Qualitative and Probabilistic Models of Full Belief

Let L be a language containing the modal operator B – for full belief. An information model is a set E of stable L-theories ([19], [21], [30], [27]). A sentence is valid if it is accepted in all theories of every model. We show that a formula A is valid if and only if it is a theorem of the modal system S5. The second part of the paper considers the possibility of providing probabilistic foundations for full belief. We study a proposal presented by Bas van Fraassen in [31]. Some of the results proved in [31] are generalized (especially theorem 5.2) and the dynamic aspects of the model are discussed. We show that a characterizations of probability kinematics compatible with van Fraassen’s proposal is cumulative inputs introduced at any stage in a series of changes are rigidly maintained through subsequent changes. Finally we consider the range of applicability of cumulative models of belief change.