belief functions in the mass space
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
A logical characterization of coherence for imprecise probabilities
International Journal of Approximate Reasoning
Exchangeability and sets of desirable gambles
International Journal of Approximate Reasoning
Irrelevant and independent natural extension for sets of desirable gambles
Journal of Artificial Intelligence Research
Artificial Intelligence
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I show that there is a common order-theoretic structure underlying many of the models for representing beliefs in the literature. After identifying this structure, and studying it in some detail, I argue that it is useful. On the one hand, it can be used to study the relationships between several models for representing beliefs, and I show in particular that the model based on classical propositional logic can be embedded in that based on the theory of coherent lower previsions. On the other hand, it can be used to generalise the coherentist study of belief dynamics (belief expansion and revision) by using an abstract order-theoretic definition of the belief spaces where the dynamics of expansion and revision take place. Interestingly, many of the existing results for expansion and revision in the context of classical propositional logic can still be proven in this much more abstract setting, and therefore remain valid for many other belief models, such as those based on imprecise probabilities.