Evidence, knowledge, and belief functions
International Journal of Approximate Reasoning - Special issue: The belief functions revisited: questions and answers
Revision rules for convex sets of probabilities
Mathematical models for handling partial knowledge in artificial intelligence
Updating beliefs with incomplete observations
Artificial Intelligence
Belief models: An order-theoretic investigation
Annals of Mathematics and Artificial Intelligence
Notes on conditional previsions
International Journal of Approximate Reasoning
Axiomatic characterization of the AGM theory of belief revision in a temporal logic
Artificial Intelligence
Marginal extension in the theory of coherent lower previsions
International Journal of Approximate Reasoning
Imprecise probability trees: Bridging two theories of imprecise probability
Artificial Intelligence
Updating coherent previsions on finite spaces
Fuzzy Sets and Systems
International Journal of Approximate Reasoning
Conservative inference rule for uncertain reasoning under incompleteness
Journal of Artificial Intelligence Research
Notes on desirability and conditional lower previsions
Annals of Mathematics and Artificial Intelligence
Making decisions using sets of probabilities: updating, time consistency, and calibration
Journal of Artificial Intelligence Research
Conglomerable natural extension
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
Hi-index | 0.00 |
Probabilistic reasoning is often attributed a temporal meaning, in which conditioning is regarded as a normative rule to compute future beliefs out of current beliefs and observations. However, the well-established 'updating interpretation' of conditioning is not concerned with beliefs that evolve in time, and in particular with future beliefs. On the other hand, a temporal justification of conditioning was proposed already by De Moivre and Bayes, by requiring that current and future beliefs be consistent. We reconsider the latter approach while dealing with a generalised version of the problem, using a behavioural theory of imprecise probability in the form of coherent lower previsions as well as of coherent sets of desirable gambles, and letting the possibility space be finite or infinite. We obtain that using conditioning is normative, in the imprecise case, only if one establishes future behavioural commitments at the same time of current beliefs. In this case it is also normative that present beliefs be conglomerable, which is a result that touches on a long-term controversy at the foundations of probability. In the remaining case, where one commits to some future behaviour after establishing present beliefs, we characterise the several possibilities to define consistent future assessments; this shows in particular that temporal consistency does not preclude changes of mind. And yet, our analysis does not support that rationality requires consistency in general, even though pursuing consistency makes sense and is useful, at least as a way to guide and evaluate the assessment process. These considerations narrow down in the special case of precise probability, because this formalism cannot distinguish the two different situations illustrated above: it turns out that the only consistent rule is conditioning and moreover that it is not rational to be willing to stick to precise probability while using a rule different from conditioning to compute future beliefs; rationality requires in addition the disintegrability of the present-time probability.