In standard Bayesian probability revision, the adoption of full beliefs (propositions with probability 1) is irreversible. Once an agent has full belief in a proposition, no subsequent revision can remove that belief. This is an unrealistic feature, and it also makes probability revision incompatible with belief change theory, which focuses on how the set of full beliefs is modified through both additions and retractions. This problem in probability theory can be solved in a model that (i) lets the codomain of (...) the probability function be a hyperreal-valued rather than the real-valued closed interval [0, 1], and (ii) identifies the full beliefs as the propositions whose probability is either 1 or infinitesimally smaller than 1. In this model, changes in the probability function will result in changes in the set of full beliefs (belief set), which constitutes a submodel that can be conceived as the “tip of the iceberg” within the larger model that also contains beliefs on lower levels of probability. The patterns of change in the set of full beliefs in this modified Bayesian model coincides with the corresponding pattern in a slightly modified version of AGM revision, which is commonly conceived as the gold standard of (dichotomous) belief change. The modification only concerns the marginal case of revision by an inconsistent input sentence. These results show that probability revision and dichotomous belief change can be unified in one and the same framework, or – if we so wish – that belief change theory can be subsumed under a modified version of probability revision that allows for iterated change and for the removal of full beliefs. (shrink)

Theories of rational decision making often abstract away from computational and other resource limitations faced by real agents. An alternative approach known as resource rationality puts such matters front and center, grounding choice and decision in the rational use of finite resources. Anticipated by earlier work in economics and in computer science, this approach has recently seen rapid development and application in the cognitive sciences. Here, the theory of rationality plays a dual role, both as a framework for normative assessment (...) and as a source of scientific hypotheses about how mental processes in fact work. The latter project, often called rational analysis, depends for its success on a fine-grained characterization of the computational problem facing a decision maker, which may in turn depend on realistic assumptions about what the relevant agent is like. As a consequence, resource rationality involves a delicate, but often fruitful interplay between the normative and the descriptive. (shrink)