Conditionals, probability, and belief revision

A famous result obtained in the mid-seventies by David Lewis shows that a straightforward interpretation of probabilities of conditionals as conditional probabilities runs into serious trouble. In this paper we try to circumvent this trouble by defining extensions of probability functions, called conditional probability functions. We further defend the position that rational partial beliefs (about conditionals) are better represented by sets of (conditional) probability functions satisfying certain constraints than by a single (conditional) probability function. From this position it is possible to distinguish several notions of belief updating, which results in questioning the intimate relation some authors have claimed to exist between the Ramsey test for conditionals and belief revision