Probability-Based Contraction

Abstract Models employing hyperreal probabilities can be used to represent epistemic agents that have both credences (represented by propositions whose probability has a non-unit standard part) and full beliefs (represented by propositions with a probability at most infinitesimally smaller than 1). This article introduces operations of belief contraction in such models. Contraction is a process in which a proposition that was initially fully believed becomes a credence. We investigate two operations for such probability-based belief contraction. The first operation, which employs Jeffrey revision, gives rise to an operation that is close to the AGM operation of full meet contraction. The second, somewhat more complex, operation is of a more general type, and has AGM partial meet contraction as a special case. In both models, standard relations of epistemic entrenchment can be constructed from the probability function, which reveals a possibly somewhat surprising connection between probability and epistemic entrenchment.